Nonlinear finite element methods

Nonlinear Finite Element Methods

Volumn , Issue , 2008, Pages 1-559

  Wriggers, Peter ^a  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84892243031     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-540-71001-1     Document Type: Book

References (546)

1. Ainsworth M. and Oden J.T. A procedure for a posteriori error estimation for h-p finite element methods. Computer Methods in Applied Mechanics and Engineering, 101:73-96 (1992).
2. Akers R., Baffes P., Kant E., Randall C. and Steinberg R.Y. Automatic synthesis of numerical codes for solving partial differential equations. Mathematics and Computers in Simulation, 45:3-22 (1998).
3. Alart P. and Curnier A. A mixed formulation for frictional contact problems prone to Newton like solution methods. Computer Methods in Applied Mechanics and Engineering, 92:353-375 (1991).
4. Altenbach J. and Altenbach H. Einführung in die Kontinuumsmechanik. Teubner- Verlag, Stuttgart (1994).
5. Andelfinger U. Untersuchungen zur Zuverlässigkeit Hybrid-Gemischter Finiter Elemente für Flächentragwerke. Dissertation, Institut für Baustatik der Universität Stuttgart (1991). Bericht Nr. 13.
6. Andelfinger U. and Ramm E. EAS-elements for two-dimensional, three-dimensional plate and shell structures and their equivalence to HR-elements. International Journal for Numerical Methods in Engineering, 36:1311-1337 (1993).
7. Archer G.C. A technique for the reduction of dynamic degrees of freedom. Earthquake Engineering and Structural Dynamics, 30:127-145 (2001).
8. Argyris J.H. An excursion into large rotations. Computer Methods in Applied Mechanics and Engineering, 32:85-155 (1982).
9. Argyris J.H., Doltsinis J.S., Pimenta P.M. and Wuestenberg H. Thermomechanical response of solids at high strains - natural approach. Computer Methods in Applied Mechanics and Engineering, 32:3-57 (1982).
10. Argyris J.H. and Kleiber M. Incremental formulation in nonlinear mechanics and large strain elasto-plasticity - Natural approach. I. Computer Methods in Applied Mechanics and Engineering, 11:215-247 (1977).
11. Argyris J.H., Pister K.S., Szimmat J. and Willam K.J. Unified concepts of constitutive modelling and numerical solution methods for concrete creep problems. Computer Methods in Applied Mechanics and Engineering, 10:199-246 (1976).
12. Arnold D.N., Falk R.S. and Winther R. Preconditioning discret approximations of the reissner-mindlin plate model. Mathematical Modelling and Numerical Analysis, 31:517-557 (1997).
13. Atluri S.N. On constitutive relations at finite strain: hypo-elasticity and elastoplasticity with isotropic and kinematic hardening. Computer Methods in Applied Mechanics and Engineering, 43:137-171 (1984).
14. Axelsson O. Iterative Solution Methods. Cambridge University Press, Cambridge (1994).
15. Axelsson O. and Barker V.A. Finite Element Solution of Boundary Value Problems: Theory and Computation. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (2001).
16. Babuska I. and Rheinboldt W. Error estimates for adaptive finite element computations. SIAM Journal on Numerical Analysis, 15:736-754 (1978).
17. Babuska I., Strouboulis T., Upadhyay C.S., Gangaraj S.K. and Copps K. Validation of a posteriori error estimators by numerical approach. International Journal for Numerical Methods in Engineering, 37:1073-1123 (1994).
18. Babuska I., Szabo B.A. and Katz I.N. The p-Version of the Finite Element Method. SIAM Journal on Numerical Analysis, 18(3):515-545 (1981).
19. Balay S., Buschelman K., Eijkhout V., Gropp W.D., Kaushik D., Knepley M.G., McInnes L.C., Smith B.F. and Zhang H. PETSc users manual. Technical Report ANL-95/11 - Revision 2.1.5, Argonne National Laboratory, Argonne (2004).
20. Balay S., Buschelman K., Gropp W.D., Kaushik D., Knepley M.G., McInnes L.C., Smith B.F. and Zhang H. PETSc Web page (2001). Http://www.mcs.anl.gov/ petsc.
21. Bank R.E. PLTMG: A software package for solving elliptic partial differential equations. Technical Report Vol. 7, Society for Industrial and Applied Methematics, Philadelphia (1990).
22. Bartels S. and Carstensen C. Each averaging technique yields reliable a posteriori error control in fem on unstructured grids. Part ii: High order fem. Mathematics of Computation, 71:971-994 (2002).
23. Bartholomew-Biggs M., Brown S., Christianson B. and Dixon L. Automatic differentiation of algorithms. Journal of Computational and Applied Mathematics, 124:171-190 (2000).
24. Basar Y. and Ding Y. Finite-rotation elements for nonlinear analysis of thin shell structures. International Journal of Solids & Structures, 26:83-97 (1990).
25. Basar Y. and Ding Y. Shear deformation models for large strain shell analysis. International Journal of Solids & Structures, 34:1687-1708 (1996).
26. Bass J.M. and Oden J.T. Adaptive finite element methods for a class of evolution problems in viscoplasticity. International Journal of Engineering Science, 25:623-653 (1987).
27. Bastian P. and Wittum G. On robust and adaptive multi-grid methods. In P.W. Hemker et al., editors, Multigrid methods IV. Proceedings of the fourth European multigrid conference, pages 1-17. Birkhaeuser, ISNM, Int. Ser. Numer. Math. Volume 116, Amsterdam (1994).
28. Bathe K.J. Finite Element Procedures in Engineering Analysis. Prentice-Hall, Englewood Cliffs, New Jersey (1982).
29. Bathe K.J. Finite-Elemente-Methoden, Matrizen und lineare Algebra. Die Methode der finiten Elemente. L"osung von Gleichgewichtsbedingungen und Bewegungsgleichungen; Deutsche "Ubersetzung von P. Zimmermann. Springer-Verlag, Berlin- Heidelberg-New York (1986).
30. Bathe K.J. Finite Element Procedures. Prentice-Hall, Englewood Cliffs, New Jersey (1996).
31. Bathe K.J. and Bolourchi S. Large displacement analysis of three-dimensional beam structures. International Journal for Numerical Methods in Engineering, 14:961-986 (1979).
32. Bathe K.J. and Chaudhary A.B. A solution method for planar and axisymmetric contact problems. International Journal for Numerical Methods in Engineering, 21:65-88 (1985).
33. Bathe K.J. and Dvorkin E.N. A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation. International Journal for Numerical Methods in Engineering, 21:367-383 (1985).
34. Bathe K.J. and Gracewski S. On nonlinear dynamic analysis using substructuring and mode superposition. Computers and Structures, 13:699-707 (1981).
35. Bathe K.J., Ramm E. and Wilson E.L. Finite element formulation for large deformation analysis. International Journal for Numerical Methods in Engineering, 9:353-386 (1975).
36. Baumann M., Klarmann R. and Schweizerhof K. Algorithmen zur Optimierung von Gleichungssystemen bei Finite-Element-Berechnungen. Technical Report 2/1990, Institut für Baustatik, Karlsruhe (1990).
37. Bazant Z.P. and Cedolin L. Stability of Structures. Oxford University Press, New York (1991).
38. Bazant Z.P. and Cedolin L. Stability of Structures: Elastic, Inelastic, Fracture, and Damage Theories. Dover Publications, New York (2003).
39. Bazaraa M.S., Sherali H.D. and Shetty C.M. Nonlinear Programming, Theory and Algorithms. Wiley, Chichester, second edition (1993).
40. Beall M. and Shephard M. Object-oriented framework for reliable numerical simulations. Engineering with Computers, 15:61-72 (1999).
41. Becker A. Berechnung ebener Stabtragwerke nach der Flies̈ gelenktheorie II. Ordnung unter Ber"ucksichtigung der Normal- und Querkraftinteraktion mit Hilfe der Methode der Finiten Elemente. Technical report, Diplomarbeit am Institut für Baumechanik und Numerische Mechanik der Universität Hannover (1985).
42. Becker E. and Bürger W. Kontinuumsmechanik. B.G. Teubner, Stuttgart (1975).
43. Becker R. and Rannacher R. A feed-back approach to error control in finite element methods: Basic analysis and examples. EAST-WEST Journal of Numerical Mathematics, 4:237-264 (1996).
44. Belytschko T. and Bindeman L.P. Assumed strain stabilization of the 4-node quadrilateral with 1-point quadrature for nonlinear problems. Computer Methods in Applied Mechanics and Engineering, 88(3):311-340 (1991).
45. Belytschko T. and Bindeman L.P. Assumed strain stabilization of the eight node hexahedral element. Computer Methods in Applied Mechanics and Engineering, 105(2):225-260 (1993).
46. Belytschko T., Chiapetta T. and Bartel R.L. Efficient large-scale non-linear transient analysis by finite elements. International Journal for Numerical Methods in Engineering, 10:579-596 (1976).
47. Belytschko T., Liu W.K. and Moran B. Nonlinear finite elements for continua and structures. Wiley, Chichester (2000).
48. Belytschko T., Ong J.S.J., Liu W.K. and Kennedy J.M. Hourglass control in linear and nonlinear problems. Computer Methods in Applied Mechanics and Engineering, 43:251-276 (1984).
49. Bergan P.G., Horrigmoe G., Krakeland B. and Soreide T.H. Solution techniques for non-linear finite element problems. International Journal for Numerical Methods in Engineering, 12:1677-1696 (1978).
50. Bertsekas D.P. Constrained Optimization and Lagrange Multiplier Methods. Academic Press, New York (1984).
51. Besseling J.F. and van der Giessen E. Mathematical Modelling of Inelastic Deformations. Chapman & Hall, London (1994).
52. Betsch P. Statische und dynamische Berechnungen von Schalen endlicher elastischer Deformationen mit gemischten Finiten Elementen. Dissertation, Institut für Baumechanik und Numerische Mechanik der Universität Hannover (1996). Bericht Nr. F 96/4.
53. Betsch P., Gruttmann F. and Stein E. A 4-node finite shell element for the implementation of an assumed general hyperelastic 3d-elasticity at finite strains. Computer Methods in Applied Mechanics and Engineering, 130:57-79 (1996).
54. Betsch P., Meyer L. and Stein E. On the parametrization of finite rotations in computational mechanics: A classification of concepts with application to smooth shells. Computer Methods in Applied Mechanics and Engineering, 155:273-305 (1998).
55. Betsch P. and Stein E. An assumed strain approach avoiding artificial thickness straining for a nonlinear 4-node shell element. Communications in Applied Numerical Methods, 11:899-909 (1995).
56. Betsch P. and Steinmann P. Conservation properties of a time finite element method. Part i: Time-stepping schemes for n-body problems. International Journal for Numerical Methods in Engineering, 49:599-638 (2000).
57. Bidmon W. Zum Weiterreißverhalten von beschichteten Geweben. Dissertation, Institut für Werkstoffe im Bauwesen der Universität Stuttgart (1989). Mitteilung 1989/2.
58. Bischof C., Buecker H.M., Lang B., Rasch A. and Risch J.W. Extending the functionality of the general-purpose finite element package sepran by automatic differentiation. International Journal for Numerical Methods in Engineering, 58:2225-2238 (2003).
59. Bischof C., Hovland P. and Norris B. Implementation of automatic differentiation tools. In: C. Norris and J.J.B. Fenwick, editors, Proceedings of the ACM SIGPLAN Workshop on Partial Evaluation and Semantics-Based Program Manipulation. ACM Press, New York (2002).
60. Bischoff M. and Ramm E. Shear deformable shell elements for large strains and rotations. International Journal for Numerical Methods in Engineering, 40: 4427-4449 (1997).
61. Bischoff M., Ramm E. and Braess D. A class of equivalent enhanced assumed strain and hybrid stress finite elements. Computational Mechanics, 22:443-449 (1999a).
62. Bischoff M., Wall W.A., Bletzinger K.U. and Ramm E. Models and finite elements for thin-walled structures. In E. Stein, R. de Borst and T.J.R. Hughes, editors, Encyclopedia of Computational Mechanics, pages 59-137. Wiley, Chichester (2004).
63. Bischoff M., Wall W.A. and Ramm E. Stabilized enhanced assumed strain elements for large strain analysis without artificial kinematic modes. In W. Wunderlich, editor, ECCM 99, pages 1-19. Lehrstuhl für Statik, München (1999b).
64. Bodner S.R. and Partom Y. Constitutive equations for elastic viscoplastic strain hardening materials. Journal of Applied Mechanics, 42:385-389 (1975).
65. Boerner E., Loehnert S. and Wriggers P. A new finite element based on the theory of a cosserat point - extension to initially distorted elements for 2d plane strain. International Journal for Numerical Methods in Engineering, 71:454-472 (2007).
66. Boerner E. and Wriggers P. A macro-element for incompressible finite deformations based on a volume averaged deformation gradient. Computational Mechanics 42:407-416 (2008).
67. Boersma A. and Wriggers P. An algebraic multigrid solver for finite element computations in solid mechanics. Engineering Computations, 14:202-215 (1997).
68. Bolotin V. and Armstrong H. The dynamic stability of elastic systems. American Journal of Physics, 33:752 (1965).
69. Bonet J. and Bhargava P. A uniform deformation gradient hexahedron element with artificial hourglass control. International Journal for Numerical Methods in Engineering, 38:2809-2828 (1995).
70. Bonet J. and Burton A.J. A simple average nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit application. Communications in Numerical Methods in Engineering, 14:437-449 (1998).
71. Braess D. Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics. Cambridge University Press, Cambridge (2007).
72. Brandt A. Algebraic multigrid theory: The symmetric case. Applied Mathematics and Computation, 19:23-56 (1986).
73. Brandt A., McCormick S.F. and Ruge J.W. Algebraic multigrid (amg) for sparse matrix equations. In E.D. J., editor, Sparsity and Its Applications. Cambridge University Press, Cambridge (1985).
74. Brank B., Briseghella L., Tonello N. and Damjanic F.B. On non-linear dynamics of shells: implementation of energy-momentum conserving algorithm for a finite rotation shell model. International Journal for Numerical Methods in Engineering, 42:409-42 (1998).
75. Bremer C. Algorithmen zum effizienten Einsatz der Finite-Element-Methode. Technical Report 86-48, Institut für Statik, Braunschweig (1986).
76. Brendel B. and Ramm E. Nichtlineare stabilit"atsuntersuchungen mit der methode der finiten elemente. Ingenieur-Archiv, 51:337-362 (1982).
77. Brenner S.C. and Scott L.R. The Mathematical Theory of Finite Element Methods. Springer, New York (2002).
78. Brezzi F. and Fortin M. Mixed and Hybrid Finite Element Methods. Springer, Berlin, Heidelberg, New York (1991).
79. Briseghella L., Majorana C. and Pellegrino C. Dynamic stability of elastic structures: A finite element approach. Computers and Structures, 69:11-25 (1998).
80. Bucher C. Stabilization of explicit time integration by modal reduction. In W.A. Wall, K.U. Bletzinger and K. Schweizerhof, editors, Trends in Computational Structural Mechanics, pages 429-437. Lehrstuhl für Statik, Barcelona, Spain (2001).
81. Büchter N. and Ramm E. Shell theory versus degeneration - A comparison in large rotation finite element analysis. International Journal for Numerical Methods in Engineering, 34:39-59 (1992).
82. Büchter N., Ramm E. and Roehl D. Three-dimensional extension of non-linear shell formulation based on the enhanced assumed strain concept. International Journal for Numerical Methods in Engineering, 37:2551-2568 (1994).
83. Bufler H. Pressure loaded structures under large deformations. Zeitschrift für angewandte Mathematik und Mechanik, 64:287-295 (1984).
84. Campello E.M.B., Pimenta P.M. and Wriggers P. A triangular finte shell element based on a fully nonlinear shell formulation. Computational Mechanics, 31: 505-518 (2003).
85. Campello E.M.B., Pimenta P.M. andWriggers P. Elastic-plastic analysis of metallic shells at finite strains. to appear: Computational Mechanics (2008).
86. Carstensen C. and Bartels S. Each averaging technique yields reliable a posteriori error control in fem on unstructured grids. Part i: Low order conforming, nonconforming and mixed fem. Mathematics of Computation, 71:945-969 (2002).
87. Carstensen C. and Funken S. Averaging technique for fe - a posteriori error control in elasticity. Part i: Conforming fem. Computer Methods in Applied Mechanics and Engineering, 190:2483-2498 (2001).
88. Carstensen C., Scherf O. and Wriggers P. Adaptive finite elements for elastic bodies in contact. SIAM Journal of Scientific Computing, 20:1605-1626 (1999).
89. Castanier M.P., Tan Y.C. and Pierre C. Characteristic constraint modes for component mode synthesis. AIAA Journal, 39:1182-1187 (2001).
90. Chadwick P. Continuum Mechanics, Concise Theory and Problems. Dover Publications, Mineola (1999).
91. Chadwick P. and Ogden R.W. A theorem of tensor calculus and its application to isotropic elasticity. Archives of Rational Mechanics, 44:54-68 (1971).
92. Chapelle D. and Bathe K.J. The inf-sup test. Computers and Structures, 47: 537-545 (1993).
93. Chuong C.J. and Fung Y. Three-dimensional stress distribution in arteries. Journal of Biomechanical Engineering, 105:268-274 (1983).
94. Ciarlet P.G. Mathematical Elasticity I: Three-dimensional Elasticity. North- Holland, Amsterdam (1988).
95. Ciarlet P.G. Introduction to Numerical Linear Algebra and Optimization, English Translation of 1982 Edition in Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge (1989).
96. Cirak F., Ortiz M. and Schröder P. Subdivision surfaces: A new paradigm for thin shell finite-element analysis. International Journal for Numerical Methods in Engineering, 47:2039-2072 (2000).
97. Crisfield M.A. A fast incremental/iterative solution prodedure that handles snap through. Computers and Structures, 13:55-62 (1981).
98. Crisfield M.A. Non-linear Finite Element Analysis of Solids and Structures, volume 1. Wiley, Chichester (1991).
99. Crisfield M.A. Non-linear Finite Element Analysis of Solids and Structures, volume 2. Wiley, Chichester (1997).
100. Crisfield M.A., Moita G.F., Jelenic G. and Lyons L.P.R. Enhanced lower-order element formulations for large strains. Computational Mechanics, 17:62-73 (1995).
101. Crisfield M.A. and Shi J. A review of solution procedures and path-following techniques in relation to the non-linear finite element analysis of structures. In P. Wriggers and W. Wagner, editors, Computational Methods in Nonlinear Mechanics. Springer, Berlin (1991).
102. Crisfield M.A. and Shi J. A co-rotational element/time-integration strategy for nonlinear dynamics. International Journal for Numerical Methods in Engineering, 37:1897-1913 (1994).
103. Crisfield M.A. and Shi J. An energy conserving co-rotational procedure for nonlinear dynamics with finite elements. Nonlinear Dynamics, 9(1):37-52 (1996).
104. Cuitino A. and Ortiz M. A material-independent method for extending stress update algorithms from small-strain plasticity to finite plasticity with multiplicative kinematics. Engineering Computations, 9:437-451 (1992).
105. Curnier A. A theory of friction. International Journal of Solids & Structures, 20:637-647 (1984).
106. Curnier A. and Alart P. A generalized Newton method for contact problems with friction. Journal of Theoretical and Applied Mechanics, 7:67-82 (1988).
107. Curnier A., He Q.C. and Telega J.J. Formulation of unilateral contact between two elastic bodies undergoing finite deformation. C. R. Academy Science Paris, 314:1-6 (1992).
108. Cuthill E. and McKee J. Reducing the bandwith of sparse symmetric matrices. ACM Publications P-69, pages 157-172 (1969).
109. Dafalias Y.F. The plastic spin. Journal of Applied Mechanics, 52:865-871 (1985).
110. Davis T.A. and Duff I.S. A combined unifrontal/multifrontal method for unsymmetric sparse matrices. ACM Transactions on Mathematical Software, 25:1-19 (1999).
111. Dennis J.E. and Schnabel R.B. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs, New Jersey (1983).
112. Desai C.S. and Siriwardane H.J. Constitutive Laws for Engineering Materials. Prentice-Hall, Englewood Cliffs, New Jersey (1984).
113. Dhatt G. and Touzot G. The Finite Element Method Displayed. Wiley, Chichester (1985).
114. Doblare M. Non-linear dynamics of three-dimensional rods: exact energy and momentum conserving algorithms. International Journal for Numerical Methods in Engineering, 38:1431-1473 (1995).
115. Dohrmann C., Heinstein M., Jung J., Key S.W. and Witkowski W. Nodebased uniform strain elements for three-node triangular and four-node tetra hedral mesh. International Journal for Numerical Methods in Engineering, 47: 1549-1568 (2000).
116. Doll S. and Schweizerhof K. On the development of volumetric strain energy functions. Transactions of the ASME - E - Journal of Applied Mechanics, 67:17-21 (2000).
117. Dostal Z. A proportioning based algorithm for bound constraint quadratic programming with the rate of convergence. Numerical Algorithms, 34:293-302 (2003).
118. Douglas C., Haase G. and Langer U. A Tutorial on Elliptic PDE Solvers and their Parallelization. SIAM, Philadelphia (2003).
119. Drucker D.C. and Prager W. Soil mechanics and plastic analysis or limit design. Quarterly Appl. Math., 10:157-165 (1952).
120. Duff I.S. Ma57 - a new code for the solution of sparse symmetric definite and indefinite systems. ACM Transactions on Mathematical Software, 30:118-154 (2004).
121. Duff I.S., Erisman A.M. and Reid J.K. Direct Methods for Sparse Matrices. Clarendon Press, Oxford (1989).
122. Duffet G. and Reddy B.D. The analysis of incompressible hyperelastic bodies by the finite element method. Computer Methods in Applied Mechanics and Engineering, 41:105-120 (1983).
123. Düster A., Bröker H. and Rank E. The p-version of the finite element method for three-dimensional curved thin walled structures. International Journal for Numerical Methods in Engineering, 52:673-703 (2001).
124. Düster A., Hartmann S. and Rank E. p-FEM applied to finite isotropic hyperelastic bodies. Computer Methods in Applied Mechanics and Engineering, 192: 5147-5166 (2003).
125. Düster A., Niggl A., Nübel V. and Rank E. A numerical investigation of high-order finite elements for problems of elastoplasticity. Journal of Scientific Computing, 17(1):397-404 (2002).
126. Duvaut G. and Lions J.L. Inequalities in Mechanics and Physics. Springer Verlag, Berlin (1976).
127. Dvorkin E.N. and Bathe K.J. A continuum mechanics based four-node shell element for general nonlinear analysis. Engineering Computations, 1:77-88 (1984).
128. Dvorkin E.N., Onate E. and Oliver J. On a nonlinear formulation for curved Timoshenko beam elements considering large displacement/rotation increments. International Journal for Numerical Methods in Engineering, 26:1597-1613 (1988).
129. Dvorkin E.N., Pantuso D. and Repetto A. A formulation of theMITC4 shell element for finite strain elasto-plastic analysis. Computer Methods in Applied Mechanics and Engineering, 125:17-40 (1995).
130. Eberlein R. Finite-Elemente-Konzepte für Schalen mit großen elastischen und plastischen Verzerrungen. Dissertation, Institut für Mechanik IV der Technischen Hochschule Darmstadt (1997).
131. Eberlein R. and Wriggers P. Finite element concepts for finite elastoplastic strains and isotropic stress response in shells: Theoretical and computational analysis. Computer Methods in Applied Mechanics and Engineering, 171:243-279 (1999).
132. Eberlein R., Wriggers P. and Taylor R. A fully non-linear axisymmetrical quasikirchhoff- type shell element for rubberlike materials. International Journal for Numerical Methods in Engineering, 36:4027-4043 (1993).
133. Ehrlich D. and Armero F. Finite element methods for the analysis of softening plastic hinges in beams and frames. Computational Mechanics, 35(4):237-264 (2005).
134. Ekh M., Johansson A., Thorberntsson H. and Josefson B. Models for Cyclic Ratchetting Plasticity-Integration and Calibration. Journal of Engineering Materials and Technology, 122:49 (2000).
135. Elguedj T., Bazilevs Y., Calo V.M. and Hughes T.J.R. B̄ and F̄ projection methods for nearly incompressible linear and nonlinear elasticity and plasticity using higher-order NURBS elements. Computer Methods in Applied Mechanics and Engineering (2008).
136. Elman H.C., Silvester D.J. and Wathen A.J. Finite Elements and Fast Iterative Solvers with Applications in Incompressible Fluid Dynamics. Oxford University Press, Oxford (2005).
137. van Engelen R.A., Wolters L. and Cats G. Ctadel: A generator of efficient code for PDE-based scientific applications. Technical report, Leiden Institute of Advanced Computer Science, http://www.liacs.nl/TechRep/1995/tr95-26.ps.gz, (1995).
138. Eriksson E. On some path-related measures for non-linear structural f. e. problems. International Journal for Numerical Methods in Engineering, 26:1791-1803 (1988).
139. Eringen A. Nonlinear Theory of Continuous Media. McGraw-Hill, New York, London (1962).
140. Eringen A. Mechanics of Continua. Wiley, New York, London, Sidney (1967).
141. Eschenauer H. and Schnell W. Elastizitätstheorie. BI Wissenschaftsverlag, Mannheim, dritte edition (1993).
142. Eyheramendy D. and Zimmermann T. Object-oriented symbolic derivation and automatic programming of finite elements in mechanics. Engineering with Computers, 15(1):12-36 (2000).
143. Farhat C. and Roux F. A method of finite element tearing and interconnecting and its parallel solution algorithm. International Journal for Numerical Methods in Engineering, 32(6):1205-1227 (1991).
144. Felippa C.A. A historical outline of matrix structural analysis: A play in three acts. Technical Report CU-CAS-00-13, Center for Aerospace Structures, University of Colorado (2000).
145. Feucht M. Ein gradientenabhängiges Gursonmodell zur Beschreibung duktiler Schädigung mit Entfestigung. Dissertation, Institut für Mechanik der TU Darmstadt (1999). Bericht Nr. D 17.
146. Findley W.N., Lai J.S. and Onaran K. Creep and Relaxation of Nonlinear Viscoelastic Materials. Dover Publications, New York (1989).
147. Fischer K.A. andWriggers P. Mortar based frictional contact formulation for higher order interpolations using the moving friction cone. Computer Methods in Applied Mechanics and Engineering, 195:5020-5036 (2006).
148. Fletcher R. Conjugated gradient methods for indefinite systems. Lecture Notes in Mathematics, 506:773-789 (1976).
149. Flory P. Thermodynamic relations for high elastic materials. Transactions of the Faraday Society, 57:829-838 (1961).
150. Fourment L. and Chenot J.L. Error estimators for viscoplastic materials: Applications to forming processes. International Journal for Numerical Methods in Engineering, 38:469-490 (1995).
151. Fredriksson B. Finite element solution of surface nonlinearities in structural mechanics with special emphasis to contact and fracture mechanics problems. Computers and Structures, 6:281-290 (1976).
152. Fried I. Orthogonal trajectory accession to the nonlinear equilibrium curve. Computer Methods in Applied Mechanics and Engineering, 15:283-297 (1984).
153. Fritzson P. and Fritzson D. The need for high-level programming support in scientific computing applied to mechanical analysis. Computers and Structures, 45:387-395 (1984).
154. Fujii F. and Ramm E. Computational bifurcation theory: path-tracing, pinpointing and path-switching. Engineering Structures, 19:385-392 (1997).
155. Gear C.W. Numerical Initial Value Problems in Ordinary Differential Equations. Prentice-Hall, Englewood Cliffs (1971).
156. Geradin M. and Rixen D. Mechanical Vibrations. Wiley, Chichester, second edition (1997).
157. Giannokopoulos A.E. The return mapping method for the integration of friction constitutive relations. Computers and Structures, 32:157-168 (1989).
158. Glaser S. and Armero F. On the formulation of enhanced strain finite elements in finite deformations. Engineering Computations, 14:759-791 (1997).
159. Glowinski R. and Le Tallec P. Finite element analysis in nonlinear incompressible elasticity. In Finite Element, Vol. V: Special Problems in Solid Mechanics. Prentice-Hall, Englewood Cliffs, New Jersey (1984).
160. Golub G. and Ortega J.M. Scientific Computing, Eine Einführung in das wissenschaftliche Rechnen und Parallele Numerik. Teubner-Verlag, Stuttgart (1996).
161. Golub G.H. and van Loan C.F. Matrix Computations. John Hopkins University Press, Baltimore (1989).
162. Gonnet G. New results for random determination of equivalence of expression. In B.W. Char, editor, Proceedings of 1986 ACM Symposium on Symbolic and Algebraic Computation, pages 127-131. ACM, Waterloo (1986).
163. Gonzalez O. Exact energy and momentum conserving algorithms for general models in nonlinear elasticity. Computer Methods in Applied Mechanics and Engineering, 190(13-14):1763-1783 (2000).
164. Gould N.I.M., Hu Y. and Scott J.A. A numerical evaluation of sparse direct solvers for the solution of large sparse, symmetric linear systems of equations. Technical Report RAL-TR-2005-00, Computational Science and Engineering Department, Atlas Centre, Rutherford Appleton Laboratory, Oxfordshire (2005).
165. Govindjee S. and Simo J.C. Mullin's effect and the strain amplitiude dependence of the storage modulus. International Journal of Solids & Structures, 29:1737-1751 (1992).
166. Griewank A. Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. SIAM, Philadelphia (2000).
167. Griewank A. and Walther A. Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. SIAM, Philadelphia, second edition (2008).
168. Gross D., Hauger W., Schnell W. andWriggers P. Technische Mechanik 4. Springer, Berlin, third edition (1999).
169. Gruttmann F. Theorie und Numerik dünnwandiger Faserverbundstrukturen. Habilitation, Institut für Baumechanik und Numerische Mechanik der Universität Hannover (1996). Bericht Nr. F 96/1.
170. Gruttmann F., Sauer R. and Wagner W. A geometrical non-linear eccentric 3D-beam element with arbitrary cross-sections. Computer Methods in Applied Mechanics and Engineering, 160:383-400 (1998).
171. Gruttmann F., Sauer R. and Wagner W. Theory and numerics of three-dimensional beams with elastoplastic material behaviour. International Journal for Numerical Methods in Engineering, 48:1675-1702 (2000).
172. Gruttmann F. and Stein E. Tangentiale Steifigkeitsmatrizen bei Anwendung von Projektionsverfahren in der Elastoplastizitätstheorie. Ingenieur-Archiv, 58:15-24 (1988).
173. Gruttmann F. andWagner W. A linear quadrilateral shell element with fast stiffness computation. Computer Methods in Applied Mechanics and Engineering, 194 (39-41):4279-4300 (2005).
174. Gruttmann F., Wagner W. and Wriggers P. A nonlinear quadrilateral shell element with drilling degrees of freedom. Ingenieur Archiv, 62:474-486 (1992).
175. Guo Y., Ortiz M., Belytschko T. and Repetto E.A. Triangular composite finite elements. International Journal for Numerical Methods in Engineering, 47: 287-316 (2000).
176. Gurson A.L. Continuum theory of ductile rupture by void nucleation and growth, Part i. Journal Engineering Material Technology, 99:2-15 (1977).
177. Haase G., Langer U., Reitzinger S. and Schöberl J. Algebraic multigrid methods based on element preconditioning. International Journal of Computer Mathematics, 78(4):575-598 (2001).
178. Habraken A. and Cescotto S. An automatic remeshing technique for finite element simulation of forming processes. International Journal for Numerical Methods in Engineering, 30:1503-1525 (1990).
179. Hackbusch W. Iterative Solution of Large Sparse Systems. Springer, New York (1994).
180. Hackbusch W. Multi-Grid Methods and Applications. Springer, New York (2003).
181. Häggblad B. and Sundberg J.A. Large strain solutions of rubber components. Computers and Structures, 17:835-843 (1983).
182. Hallquist J.O. Nike2d: An implicit, finite-deformation, finite element code for analysing the static and dynamic response of two-dimensional solids. Technical Report UCRL-52678, University of California, Lawrence Livermore National Laboratory (1979).
183. Hallquist J.O., Goudreau G.L. and Benson D.J. Sliding interfaces with contactimpact in large-scale lagrange computations. Computer Methods in Applied Mechanics and Engineering, 51:107-137 (1985).
184. Hallquist J.O., Schweizerhof K. and Stillman D. Efficiency refinements of contact strategies and algorithms in explicit fe programming. In D.R.J. Owen, E. Hinton and E. Onate, editors, Proceedings of COMPLAS III, pages 359-384. Pineridge Press (1992).
185. Han C.S. Eine h-adaptive Finite-Element-Methode für elasto-plastische Schalenprobleme in unilateralem Kontakt. Dissertation, Institut für Baumechanik und Numerische Mechanik der Universität Hannover (1999). Bericht Nr. F 99/2.
186. Han C.S. and Wriggers P. A simple local a posteriori bending indicator for axisymmetrical membrane and bending shell elements. Engineering Computations, 15:977-988 (1998).
187. Hart E.W. Constitutive relations for the nonelastic deformation of metals. Trans. ASME, Journal of Engineering Materials and Technology, 98:193-201 (1976).
188. Hassler M. and Schweizerhof K. On the static interaction of fluid and gas loaded multi-chamber systems in large deformation finite element analysis. Computer Methods in Applied Mechanics and Engineering, 197:1725-1749 (2008).
189. Hauptmann R. Strukturangepasste geometrisch nichtlineare finite Elemente für Flächentragwerke. Dissertation, Institut für M der Universität Fredericiana Karlsruhe (1997). Bericht Nr. M 97/3.
190. Hauptmann R. and Schweizerhof K. A systematic development of 'solid-shell' element formulation for linear and nonlinear analyses employing only displacement degree of freedom. International Journal for Numerical Methods in Engineering, 42:49-69 (1998).
191. Heisserer U., Hartmann S., Yosibash Z. and Düster A. On volumetric locking-free behavior of p-version finite elements under finite deformations. Communications in Numerical Methods in Engineering. DOI: 10.1002/cnm.1008 (in press) (2007).
192. Henning A. Traglastberechnung ebener Rahmen - Theorie II. Ordnungschweizerhof und Interaktion. Technical Report 75-12, Institut für Statik, Braunschweig (1975).
193. Hilber H., Hughes T.R.J. and Taylor R.L. Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Engineering and Structural Dynamics, 5:283-292 (1977).
194. Hill R. The Mathematical Theory of Plasticity. Clarendon Press, Oxford (1950).
195. Hill R. A general theory of uniqueness and stability in elasto-plastic solids. Journal of Mechanics and Physics of Solids, 6:236-249 (1958).
196. Hill R. Constitutive inequalities for isotropic elastic solids under finite strain. Proceedings of the Royal Society, London, A314:457-472 (1970).
197. Hinton E. and Owen D.R.J. An Introduction to Finite Element Computations. Pineridge Press, Swansea (1979).
198. Hinton E., Rock T. and Zienkiewicz O.C. A note on mass lumping and related processes in the finite element method. Earthquake Engineering and Structural Dynamics, 4:245-249 (1976).
199. Hofstetter G. and Mang H.A. Computational Mechanics of Reinforced Concrete Structures. Vieweg, Berlin (1995).
200. Hoger A. The stress conjugate to logarithmic strain. International Journal of Solids & Structures, 23:1645-1656 (1987).
201. Hohenemser K. and Prager W. Über die ansätze der mechanik isotroper kontinua. Zeitschrift für angewandte Mathematik und Mechanik, 12:216-226 (1932).
202. Hoit M. and Wilson E.L. An equation numbering algorithm based on a minimum front criteria. Computers and Structures, 16:225-239 (1983).
203. Holmes P., Lumley J.L. and Berkooz G. Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press, Cambridge (1996).
204. Holzapfel G., Eberlein R., Wriggers P. and Weizsäcker H. Large strain analysis of soft biological and rubber-like membranes: Formulation and finite element analysis. Computer Methods in Applied Mechanics and Engineering, 132:45-61 (1996a).
205. Holzapfel G., Eberlein R., Wriggers P. and Weizsäcker H. A new axisymmetrical membrane element for anisotropic, finite strain analysis of arteries. Communications in Applied Numerical Methods, 12:507-517 (1996b).
206. Holzapfel G.A. Nonlinear Solid Mechanics. Wiley, Chichester (2000).
207. Hueck U., Reddy B. and Wriggers P. On the stabilization of the rectangular fournode quadrilateral element. Communications in Applied Numerical Methods, 10:555-563 (1994).
208. Hueck U. and Wriggers P. A formulation for the four-node quadrilateral element, Part i: Plane element. International Journal for Numerical Methods in Engineering, 38:3007-3037 (1995).
209. Hughes T.J.R. Generalization of selective integration procedures to anisotropic and nonlinear media. International Journal for Numerical Methods in Engineering, 15:1413-1418 (1980).
210. Hughes T.J.R. and Brezzi F. On drilling degrees of freedom. Computer Methods in Applied Mechanics and Engineering, 72:105-121 (1989).
211. Hughes T.J.R., Cottrell J.A. and Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 194(39-41):4135-4195 (2005).
212. Hughes T.J.R. and Liu W.K. Nonlinear Finite Element Analysis of Shells: Part I. Threedimensional Shells. Computer Methods in Applied Mechanics and Engineering, 26:331-362 (1981).
213. Hughes T.J.R., Taylor R.L. and Kanoknukulchai W. A Simple and Efficient Finite Element for Plate Bending. International Journal for Numerical Methods in Engineering, 11:1529-1547 (1977a).
214. Hughes T.J.R. and Tezduyar T.E. Finite elements based upon mindlin plate theory with particular reference to the four-node bilinear isoparametric element. Journal of Applied Mechanics, 48:587-596 (1981).
215. Hughes T.R.J. The Finite Element Method. Prentice Hall, Englewood Cliffs, New Jersey (1987).
216. Hughes T.R.J., Taylor R.L. and Kanoknukulchai W. A finite element method for large displacement contact and impact problems. In K.J. Bathe, editor, Formulations and Computational Algorithms in FE Analysis, pages 468-495. MIT Press, Boston (1977b).
217. Ibrahimbegovic A. Finite Elastoplastic Deformations of Space-Curved Membranes. Computer Methods in Applied Mechanics and Engineering, 119:371-394 (1994).
218. Ibrahimbegovic A. A finite element implementaion of geometrically nonlinear Reissner's beam theory: Three-dimensional curved beam elements. Computer Methods in Applied Mechanics and Engineering, 122:11-26 (1995).
219. Ibrahimbegovic A., Taylor R.L. and Wilson E.L. A robust quadrilateral membrane element with drilling degrees of freedom. International Journal for Numerical Methods in Engineering, 30:445-457 (1990).
220. Idelsohn S.R. and Cardona A. Reduction methods and explicit time integration. Advances in Engineering Software, 6:36-44 (1984).
221. Idelsohn S.R. and Cardona A. A reduction method for nonlinear structural dynamic analysis. Computer Methods in Applied Mechanics and Engineering, 49:253-279 (1985).
222. Irons B. Quadrature rules for brick based finite elements. International Journal for Numerical Methods in Engineering, 3:293-294 (1971).
223. Irons B. and Ahmad S. Techniques of Finite Elements. Ellis Horwood, Chichester, U.K. (1986).
224. Isaacson E. and Keller H.B. Analysis of Numerical Methods. Wiley, London (1966).
225. Itskov M. Computation of the exponential and other isotropic tensor functions and their derivatives. Computer Methods in Applied Mechanics and Engineering, 192:3985-3999 (2003).
226. Iura M. and Atluri S.N. Formulation of a membrane finite element with drilling degrees of freedom. Computational Mechanics, 39:417-428 (1992).
227. Jaquotte O.P. and Oden J.T. An accurate and efficient a posteriori control of hourglass instabilities in underintegrated linear and nonlinear elasticity. Computer Methods in Applied Mechanics and Engineering, 55:105-128 (1986).
228. Jelenic G. and Saje M. A kinematically exact space finite strain beam model - finite element formulations by generalised virtual work principle. Computer Methods in Applied Mechanics and Engineering, 120:131-161 (1995).
229. Jepson A. and Spence A. Folds in solutions of two parameter systems amd theri calculation, Part i. SIAM Journal on Numerical Analysis, 22:347-368 (1985).
230. Joe B. Quadrilateral mesh generation in polygonal regions. Computer Aided Design, 27:209-222 (1995).
231. Johansson G., Ekh M. and Runesson K. Computational modeling of inelastic large ratcheting strains. International Journal of Plasticity, 21(5):955-980 (2005).
232. Johnson C. Numerical Solution of Partial Differential Equations by the Finite Element Method. Cambridge University Press, Cambridge (1987).
233. Johnson C. and Hansbo P. Adaptive finite element methods in computational mechanics. Computer Methods in Applied Mechanics and Engineering, 101: 143-181 (1992).
234. Ju W. and Taylor R.L. A perturbed lagrange formulation for the finite element solution of nonlinear frictional contact problems. Journal of Theoretical and Applied Mechanics, 7:1-14 (1988).
235. Jung M. and Langer U. Methode der finiten Elemente für Ingenieure. Teubner (2001).
236. Kahn R. Finite-element-berechnungen ebener stabwerke mit flissgelenken und grossen verschiebungen. Technical Report F 87/1, Forschungs- und Seminarberichte aus dem Bereich der Mechanik der Universität Hannover (1987).
237. Kane C., Marsden J.E. and Ortiz M. Symplectic-energy-momentum preserving variational integrators. Journal of Mathematical Physics, 40(7):3353 (1999).
238. Kappus R. Zur Elastizitätstheorie endlicher Verschiebungen. Zeitschrift für angewandte Mathematik und Mechanik, 19:271-361 (1939).
239. Keller H.B. Numerical solution of bifurcation and nonlinear eigenvalue problems. In P. Rabinowitz, editor, Application of Bifurcation Theory, pages 359-384. Academic Press, New York (1977).
240. Khan A.S. and Huang S. Continuum Theory of Plasticity. Wiley, Chichester, New York (1995).
241. Kickinger F. Algebraic multigrid solver for discrete elliptic second order problems. Technical Report 96-5, Department of Mathematics, Johannes Kepler University, Linz (1996).
242. Kikuchi N. and Oden J.T. Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. SIAM, Philadelphia (1988).
243. Kirby R.C., Knepley M., Logg A. and Scott L.R. Optimizing the evaluation of finite element matrices. SIAM Journal on Scientific Computing, 27:741-758 (2005).
244. Kirsch U., Bogomolni M. and Sheinman I. Nonlinear dynamic reanalysis for structural optimization. In van CampenD. H., L.M. D. and van den Oever W. P. J. M, editors, Proceedings of the Fifth EUROMECH Nonlinear Dynamics Conference (ENOC). Eindhoven (2005).
245. Koiter W.T. A consistent first approximation in the general theory of thin elastic shells. In W.T. Koiter, editor, The Theory of Thin Elastic Shells, pages 12-33. North-Holland, Amsterdam (1960).
246. Konyukhov A. and Schweizerhof K. A special focus on 2d formulations for contact problems using a convective description. International Journal for Numerical Methods in Engineering, 66:1432-1465 (2006).
247. Korelc J. Automatic generation of finite-element code by simultaneous optimization of expressions. Theoretical Computer Science, 187:231-248 (1997).
248. Korelc J. Multi-language and multi-environment generation of nonlinear finite element codes. Engineering with Computers, 18:312-327 (2002).
249. Korelc J. and Wriggers P. Consistent gradient formulation for a stable enhanced strain method for large deformations. Engineering Computations, 13:103-123 (1996a).
250. Korelc J. and Wriggers P. Improved enhanced strain 3-d element with Taylor expansion of shape functions. Computational Mechanics, 19:30-40 (1996b).
251. Korneev V.G., Langer U. and Xanthis L. On fast domain decomposition solving procedures for hp-discretizations of 3d elliptic problems. Computational Methods in Applied Mathematics, 3:536-559 (2003).
252. Kosloff D. and Frazier G.A. Treatment of hourglass pattern in low order finite element codes. International Journal for Numerical and Analytical Methods in Geomechanics, 2:57-72 (1978).
253. Kocvara M. and Mande l.J. A multigrid method for three dimensional elasticity and algebraic convergence estimates. Applied Mathematics and Computation, 23:121-135 (1987).
254. Kragelsky I.V. and Alisin V.V. Tribology - Lubrication, Friction, and Wear. Professional Engineering Publishing (2001).
255. Kragelsky I.V., Dobychin M.N. and Kombalov V.S. Friction and Wear - Calculation Methods (Translated from The Russian by N. Standen). Pergamon Press, Oxford (1982).
256. Krätzig W.B. 'Best' transverse shearing and stretching shell theory for non-linear finite element simulations. Computer Methods in Applied Mechanics and Engineering, 103:135-160 (1993).
257. Krempl E., McMahon J. and Yao D. Viscoplasticity based on overstress with a differential growth law for the equilibrium stress. Mechanics of Materials, 5: 35-48 (1986).
258. Kreuzer E. and Kust O. Analysis of long torsional strings by proper orthogonal decomposition. Archive of Applied Mechanics, 184:68-80 (1995).
259. Krstulovic-Opara L., Wriggers P. and Korelc J. A c1-continuous formulation for 3d finite deformation frictional contact. Computational Mechanics, 29:27-42 (2002).
260. Krysl P., Lall S. and Marsden J.E. Dimensional model reduction in non-linear finite element dynamics of solids and structures. International Journal for Numerical Methods in Engineering, 51:479-504 (2001).
261. Kühborn A. and Schoop H. A Nonlinear Theory for Sandwich Shells Including the Wrinkling Phenomenon. Ingenieur-Archiv, 62:413-427 (1992).
262. Kuhl D. and Crisfield M.A. Energy-conserving and decaying algorithms in nonlinear structural dynamics. International Journal for Numerical Methods in Engineering, 45(5):569-599 (1999).
263. Kuhl D. and Ramm E. Constraint energy momentum algorithm and its application to nonlinear dynamics of shells. Computer Methods in Applied Mechanics and Engineering, 136:293-315 (1996).
264. Ladeveze P. Constitutive relation error estimators for time-dependent nonlinear f.e. analysis. In S. Idelsohn, E. Onate and E. Dvorkin, editors, Computational Mechanics. CIMNE, Barcelona (1998).
265. Ladeveze P. and Leguillon D. Error estimate procedure in the finite element method and applications. SIAM Journal on Numerical Analysis, 20:485-509 (1983).
266. Ladeveze P. and Pelle J.P. Mastering Calculations in Linear and Nonlinear Mechanics. Springer, Mechanical Engineering Series, New York (2005).
267. Langer U. Multigrid - methoden. Technical report, Institut für Mathematik, Johannes Kepler Universität Linz (1996).
268. Larsson R., Runesson K. and Ottosen N. Discontinuous displacement approximation for capturing plastic localization. International Journal for Numerical Methods in Engineering, 36:2087-2105 (1993).
269. Lasry D. and Belytschko T. Localization limiters in transient problems. International Journal of Solids & Structures, 24:581-597 (1988).
270. Laursen T.A. Computational Contact and Impact Mechanics. Springer, Berlin, New York, Heidelberg (2002).
271. Laursen T.A. and Meng X.N. A new solution procedure for application of energyconserving algorithms to general constitutive models in nonlinear elastodynamics. Computer Methods in Applied Mechanics and Engineering, 190(46-47): 6309-6322 (2001).
272. Laursen T.A. and Simo J.C. Algorithmic symmetrization of Coulomb frictional problems using augmented Lagrangians. Computer Methods in Applied Mechanics and Engineering, 108:133-146 (1993a).
273. Laursen T.A. and Simo J.C. A continuum-based finite element formulation for the implicit solution of multibody, large deformation frictional contact problems. International Journal for Numerical Methods in Engineering, 36:3451-3485 (1993b).
274. Leblond J.B., Perrin G. and Devaux J. Bifurcation effects in ductile metals with nonlocal damage. Journal of Applied Mechanics, 61:236-242 (1994).
275. Lee E.H. and Liu D.T. Finite strain elasto-plastic theory with applications to plane-wave analysis. Journal of Applied Mechanics, 38:19-27 (1967).
276. Leger P. Mode superposition methods. In M. Papadrakakis, editor, Solving Largescale Problems in Mechanics, pages 225-257. Wiley, New York (1993).
277. Leppin C. and Wriggers P. Numerical simulations of the behaviour of cohesionless soil. In D.R.J. Owen, E. Hinton and E. Onate, editors, Proceedings of COMPLAS 5. CIMNE, Barcelona (1997).
278. Libai A. and Simmonds J.G. Large-strain constitutive laes for the cylindrical deformation of shells. International Journal of Nonlinear Mechanics, 16:91-103 (1992).
279. Loehnert S., Boerner E., Rubin M. and Wriggers P. Response of a nonlinear elastic general cosserat brick element in simulations typically exhibiting locking and hourglassing. Computational Mechanics, 36:255-265 (2005).
280. Logg A. Automating the finite element method. Archives of Computational Methods in Engineering, 14:93-138 (2007).
281. Löhner R. Progress in grid generation via the advancing front technique. Engineering Computations, 12:186-210 (1996).
282. Lu J. Exact expansions of arbitrary tensor functions and their derivatives. International Journal of Solids & Structures, 41:337-349 (2004).
283. Lubliner J. A model of rubber viscoelasticity. Mechancis Research Communications, 12:93-99 (1985).
284. Lubliner J. Plasticity Theory. MacMillan, London (1990).
285. Luenberger D.G. Linear and Nonlinear Programming. Addison-Wesley, Reading, MA, second edition (1984).
286. Lumpe G. Geometrisch nichtlineare berechnung von räumlichen stabwerken. Technical Report 28, Institut für Statik, Universität Hannover (1982).
287. MacNeal R.H. and Harder R.L. A Proposed Standard Set of Problems to Test Finite Element Accuracy. Finite Elements in Analysis and Design, 1:3-20 (1985).
288. Mahnken R., Caylaka I. and Laschet G. Two mixed finite element formulations with area bubble functions for tetrahedral elements. Computer Methods in Applied Mechanics and Engineering, 197:1147-1165 (2008).
289. Mäkinen J. Total lagrangian Reissner's geometrically exact beam element without singularities. International Journal for Numerical Methods in Engineering, 70:1009-1048 (2007).
290. Malkus D.S. and Hughes T.J.R. Mixed finite element methods - Reduced and selective integration techniques: A unification of concepts. Computer Methods in Applied Mechanics and Engineering, 15:63-81 (1978).
291. Malvern L.E. Introduction to the Mechanics of a Continuous Medium. Prentice- Hall, Englewood Cliffs, New Jersey (1969).
292. Mandel J. Thermodynamics and Plasticity. In Foundations of Continuum Thermodynamics, Delgado Domingers, J. J. and Nina, N. R. andWhitelaw, J. H. (Eds.). MacMillan, London (1974). 283-304.
293. Marsden J.E. and Hughes T.J.R. Mathematical Foundations of Elasticity. Prentice- Hall, Englewood Cliffs, NJ (1983).
294. Matthies H. and Strang G. The solution of nonlinear finite element equations. International Journal for Numerical Methods in Engineering, 14:1613-1626 (1979).
295. Maugin G.A. The Thermomechanics of Plasticity and Fracture. Cambridge University Press, Cambridge, New York (1992).
296. Meisel M. and Meyer A. Implementierung eines parallelen vorkonditionierten Schur- Komplement CG-Verfahrens in das Programmpaket FEAP. Technical Report SPC 95-2, Institut für Mathematik, TU Chemnitz-Zwickau (1995).
297. Meyer A. A parallel preconditioned conjugate gradient method using domain decomposition and inexact solvers on each subdomain. Computing, 45 (1990).
298. Meyer M. and Matthies H. Efficient model reduction in non-linear dynamics using the Karhunen-Loeve expansion and dual-weighted-residual methods. Computational Mechanics, 31:179-191 (2003).
299. Meynen S., Boersma A. andWriggers P. Application of a parallel algebraic multigrid method for the solution of elasto-plastic shell problems. Numerical Linear Algebra with Application, 4:223-238 (1997).
300. Michalowski R. and Mroz Z. Associated and non-associated sliding rules in contact friction problems. Archives of Mechanics, 30:259-276 (1978).
301. Miehe C. Kanonische modelle multiplikativer elasto-plastizit"at. thermodynamische formulierung und numerische implementation. Technical Report F 93/1, Forschungs- und Seminarberichte aus dem Bereich der Mechanik der Universität Hannover (1993).
302. Miehe C. Aspects of the Formulation and Finite Element Implementation of Large Strain Isotropic Elasticity. International Journal for Numerical Methods in Engineering, 37:1981-2004 (1994).
303. Miehe C. A formulation of finite elastoplasticity in shells based on dual co- and contra-variant eigenvectors normalized with respect to a plastic metric. In D.R.J. Owen, E. Onate and E. Hinton, editors, Computational Plasticity, Fundamentals and Applications. CIMNE, Barcelona (1997). 1922-1929.
304. Miehe C. A theoretical and computational model for isotropic elastoplastic stress analysis in shells at large strains. Computer Methods in Applied Mechanics and Engineering, 155:193-233 (1998).
305. Miehe C. and Schröder J. Post-critical discontinous localization analysis of smallstrain softening elastoplastic solids. Archive of Applied Mechanics, 64:267-285 (1994).
306. Mittelmann H.D. and Weber H. Numerical methods for bifurcation problems - a survey and classification. In H.D. Mittelmann and H. Weber, editors, Bifurcation Problems and their Numerical Solution, ISNM 54, pages 1-45. Birkhäuser, Basel, Boston, Stuttgart (1980).
307. Moita G.F. and Crisfield M.A. A finte element formulation for 3-d continua using the co-rotational technique. International Journal for Numerical Methods in Engineering, 39(22):3775-3792 (1996).
308. Mooney M. A theory of large elastic deformations. Journal for Applied Physics, 11:582-592 (1940).
309. Moreau J.J. Application of convex analysis to the treatment of elastoplastic strucures. In P. Germain and B. Nayroles, editors, Applications of Methods of Functional Analysis to Problems in Mechanics. Springer-Verlag, Berlin (1976).
310. Morman K.N. The generalized strain measure with applications to nonhomogeneous deformations in rubber-like solids. Journal of Applied Mechanics, 53:726-728 (1987).
311. Mueller-Hoeppe D.S., Loehnert S. and Wriggers P. A finite deformation brick element with inhomogeneous mode enhancement, on-line first. International Journal for Numerical Methods in Engineering (2008).
312. Nadler B. and Rubin M. A new 3-d finite element for nonlinear elasticity using the theory of a cosserat point. International Journal of Solids and Structures, 40:4585-4614 (2003).
313. Naghdi P.M. The Theory of Shells, volume VIa/2 of Handbuch der Physik, Mechanics of Solids II. Springer, Berlin (1972).
314. Nagtegaal J.C. On the implementation of inelastic constitutive equations with special reference to large deformation problems. Computer Methods in Applied Mechanics and Engineering, 33(1-3):469-484 (1982).
315. Nagtegaal J.C., Parks D.M. and Rice J.C. On numerically accurate finite element solutions in the fully plastic range. Computer Methods in Applied Mechanics and Engineering, 4: 153-177 (1990).
316. Needleman A. A numerical study of necking in circular cylindrical bars. Journal of Mechanics and Physics of Solids, 20:111-127 (1972).
317. Needleman A. and Rice J.R. Limits to ductility set by plastic flow localization. In D.P. Koistinen and N.-W. Wang, editor, Mechanics of Sheet Metal Forming, pages 237-267. Plenum Press, New York (1978).
318. Newmark N.M. A method of computation for structural dynamics. Proceedings of ASCE, Journal of Engineering Mechanics, 85:67-94 (1959).
319. Nguyen Q. Stability and Nonlinear Solid Mechanics. Wiley, New York (2000).
320. Nickell R.E. Nonlinear dynamics by mode superposition. Computer Methods in Applied Mechanics and Engineering, 7:107-129 (1976).
321. Noor A.K. Recent advances and applications of reduction methods. Applied Mechanics Review, 47:125-146-94 (1994).
322. Oden J.T. Exterior penalty methods for contact problems in elasticity. In W.Wunderlich, E. Stein and K.J. Bathe, editors, Nonlinear Finite Element Analysis in Structural Mechanics. Springer, Berlin (1981).
323. Oden J.T. and Key J.E. Numerical analysis of finite axisymmetrical deformations of incompressible elastic solids of revolution. International Journal of Solids & Structures, 6:497-518 (1970).
324. Oden J.T. and Martins J.A.C. Models and computational methods for dynamic friction phenomena. Computer Methods in Applied Mechanics and Engineering, 52:527-634 (1986).
325. Oden J.T., Zohdi T. and Rodin G.J. Hierarchical modelling of heterogeneous bodies. Computer Methods in Applied Mechanics and Engineering, 138:273-298 (1996).
326. Ogden R.W. Large deformation isotropic elasticity: On the correlation of theory and experiment for incompressible rubberlike solids. Proceedings of the Royal Society of London, 326:565-584 (1972).
327. Ogden R.W. Elastic deformations of rubberlike solids. In H.G. Hopkins and M.J. Sewell, editors, Mechanics of Solids, The Rodney Hill 60th Anniversary Volume, pages 499-537. Pergamon Press, Oxford (1982).
328. Ogden R.W. Non-Linear Elastic Deformations. Ellis Horwood and John Wiley, Chichester (1984).
329. Oliver J. Continuum modeling of strong discontinuities in solid mechanics using damage models. Computational Mechanics, 17:49-61 (1995).
330. Oliver J., Huespe A.E., Blanco S. and Linero D.L. Stability and robustness issues in numerical modeling of material failure with the strong discontinuity approach. Computer Methods in Applied Mechanics and Engineering, 195: 7093-7114 (2006).
331. Onate E. and Cervera M. Derivation of thin plate bending elements with one degree of freedom per node: A simple three node triangle. Engineering computations, 10(6):543-561 (1993).
332. Oran C. and Kassimali A. Large deformations of framed structures under static and dynamic loads. Computers and Structures, 6:539-547 (1976).
333. Ortega J. and Rheinboldt W. Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York (1970).
334. Ortiz M. and Quigley J.J. Adaptive mesh refinement in strain localization problems. Computer Methods in Applied Mechanics and Engineering, 90:781-804 (1991).
335. Owen D.R.J. and Hinton E. Finite Elements in Plasticity: Theory and Practice. Pineridge Press, Swansea, U.K. (1980).
336. Owen S.J. A Survey of Unstructured Mesh Generation Technology. http://www.andrew.cmu.edu/user/sowen/survey/index.html (1999).
337. Pamin J. Gradient-Dependent Plasticity in Numerical Simulation of Localization Phenomena. Ph.D. thesis, Delft University of Technology, Delft (1994).
338. Papadrakakis M. Solving Large-Scale Linear Problems in Solid and Structural Mechanics, in Solving Large-Scale Problems in Mechanics. Wiley & Sons, Chichester (1993).
339. Parisch H. A consistent tangent stiffness matrix for three-dimensional non-linear contact analysis. International Journal for Numerical Methods in Engineering, 28:1803-1812 (1989).
340. Parisch H. An investigation of a finite rotation four node assumed strain element. International Journal for Numerical Methods in Engineering, 31:127-150 (1991).
341. Peric D., Hochard C., Dutko M. and Owen D.R.J. Transfer operators for evolving meshes in small strain elasto-plasticity. Computer Methods in Applied Mechanics and Engineering, 137:331-344 (1996).
342. Peric D. and Owen D.R.J. Computational model for contact problems with friction based on the penalty method. International Journal for Numerical Methods in Engineering, 36:1289-1309 (1992).
343. Peric D. and Owen D.R.J. On error estimates and adaptivity in elastoplastic solids: Applications to the numerical simulation of strain localization in classical and cosserat continua. International Journal for Numerical Methods in Engineering, 37:1351-1379 (1994).
344. Peric D. and Owen D.R.J. Finite-element applications to the nonlinear mechanics of solids. Reports on Progress in Physics, 61:1495-1574 (1997).
345. Peric D., Owen D.R.J. and Honnor M.E. A model for finite strain elasto-plasticity based on logarithmic strains: Computational issues. Computer Methods in Applied Mechanics and Engineering, 94(1):35-61 (1992).
346. Peri'c D., Vaz M. and Owen D.R.J. On adaptive strategies for large deformations of elasto-plastic solids at finite strains: Computational issues and industrial applications. Computer Methods in Applied Mechanics and Engineering, 176 (1-4):279-312 (1999).
347. Perzyna P. The constitutive equations for rate sensitive plastic materials. Quarterly Applied Mathematics, 20:321-332 (1963).
348. Perzyna P. Fundamental problems in viscoplasticity. Advances in Applied Mechanics, 9:243-377 (1966).
349. Petersen C. Statik und Stabilität der Baukonstruktionen. Vieweg & Sohn, Berlin (1980).
350. Petryk H. and Thermann K. On discretized plasticity problems with bifurcations. International Journal of Solids & Structures, 29:745-765 (1992).
351. Pflüger A. Stabilitätsprobleme in der Elastostatik. Springer-Verlag, Berlin, Heidelberg, New York, dritte edition (1975).
352. Pian T.H.H. Derivation of element stiffness matrices by assumed stress distributions. AIAA-J. 2, 7:1333-1336 (1964).
353. Pian T.H.H. and Sumihara K. Rational approach for assumed stress finite elements. International Journal for Numerical Methods in Engineering, 20: 1685-1695 (1984).
354. Pietraszkiewicz W. Geometrically nonlinear theories of thin elastic shells. Technical Report 55, Mitteilungen des Instituts für Mechanik der Ruhr-Universität Bochum (1978).
355. Pietrzak G. and Curnier A. Large deformation frictional contact mechanics: continuum formulation and augmented lagrangean treatment. Computer Methods in Applied Mechanics and Engineering, 177:351-381 (1999).
356. Pimenta P. and Yojo T. Geometrically exact analysis of spatial frames. Applied Mechanics Review, 46:118-128 (1993).
357. Pimenta P.M., Campello E.M.B. andWriggers P. A fully nonlinear multi-parameter shell model with thickness variation and a triangular shell finite element formulation. Computational Mechanics, 34:181-193 (2004).
358. Planinc I. and Saje M. A quadratically convergent algorithm for the computation of stability points: The application of the determinant of the tangent stiffness matrix. Computer Methods in Applied Mechanics and Engineering, 169:89-105 (1999).
359. Prager W. Probleme der Plastizitätstheorie. Birkäuser, Basel, Stuttgart (1955).
360. Prager W. Einführung in die Kontinuumsmechanik. Birkäuser, Basel, Stuttgart (1961).
361. Puso M.A. A highly efficient enhanced assumed strain physically stabilized hexahedral element. International Journal for Numerical Methods in Engineering, 49:1029-1064 (2000).
362. Puso M.A. A 3D mortar method for solid mechanics. International Journal for Numerical Methods in Engineering, 59(3):315-336 (2004).
363. Puso M.A. and Laursen T.A. A mortar segment-to-segment contact method for large deformation solid mechanics. Computer Methods in Applied Mechanics and Engineering, 193:601-629 (2004).
364. Puso M.A. and Solberg J. A stabilized nodally integrated tetrahedral. International Journal for Numerical Methods in Engineering, 67:841-867 (2006).
365. Ramm E. Geometrisch nichtlineare Elastostatik und Finite Elemente. Technical Report Nr. 76-2, Institut für Baustatik der Universität Stuttgart (1976).
366. Ramm E. Strategies for tracing the nonlinear response near limit points. In W.Wunderlich, E. Stein and K.J. Bathe, editors, Nonlinear Finite Element Analysis in Structural Mechanics. Springer, Berlin, Heidelberg, New York (1981).
367. Ramm E. and Cirak F. Adaptivity for nonlinear thin-walled structures. In D.R.J. Owen, E. Hinton and E. Onate, editors, Proceedings of COMPLAS 5, pages 145-163. CIMNE, Barcelona (1997).
368. Ramm E., Rank E., Rannacher R., Schweizerhof K., Stein E., Wendland W., Wittum G., Wriggers P. and Wunderlich W. Error-Controlled Adaptive Finite Elements in Solid Mechanics. Wiley, Chichester (2003).
369. Raniecki B. and Bruhns O. Bounds to bifurcation stresses in solids with nonassociated plastic flow law at finite strain. Journal of the Mechanics and Physics of Solids, 29:153-172 (1981).
370. Rank E., Schweingruber M. and Sommer M. Adaptive mesh generation and transformation of triangular to quadrilateral meshes. Communications in Numerical Methods in Engineering, 9:121-129 (1993).
371. Rankin C.C. and Brogan F.A. An element independent corotational procedure for the treatment of large roations. In L.H. Sobel and K. Thomas, editors, Collapse Analysis of Structures, pages 85-100. ASME, New York (1984).
372. Rannacher R. and Suttmeier F.T. A feed back approach to error control in finite element methods: Application to linear elasticity. Computational Mechanics, 19(5):434-446 (1997a).
373. Rannacher R. and Suttmeier F.T. A posteriori error control in finite element methods via duality techniques: Application to perfect plasticity. Technical Report 97-16, Institut for Applied Mathematics, SFB 359, University of Heidelberg (1997b).
374. Rannacher R. and Suttmeier F.T. A posteriori error control in finite element methods via duality techniques: Application to perfect plasticity. Computational Mechanics, 21(2):123-133 (1998).
375. Rannacher R. and Suttmeier F.T. A posteriori error estimation and mesh adaptation for finite element models in elasto-plasticity. Computer Methods in Applied Mechanics and Engineering, 176(1-4):333-361 (1999).
376. Reddy B.D. and Simo J.C. Stability and convergence of a class of enhanced strain methods. SIAM Journal of Numerical Analysis, 32:1705-1728 (1995).
377. Reese S. Theorie und Numerik des Stabilitätsverhalten hyperelastischer Festkörper. Technical Report D 17, Institut für Mechanik der TH Darmstadt (1994).
378. Reese S. On a consistent hourglass stabilization technique to treat large inelastic deformations and thermo-mechanical coupling in plane strain problems. International Journal for Numerical Methods in Engineering, 57:1095-1127 (2003).
379. Reese S. On a physically stabilized one point finite element formulation for threedimensional finite elasto-plasticity. Computer Methods in Applied Mechanics and Engineering, 194:4685-4715 (2005).
380. Reese S. and Govindjee S. A theory of finite viscoelasticity and numerical aspects. International Journal of Solids & Structures, 35:3455-3482 (1998).
381. Reese S. and Wriggers P. A finite element method for stability problems in finite elasticity. International Journal for Numerical Methods in Engineering, 38: 1171-1200 (1995).
382. Reese S. and Wriggers P. A new stabilization concept for finite elements in large deformation problems. International Journal for Numerical Methods in Engineering, 48:79-110 (2000).
383. Reese S., Wriggers P. and Reddy B.D. A new locking-free brick element formulation for continuous large deformation problems. In Proceedings of WCCM IV in Buenos Aires (1998).
384. Reese S., Wriggers P. and Reddy B.D. A new locking-free brick element technique for large deformation problems in elasticity. Computers and Structures, 75: 291-304 (2000).
385. Rehle N. Adaptive Finite Element Verfahren bei der Analyse von Flächentragwerken. Technical Report Nr. 20, Institut für Baustatik der Universität Stuttgart (1996).
386. Reissner E. On one-dimensional finite strain beam theory, the plane problem. Journal of Applied Mathematics and Physics, 23:795-804 (1972).
387. Reitinger R. and Ramm E. Buckling and imperfection sensitivity in the optimization of shell structures. Thin-Walled Structures, 23:159-177 (1995).
388. Rheinboldt W. Numerical analysis of continuation methods for nonlinear structural problems. Computers and Structures, 13:103-113 (1981).
389. Rheinboldt W. Methods for Solving Systems of Nonlinear Equations. Society for Industrial and Applied Mathematics, Philadelphia (1984).
390. Rheinboldt W. Error estimates for nonlinear finite element computations. Computers and Structures, 20:91-98 (1985).
391. Ribó R., Bugeda G. and Oñate E. Some algorithms to correct a geometry in order to create a finite element mesh. Computers and Structures, 80(16-17):1399-1408 (2002).
392. Riccius J., Schweizerhof K. and Baumann M. Combination of adaptivity and mesh smoothing for the finite element analysis of shells with intersections. International Journal for Numerical Methods in Engineering, 40:2459-2474 (1997).
393. Riks E. The application of Newtons method to the problem of elastic stability. Journal of Applied Mechanics, 39:1060-1066 (1972).
394. Riks E. Some computational aspects of stability analysis of nonlinear structures. Computer Methods in Applied Mechanics and Engineering, 47:219-260 (1984).
395. Riks E., Rankin C. and Brogan F. On the solution mode of jumping phenomena in thin-walled shell structures. Computer Methods in Applied Mechanics and Engineering, 136:59-92 (1996).
396. Rivlin R.S. Large elastic deformations of isotropic materials. Proc. of the Royal Society of London, 241:379-397 (1948).
397. Roehl D. and Ramm E. Large elasto-plastic finite element analysis of solids and shells with the enhanced assumed strain concept. International Journal of Solids & Structures, 33:3215-3237 (1996).
398. Romero I. and Armero F. An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy- momentum conserving scheme in dynamics. International Journal for Numerical Methods in Engineering, 54:1683-1716 (2002).
399. Rubin M. Cosserat Theories: Shells, Rods and Points, volume 79. Kluwer Academic Publishers, Dordrecht (2000).
400. Rubin M. and Jabareen M. An improved 3-d brick cosserat point element for irregular shaped element. Computational Mechanics 40:979-1004 (2007).
401. Rubin M. and Jabareen M. A 3d brick macro-element for non-linear elasticity. Private communication (2007).
402. Ruge J.W. Amg for problems of elasticity. Applied Mathematics and Computation, 19:293-309 (1986).
403. Saad Y. Practical use of polynomial preconditionings for the conjugate gradient method. SIAM Journal on Scientific and Statistical Computing, 4 (1985).
404. Saad Y. Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia (2003).
405. Saad Y. and Schultz M.H. Gmres: A generalized residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing, 7:856-869 (1986).
406. Sansour C. A theory and finite element formulation of shells at finite deformations involving thickness change: Circumventing the use of a rotation tensor. Ingenieur- Archiv, 65:194-216 (1995).
407. Sansour C., Sansour J. and Wriggers P. A finite element approach to the chaotic motion of geometrically exact rods undergoing plane deformations. Nonlinear Dynamics, 11:189-212 (1996).
408. Sansour C., Wriggers P. and Sansour J. Nonlinear dynamics of shells: Theory, finite element formulation and integration schemes. Nonlinear Dynamics, 13:279-305 (1997).
409. Schenk O. and Gärtner K. Solving unsymmetric sparse systems of linear equations with pardiso. Journal of Future Generation Computer Systems, 20:475-487 (2004).
410. Scherf O. Kontinuumsmechanische modellierung nichtlinearer kontaktprobleme und ihre numerische analyse mit adaptiven finite-element- methoden. Technical Report D 17, Institut für Mechanik der TH Darmstadt (1997).
411. Schöberl J. Robust Multigrid Methods for Parameter Deoendent Problems. Dissertation, Institut für Analysis und Numerik, Johannes Kepler Universität Linz (1999).
412. Schoop H. Oberflächenorientierte Schalentheorien endlicher Verschiebungen. Ingenieur-Archiv, 56:427-437 (1986).
413. Schreyer H.L. and Neilsen M.K. Analytical and numerical tests for loss of material stability. International Journal for Numerical Methods in Engineering, 39: 1721-1736 (1996).
414. Schwarz H.R. FORTRAN-Programme zur Methode der finiten Elemente. Teubner, Stuttgart (1981).
415. Schweizerhof K. Nichtlineare Berechnung von Tragwerken unter verformungsabh ängiger Belastung mit finiten Elementen. Technical Report 82-2, Institut für Baustatik, Stuttgart (1982).
416. Schweizerhof K. and Ramm E. Displacement dependent pressure loads in nonlinear finite element analysis. Computers and Structures, 18 (1984).
417. Schweizerhof K., Vielsack P., Rottner T. and Ewert E. Stability and sensitivity investigations of thin-walled shell structures using transient finite element analysis. In H. Mang, editor, 5 thWorld Congress on Computational Mechanics-WCCM V. Vienna (2002).
418. Schweizerhof K. andWriggers P. Consistent linearization for path following methods in nonlinear fe-analysis. Computer Methods in Applied Mechanics and Engineering, 59:261-279 (1986).
419. Schwetlick H. and Kretschmar H. Numerische Verfahren für Naturwissenschaftler und Ingenieure. Fachbuchverlag, Leipzig (1991).
420. Seifert B. Zur Theorie und Numerik Finiter Elastoplastischer Deformationen von Schalenstrukturen. Dissertation, Institut für Baumechanik und Numerische Mechanik der Universität Hannover (1996). Bericht Nr. F 96/2.
421. Sewell M.J. On configuration-dependent loading. Archives of Rational Mechanics, 23:321-351 (1967).
422. Sheng D. and Sloan S.W. Load stepping schemes for critical state models. International Journal for Numerical Methods in Engineering, 50:67-93 (2001).
423. Shepard M.S. and Georges M.K. Three-dimensional mesh generation by finite octree technique. International Journal for Numerical Methods in Engineering, 32: 709-749 (1991).
424. Simitses G. Dynamic Stability of Suddenly Loaded Structures. Springer-Verlag, Berlin (1990).
425. Simo J., Oliver J. and Armero F. Analysis of strong dicontinuities in rate independent softening materials. Computational Mechanics
426. Simo J., Taylor R. and Wriggers P. A note on finite element implementation of pressure boundary loading. Communications in Applied Numerical Methods, 7:513-525 (1991).
427. Simo J.C. A finite strain beam formulation. The three-dimensional dynamic problem. Part I. Computer Methods in Applied Mechanics and Engineering, 49:55-70 (1985).
428. Simo J.C. On a fully three-dimensional finite-strain viscoelastic damage model: Formulation and computational aspects. Computer Methods in Applied Mechanics and Engineering, 60:153-173 (1987).
429. Simo J.C. A framework for finite strain elastoplasticity based on the multiplicative decomposition and hyperelastic relations. Part ii: Computational aspects. Computer Methods in Applied Mechanics and Engineering, 67:1-31 (1988).
430. Simo J.C. Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Computer Methods in Applied Mechanics and Engineering, 99:61-112 (1992).
431. Simo J.C. On a stress resultant geometrically exact shell model. Part VII. Shell intersections with 5/6-DOF finite element formulations. Computer Methods in Applied Mechanics and Engineering, 108:319-339 (1993).
432. Simo J.C. Numerical analysis and simulation of plasticity. In P.G. Ciarlet and J.L. Lions, editors, Handbook of Numerical Analysis, volume 6, pages 179-499. North-Holland, Amsterdam (1998).
433. Simo J.C. and Armero F. Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes. International Journal for Numerical Methods in Engineering, 33:1413-1449 (1992).
434. Simo J.C., Armero F. and Taylor R.L. Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems. Computer Methods in Applied Mechanics and Engineering, 110:359-386 (1993b).
435. Simo J.C., Fox D.D. and Rifai M.S. On a stress resultant geometrical exact shell model. Part I: Formulation and optimal parametrization. Computer Methods in Applied Mechanics and Engineering, 72:267-304 (1989).
436. Simo J.C., Fox D.D. and Rifai M.S. On a stress resultant geometrical exact shell model. Part III: Computational aspects of the nonlinear theory. Computer Methods in Applied Mechanics and Engineering, 79:21-70 (1990).
437. Simo J.C., Hjelmstad K.D. and Taylor R.L. Numerical formulations for finite deformation problems of beams accounting for the effect of transverse shear. Computer Methods in Applied Mechanics and Engineering, 42:301-330 (1984).
438. Simo J.C. and Hughes T.J.R. Computational Inelasticity. Springer, New York, Berlin (1998).
439. Simo J.C. and Kennedy J.G. On a stress resultant geometrically exact shell model. Part V. Nonlinear plasticity: Formulation and integration algorithms. Computer Methods in Applied Mechanics and Engineering, 96:133-171 (1992).
440. Simo J.C. and Miehe C. Associative coupled thermoplasticity at finite strains: formulation, numerical analysis and implementation. Computer Methods in Applied Mechanics and Engineering, 98:41-104 (1992).
441. Simo J.C. and Ortiz M. A unified approach to finite deformation elastoplasticity based on the use of hyperelastic constitutive equations. Computer Methods in Applied Mechanics and Engineering, 49:201-215 (1985).
442. Simo J.C. and Pister K.S. Remarks on rate constitutive equations for finite deformation problems. Computer Methods in Applied Mechanics and Engineering, 46:201-215 (1984).
443. Simo J.C. and Rifai M.S. A class of assumed strain methods and the method of incompatible modes. International Journal for Numerical Methods in Engineering, 29:1595-1638 (1990).
444. Simo J.C., Rifai M.S. and Fox D.D. On a stress resultant geometrically exact shell model. Part IV. Variable thickness shells with through-the-tickness stretching. Computer Methods in Applied Mechanics and Engineering, 81:91-126 (1990B).
445. Simo J.C. and Tarnow N. The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics. Zeitschrift für angewandte Mathematik und Physik, 43:757-792 (1992).
446. Simo J.C. and Taylor R.L. Consistent tangent operators for rate-independent elastoplasticity. Computer Methods in Applied Mechanics and Engineering, 48:101-118 (1985).
447. Simo J.C. and Taylor R.L. A return mapping algorithm for plane stress elastoplasticity. International Journal for Numerical Methods in Engineering, 22:649-670 (1986).
448. Simo J.C. and Taylor R.L. Quasi-incompressible finite elasticity in principal stretches continuum basis and numerical algorithms. Computer Methods in Applied Mechanics and Engineering, 85:273-310 (1991).
449. Simo J.C., Taylor R.L. and Pister K.S. Variational and projection methods for the volume constraint in finite deformation elasto-plasticity. Computer Methods in Applied Mechanics and Engineering, 51:177-208 (1985a).
450. Simo J.C. and Vu-Quoc L. Three dimensional finite strain rod model. Part II: computational aspects. Computer Methods in Applied Mechanics and Engineering, 58:79-116 (1986).
451. Simo J.C., Wriggers P. and Taylor R.L. A perturbed Lagrangian formulation for the finite element solution of contact problems. Computer Methods in Applied Mechanics and Engineering, 50:163-180 (1985b).
452. Skeie G., Astrup O.C. and Bergan P. Application of adapted nonlinear solution strategies. In N.E.Wiberg, editor, Advances in Finite Element Technology, pages 212-236. CIMNE, Barcelona (1995).
453. Sloan S.W. A fast algorithm for constructing delaunay triangularization in the plane. Advances in Engineering Software, 9:34-55 (1987a).
454. Sloan S.W. Substepping schemes for the numerical integration of elastoplastic stress-strain relations. International Journal for Numerical Methods in Engineering, 24:893-911 (1987b).
455. Sloan S.W. A fast algorithm for generating constrained delaunay triangulations. Computers and Structures, 47:441-450 (1993).
456. Sloan S.W., Abbo A.J. and Sheng D. Refined explicit integration of elastoplastic models with automatic error control. Engineering Computations, 18:121-154 (2001).
457. Sluys L.J. Wave propagation, localization and dispersion in softening solids. Ph.D. thesis, Delft University of Technology, Delft (1992).
458. Soric J., Montag U. and Krätzig W.B. An efficient formulation of integration algorithms for elastoplastic shell analysis based on Layered finite element approach. Computer Methods in Applied Mechanics and Engineering, 148:315-328 (1997).
459. de Souza Neto E.A., Peric D., Dutko M. and Owen D.R.J. Design of simple lower-order finite elements for large-deformation analysis of nearly incompressible solids. International Journal of Solids & Structures, 33:3277-3296 (1996).
460. de Souza Neto E.A., Peric D., Huang G.C. and Owen D.R.J. Remarks on stability of enhanced strain elements in finite elasticity and elastoplasticity. In D.R.J. Owen, E. Hinton and E. Onate, editors, Proceedings of COMPLAS 4, volume 1, pages 361-372. Pineridge Press, Swansea (1995).
461. Spence A. and Jepson A.D. The numerical calculation of cusps, bifurcation points and isola formation points in two parameter problems. In T. Küpper, H.D. Mittelmann and H.Weber, editors, Numerical Methods for Bifurcation Problems, ISNM 70, pages 502-514. Birkhäuser, Basel, Boston, Stuttgart (1984).
462. Spiess H. Reduction methods in finite element analysis of nonlinear structural dynamics. Technical Report F06/2, Forschungs- und Seminarberichte aus dem Bereich der Mechanik der Universität Hannover (2006).
463. Stein E. and Ohnimus S. Dimensional adaptivity in linear elasticity with hierarchical test-spaces for h- and p-refinement processes. Engineering Computations, 12:107-119 (1996).
464. Stein E., Steinmann P. and Miehe C. Instability phenomena in plasticity: Modelling and computation. Computational Mechanics, 17:74-87 (1995).
465. Steinmann P., Larsson R. and Runesson K. On the localization properties of multiplicative hyperelasto-plastic continua with strong discontinuities. International Journal of Solids & Structures, 34:969-990 (1997).
466. Stoer J. and Bulirsch R. Numerische Mathematik 2. Springer Verlag, Berlin, Heidelberg, Wien, dritte edition (1990).
467. Strang G. and Fix G.J. An Analysis of the Finite Element Method. Prentice-Hall, Inc., Englewood Cliffs (1973).
468. Stueben K. Algebraic multigrid (amg) experiences and comparisons. Applied Mathematics and Computation, 13:419-451 (1983).
469. Sussman T. and Bathe K.J. A finite element formulation for nonlinear incompressible elastic and inelastic analysis. Computers and Structures, 26:357-409 (1987).
470. Szabó I. Höhere Technische Mechanik. Springer, Berlin, Heidelberg, Wien, fünfte edition (1977).
471. Tabor D. Friction - The present state of our understanding. Journal Lubrication Technology, 103:169-179 (1981).
472. Taylor R.L. Solution of linear equations by a profile solver. Engineering Computations, 2:334-350 (1985).
473. Taylor R.L. A mixed-enhanced formulation for tetrahedral finite elements. International Journal for Numerical Methods in Engineering, 47:205-227 (2000).
474. Taylor R.L., Beresford P.J. and Wilson E.L. A non-conforming element for stress analysis. International Journal for Numerical Methods in Engineering, 10: 1211-1219 (1976).
475. Taylor R.L., Pister K.S. and Goudreau G.L. Thermomechanical analysis of viscoelastic solids. International Journal for Numerical Methods in Engineering, 2:45-79 (1970).
476. Taylor R.L., Wilson E.L. and Sackett S.J. Direct solution of equations by frontal and varaible band, active column methods. In E.S. W. Wunderlich and K.J. Bathe, editors, Nonlinear Finite Element Analysis in Structural Mechanics, pages 33-107. Springer-Verlag, Berlin, Heidelberg (1981).
477. Thoutireddy P., Molinari J.F., Repetto E.A. and Ortiz M. Tetrahedral composite finite elements. International Journal for Numerical Methods in Engineering, 53:1337-1351 (2002).
478. Treloar L.R.G. Stress-strain data for vulcanized rubber under various types of deformation. Transactions of the Faraday Society, 40:59-70 (1944).
479. Truesdell C. and Noll W. The nonlinear field theories of mechanics. In S. Flügge, editor, Handbuch der Physik III/3. Springer, Berlin, Heidelberg, Wien (1965).
480. Truesdell C. and Toupin R. The classical field theories. In Handbuch der Physik III/1. Springer, Berlin, Heidelberg, Wien (1960).
481. Tvergaard V. Material failure by void growth to coalescence. Advances in Applied Mechanics, 27:83-151 (1989).
482. Tvergaard V. and Needleman A. Analysis of the cup-cone fracture in a round tensile bar. Archives of Mechanics, 32:157-169 (1984).
483. Vainberg M.M. Variational Methods for the Study of Nonlinear Operators. Holden Day, San Francisco (1964).
484. Verfürth R. A Review of A Posteriori Error Estimation and Adaptive Mesh- Refinement Techniques. Wiley, Teubner, Chichester, New York, Stuttgart, Leipzig (1996).
485. Vogel U. Die Traglastberechnung st"ahlerner Rahmentragwerke nach der Plastizit" atstheorie II. Ordnung. Stahlbau Verlag, K"oln (1965).
486. Vogel U. Calibrating frames, vergleichsrechnungen an verschiedenen rahmen. Der Stahlbau, 10:295-301 (1985).
487. den Vorst H.A.V. Bi-cgstab: A fast and smoothly converging variant of bi-cg for the solution of non-symmetric linear systems. SIAM Journal on Scientific and Statistical Computing, 13:631-644 (1992).
488. Vukazich M., Mish K. and Romstad K. Nonlinear dynamic response of frames using Lanczos modal analysis. Journal of Structural Engineering, 122:1418-1426 (1996).
489. Wagner W. A finite element model for non-linear shells of revolution with finite rotations. International Journal for Numerical Methods in Engineering, 29: 1455-1471 (1990).
490. Wagner W. Zur Behandlung von Stabilitätsproblemen mit der Methode der Finiten Elemente. Technical Report F91/1, Forschungs- und Seminarberichte aus dem Bereich der Mechanik der Universität Hannover (1991).
491. Wagner W. and Gruttmann F. A simple finite rotation formulation for composite shell elements. Engineering Computations, 11:145-176 (1994).
492. Wagner W., Klinkel S. and Gruttmann F. Elastic and plastic analysis of thin-walled structures using improved hexahedral elements. Computers and Structures, 80 (9-10):857-869 (2002).
493. Wagner W. and Wriggers P. A simple method for the calculation of secondary branches. Engineering Computations, 5:103-109 (1988).
494. Wang P.S. Finger: A symbolic system for automatic generation of numerical programs in finite element analysis. Journal of Symbolic Computation, 2:305-316 (1986).
495. Washizu K. Variational Methods in Elasticity and Plasticity. Pergamon Press, Oxford, second edition (1975).
496. Weber G. and Anand L. Finite defformation constitutive equations and a time integration procedure for isotropic hyperelastic-viscoelastic solids. Computer Methods in Applied Mechanics and Engineering, 79:173-202 (1990).
497. Wempner G. Finite elements, finite roataions and small strains of flexible shells. International Journal of Solids & Structures, 5:117-153 (1969).
498. Werner B. and Spence A. The computation of symmetry-breaking bifurcation points. SIAM Journal on Numerical Analysis, 21:388-399 (1984).
499. Wiberg N.E., Abdulwahab F. and Ziukas S. Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions. International Journal for Numerical Methods in Engineering, 36:3417-3440 (1994).
500. Wilson E.L. and Dovey H.H. Solution or reduction of equilibrium equations for large complex structural systems. Advances in Engineering Software, 1:19-25 (1978).
501. Wilson E.L., Taylor R.L., Doherty W.P. and Ghaboussi J. Incompatible displacements models. In Numerical and Computer Models in Structural Mechanics, Fenves S. J., Perrone N., Robinson A. R. and Schnobrich W. C. (Eds.). Academic Press, New York (1973). 43-57.
502. Wilson E.L., Yuan M. and Dickens J.M. Dynamic analysis by direct superposition of ritz vectors. Earthquake Engineering and Structural Dynamics, 10:813-821 (1982).
503. Windels R. Traglasten von Balkenquerschnitten beim Angriff von Biegemoment, Längs- und Querkraft. Der Stahlbau, 39:10-16 (1970).
504. Wohlmuth B.I. Discretization Methods and Iterative Solvers based on Domain Decomposition. Springer Verlag, Berlin, Heidelberg, New York (2000).
505. Woo K.L. and Thomas T.R. Contact of rough surfaces: A review of experimental works. Wear, 58:331-340 (1980).
506. Wood W.L. Practical Time-stepping Schemes. Clarendon Press, Oxford (1990).
507. Wood W.L., Bossak M. and Zienkiewicz O.C. An alpha modification of Newmark's method. International Journal for Numerical Methods in Engineering, 15: 1562-1566 (1981).
508. Wriggers P. On consistent tangent matrices for frictional contact problems. In G. Pande and J. Middleton, editors, Proceedings of NUMETA 87. M. Nijhoff Publishers, Dordrecht (1987).
509. Wriggers P. Finite element algorithms for contact problems. Archive of Computational Methods in Engineering, 2:1-49 (1995).
510. Wriggers P. Computational Contact Mechanics. Springer, Berlin, Heidelberg, New York (2006).
511. Wriggers P. and Boersma A. A parallel algebraic multigrid solver for problems in solid mechanics discretized by finite elements. Computers and Structures, 69:129-137 (1998).
512. Wriggers P. and Carstensen C. An efficient algorithm for the computation of stability points of dynamical systems under step load. Engineering Computations, 9:669-679 (1992).
513. Wriggers P., Eberlein R. and Gruttmann F. An axisymmetrical quasi-Kirchhofftype shell element for large plastic deformations. Archiv of Applied Mechanics, 65:465-477 (1995).
514. Wriggers P., Eberlein R. and Reese S. Comparison between shell and 3d-elements in finite plasticity. International Journal of Solids & Structures, 33:3309-3326 (1996).
515. Wriggers P. and Gruttmann F. Large deformations of thin shells: Theory and finite-element discretization, analytical and computational models of shells. In A.K. Noor, T. Belytschko and J.C. Simo, editors, ASME, CED-Vol.3, volume 135-159 (1989).
516. Wriggers P. and Gruttmann F. Thin shells with finite rotations formulated in biot stresses theory and finite-element-formulation. International Journal for Numerical Methods in Engineering, 36:2049-2071 (1993).
517. Wriggers P. and Hueck U. A formulation of the enhanced qs6-element for large elastic deformations. International Journal for Numerical Methods in Engineering, 39:3039-3053 (1996).
518. Wriggers P., Krstulovic-Opara L. and Korelc J. Smooth c1-interpolations for twodimensional frictional contact problems. International Journal for Numerical Methods in Engineering, 51:1469-1495 (2001).
519. Wriggers P. and Meynen S. Parallele algorithmen und hardware für berechnungsverfahren des ingenieurbaus. In E. Ramm, E. Stein and W. Wunderlich, editors, Finite Elemente in der Baupraxis. Ernst & Sohn, München (1995).
520. Wriggers P., Miehe C., Kleiber M. and Simo J. A thermomechanical approach to the necking problem. International Journal for Numerical Methods in Engineering, 33:869-883 (1992).
521. Wriggers P. and Reese S. A note on enhanced strain methods for large deformations. Technical Report 3/94, Bericht des Instituts für Mechanik (1994).
522. Wriggers P. and Reese S. A note on enhanced strain methods for large deformations. Computer Methods in Applied Mechanics and Engineering, 135:201-209 (1996).
523. Wriggers P., Rieger A. and Scherf O. Comparison of different error measures for adaptive finite element techniques applied to contact problems involving large elastic strains. Computer Methods in Applied Mechanics and Engineering (2000).
524. Wriggers P. and Scherf O. An adaptive finite element method for elastoplastic contact problems. In D.R.J. Owen, E. Hinton and E. Onate, editors, Proceedings of COMPLAS 4. Pineridge Press, Swansea (1995).
525. Wriggers P. and Simo J. A note on tangent stiffnesses for fully nonlinear contact problems. Communications in Applied Numerical Methods, 1:199-203 (1985).
526. Wriggers P. and Simo J. A general procedure for the direct computation of turning and bifurcation points. International Journal for Numerical Methods in Engineering, 30:155-176 (1990).
527. Wriggers P., Simo J. and Taylor R. Penalty and augmented lagrangian formulations for contact problems. In J. Middleton and G. Pande, editors, Proceedings of NUMETA Conference. Balkema, Rotterdam (1985).
528. Wriggers P. and Taylor R. A fully nonlinear axisymmetrical membrane element for rubberlike materials. Engineering Computations, 7:303-310 (1990).
529. Wriggers P., Van T.V. and Stein E. Finite-element-formulation of large deformation impact-contact-problems with friction. Computers and Structures, 37:319-333 (1990).
530. Wriggers P., Wagner W. and Miehe C. A quadratically convergent procedure for the calculation of stability points in finite element analysis. Computer Methods in Applied Mechanics and Engineering, 70:329-347 (1988).
531. Wriggers P. and Zavarise G. On the application of augmented lagrangian techniques for nonlinear constitutive laws in contact interfaces. Communications in Applied Numerical Methods, 9:815-824 (1993).
532. Wright S.J. Primal-Dual Interior-Point Methods. SIAM, Philadelphia (1997).
533. Yagawa G., Yoshimura S. and Nakao K. Automatic mesh generation of complex geometries based on fuzzy knowledge processing and computational geometry.
534. Integrated Computer-Aided Engineering, 2(4):265-280 (1995). Yosibash Z., Hartmann S., Heisserer U., Düster A., Rank E. and Szanto M.
535. Axisymmetric pressure boundary loading for finite deformation analysis using p-FEM. Computer Methods in Applied Mechanics and Engineering, 196: 1261-1277 (2007).
536. Zavarise G., Wriggers P. and Schrefler B.A. A method for solving contact problems. International Journal for Numerical Methods in Engineering, 42:473-498 (1998).
537. Zhu J.Z., Zienkiewicz O.C., Hinton E. and Wu J. A new approach to the development of automatic quadrilateral mesh generation. International Journal for Numerical Methods in Engineering, 32:849-866 (1991).
538. Zienkiewicz O.C., Bauer J., Morgan K. and Onate E. A simple and efficient element for axisymmetrical shells. International Journal for Numerical Methods in Engineering, 11:1545-1558 (1977).
539. Zienkiewicz O.C. and Cheung Y.K. The Finite Element Method in Structural and Soild Mechanics. McGraw Hill, London (1967).
540. Zienkiewicz O.C. and Taylor R.L. The Finite Element Method, 4th Ed., volume 1.
541. McGraw Hill, London (1989). Zienkiewicz O.C. and Taylor R.L. The Finite Element Method, 4th Ed., volume 2. McGraw Hill, London (1991).
542. Zienkiewicz O.C. and Taylor R.L. The Finite Element Method, volume 1. Butterworth-Heinemann, Oxford, UK, 5th edition (2000a).
543. Zienkiewicz O.C. and Taylor R.L. The Finite Element Method, volume 2. Butterworth-Heinemann, Oxford, UK, 5th edition (2000b).
544. Zienkiewicz O.C., Taylor R.L. and Too J.M. Reduced integration technique in general analysis of plates and shells. International Journal for Numerical Methods in Engineering, 3:275-290 (1971).
545. Zienkiewicz O.C. and Zhu J.Z. A simple error estimator and adaptive procedure for practical engineering analysis. International Journal for Numerical Methods in Engineering, 24:337-357 (1987).
546. Zienkiewicz O.C. and Zhu J.Z. The superconvergent patch recovery (SPR) and adaptive finite element refinement. Computer Methods in Applied Mechanics and Engineering, 101:207-224 (1992).