Geometrically nonlinear analysis of shell structures using a flat triangular shell finite element

Archives of Computational Methods in Engineering

Volumn 13, Issue 3, 2006, Pages 331-388

  Gal, Erez ^a   Levy, Robert ^b  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 37849189104     PISSN: 11343060     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02736397     Document Type: Review

References (369)

1. A. Adini and R.W. Clough (1961). Analysis of plate bending by the finite element method. Report to Natl. Sci. Foundation/USA, G7337.
2. S. Ahmad B.M. Irons and O.C. Zienkiewicz (1970). Analysis of thick and thin shell structures by curved finite elements. Int. J. Nummer. Methods Eng., 2, 419-451.
3. D.J. Allman (1970). Triangle finite element for plate bending with constant and linearly vaqrying bending moments. In Proc. IUTAM Symposium on High Speed Computing of Elastic Structures, pages 36-105, University of Liegh.
4. D.J. Allman (1984). A compatible triangular element including vertex rotations for plane elasticity analysis. Computers & Structures, 19, 1-8.
5. D.J. Allman (1988). A quadrilateral finite element including vertex rotations for plane elasticity analysis. Int. J. Num. Method Engng., 26, 717-730.
6. D.J. Allman (1988). The constant strain triangle with drilling rotations: a simple prospect for shell analysis. In Proc. 6th International Conference on The Mathematics of Finite Element and Application, pages 233-240, MAFELAP VI, Ed. Whiteman, J.R..
7. D.J. Allman (1988). Evaluation of the constant strain triangle with drilling rotation. Int. J. Num. Method Engng., 26(12), 2645-2655.
8. D.J. Allman (1991). Analysis of general shells by flat facet finite element approximation. Aeronaut. J., 95, 194-203.
9. D.J. Allman (1993). Variational validation of a membrane finite element with drilling rotations. Communications in Numerical Methods in Engineering, 9, 345-351.
10. D.J. Allman (1994). A basic flat facet finite element for the analysis of general shells. Int. J. Num. Method Engng., 37, 19-35.
11. D.J. Allman and L.S.D. Morley (2000). The "constant" bending moment three-noded triangle. Communications in Numerical Methods in Engineering, 9, 345-351.
12. K. Alvin, H.M. de la Fuente, B. Haugen and C.A. Felippa (1992). Membrane triangles with corner drilling freedoms. I. The EFF element. Finite Element Anal. Des., 12, 163-187.
13. J.H. Argyris (1964). Recent Advances in Matrix methods of Structural Analysis. Pergamon Press.
14. J.H. Argyris. (1965) Triangular elements in plate bending-conforming and nonconforming solutions. Proc. Conf. Matrix Meth. Struc. Mech., pages 11-190, Air Force Institute of Technology, Wright-Patterson A.F.B., Ohio.
15. J.H. Argyris (1965). Matrix displacement analysis of anisotropic shells by triangular elements. Aeronautical Journal of The Royal Aeronautical Society, 69, 801-805.
16. J.H. Argyris. (1982). An excursion into large rotations. Comp. Meth. Appl. Mech. & Engng., 32, 85-155.
17. J.H. Argyris, H. Balmer and I. Doltsinis (1987). Implementation of a nonlinear capability on a linear software system. Comp. Meth. Appl. Mech. & Engng., 65, 267-291.
18. J.H. Argyris and P.C. Dunne. (1975). On the application of the natural mode technique to small strain large displacement problems. In World Congress on Finite Element Methods in Structural Mechanics, Bournemouth.
19. J.H. Argyris, P.C. Dunne, G. Malejannakis and E. Schelkle (1977). A simple triangular facet shell element with applications to linear and non-linear equilibrium and elastic stability problems. Comp. Meth. Appl. Mech. & Engng., 11, 97-131. and
20. J.H. Argyris, P.C. Dunne, G. Malejannakis and E. Schelkle, Comp. Meth. Appl. Mech. & Engng., 10, 371-403.
21. J.H. Argyris, M. Haase and H.P. Mlejnek (1980). On an unconventional but natural formation of the stiffness matrix. Comp. Meth. Appl. Mech. & Engng., 22, 371-403.
22. J.H. Argyris, H. Balmer, J.St. Doltsinis, P.C. Dunne, M. Haase, G.A. Kleiber, G. Malejannakis and H P. Mlejnek (1979). Finite element method - the natural approach. Comp. Meth. Appl. Mech. & Engng., 17/18, 1-106.
23. J.H. Argyris, M. Papadrakakis and L. Karapitta (2000). Elastoplastic analysis of shells with the triangular element TRIG. In The Fourth International Colloquium on Computational of Shell & Spatial Structures, Chania-Crete, Greece.
24. J.H. Argyris and L. Tenek (1993). A natural triangular layered element for bending analysis of isotropic, sandwich, laminated composite and hybrid plates. Comp. Meth. Appl. Mech. & Engng., 109, 197-218.
25. J.H. Argyris and L. Tenek (1994). Buckling of multilayered composite plates by natural shear deformation matrix theory. Comp. Meth. Appl. Mech. & Engng., 111, 37-59.
26. J.H. Argyris and L. Tenek (1994). Linear and geometrically nonlinear bending of Isotropic and multilayered composite plates by the natural mode method. Comp. Meth. Appl Mech. & Engng., 113, 207-251.
27. J.H. Argyris and L. Tenek (1994). High-temperature bending, buckling, and post buckling of laminated composite plates using the natural mode method. Comp. Meth. Appl. Mech. & Engng., 117, 105-142.
28. J.H. Argyris and L. Tenek (1994). An efficient and locking free Sat anisotropic plate and shell triangular element. Comp. Meth. Appl. Mech. & Engng., 118, 63-119.
29. J.H. Argyris and L. Tenek (1994). A practicable and locking-free laminated shallow shell triangular element. Comp. Meth. Appl. Mech. & Engng., 119, 215-282.
30. J.H. Argyris, L. Tenek and L. Olofsson (1997). TRIG: a simple but sophisticated 3-node triangular element based on 6 rigid body and 12 straining modes for fast computational simulations of arbitrary Isotropic and laminated composite shells. Comp. Meth. Appl. Mech. & Engng., 145, 11-85.
31. D.G. Ashwell (1960). On the large deflection of a spherical shell with an inward point load. Proceeding of I.U.T.A.M. Symposium on The Theory of Thin Elastic Shells, pages 43-63, Delft, Aug. 1969, North Holland, Amsterdam.
32. S. Atluri, R.H. Gallagher and O.C. Zienkiewicz (Eds.)(1983). Hybrid and mixed finite element methods. Wiley, Chichester.
33. I. Babuska (2001). The finite element method and its reliability. Clarendon, Oxford, (England).
34. I. Babuska and T. Strouboulis (2001). The finite element and its reliability. Clarendon Press, Oxford.
35. J. Bäcklund (1973). Finite element analysis of nonlinear structures. Ph.D. Thesis, Goteborg: Chalmers Tekniska Hogskola.
36. K.J. Bathe (1982). Finite element procedures in engineering analysis. Prentice-Hall, New Jersey.
37. K.J. Bathe (1996). Finite element procedures. Prentice-Hall, New Jersey.
38. K.J. Bathe and S. Bolourchi (1980). A geometric and material nonlinear plate and shell element. Computers & Structures, 11, 23-48.
39. K.J. Bathe, D. Chapelle and P.S. Lee (2003). A shell problem "highly sensitive" to thichness change. Int. J. Num. Method Engng., 57, 1039-1052.
40. K.J. Bathe and L.W. Ho (1980). A simple and effective element for analysis of general shell structures. Computers & Structures, 13, 673-681.
41. K.J. Bathe, E. Ramm and E.L. Wilson (1975). Finite element formulations for large deformation dynamic analysis. Int. J. Num. Method Engng., 9, 353-386.
42. J.M. Battini and C. Pacoste (2001). Co-rotational beam elements with warping effects in instability problems. Comput. Methods Appl. Mech. Engrg., 191, 1755-1789.
43. J.M. Battini and C. Pacoste (2004). On the choice of local element frame for corotational triangular elements. Commun. Numer. Meth. Engrg., 20, 819-825.
44. J.L. Batoz (1977). Analyse non linéare des coques minces élastiques de formes arbitraries par élements triangulaires courbés. Ph.D. Thesis, Laval University, Quebec.
45. J.L. Batoz, K.J. Bathe and L.W. Ho (1980). A study of three noded triangular plate bending elements. Int. J. Num. Meth. Engng., 15, 1771-1812.
46. J.L. Batoz, A. Cattopadhyay and G. Dhatt (1976). Finite element large deflection analysis of shallow shells. Int. J. Num. Meth. Engng., 10, 39-58.
47. J.L. Batoz and G. Dhatt (1972). Development of two simple shell elements. AIAA Jnl., 10, 237-238.
48. J.L. Batoz, F. Hammadi, C. Zheng and W. Zhong (1998). On the linear analysis of plates and shells using a new sixteen dof flat shell element. In Advances in Finite Element Procedures and Techniques, pages 31-41, Civil-Comp Press, Edinburgh.
49. J.L. Batoz, C.L. Zheng and F. Hammadi (2001). Formulation and evaluation of new triangular, quadrilateral, pentagonal and hexagonal discrete Kirchhoff plate/shell elements. Int. J. Num. Meth. Engng., 52, 615-630.
50. G.P. Bazeley, B.M. Cheung, B.M. Irons and O.G. Zienkiewicz (1965). Triangular elements in plate bending-conforming and nonconforming solutions. In Proc. Conf. Matrix Meth. Struc. Mech., Air Force Institute of Technology, Wright-Patterson A.F.B., Ohio.
51. P.X. Bellini and A. Chulya (1987). An improved automatic incremental algorithm for the efficient solution of nonlinear finite element equations. Computers and Structures, 26, 99-110.
52. T. Belytschko (1976). A survey of numerical methods and computer programs for dynamic structural element. Nucl. Engng Des., 37, 23-34.
53. T. Belytschko (2000). Nonlinear finite elements for continua and structures. Wiley, Chichester.
54. T. Belytschko and L. Glaum (1979) Application of high order corotational stretch theories to nonlinear finite element analysis. Computers and Structures, 10, 175-182.
55. T. Belytschko and J. Hsein (1973). Nonlinear transient analysis with convected co- ordinates. Int. J. Num. Meth. Engng., 7, 255-271.
56. T. Belytschko, J. Lin and C.S. Tsay (1984). Explicit algorithms for the nonlinear dynamics of shells. Comp. Meth. Appl. Mech. Engng., 42, 225-251.
57. T. Belytschko and L. Schwer (1977). Large displacement, transient analysis of space frame. Int. J. Num. Meth. Engng., 11, 65-84.
58. T. Belytschko, H. Stolarski, W.K. Lui, N. Carpenter and J.S. Ong (1985). Stress projection for membrane and shear looking in shell finite element. Comp. Meth. Appl. Mech. Engng., 51, 221-258.
59. T. Belytschko, B.L. Wong and H. Stolarski (1989). Assumed strain stabilization procedure for the 9-node Lagrangian shell element. Int. J. Num. Meth. Engng., 28, 385-414.
60. P.G. Bergan, G. Horrigmoe, B. Krakeland and T.H. Soreide (1978). Solution of nonlinear finite element problems. Int. J. Numer. Meths. Eng., 12, 1677-1696.
61. P.G. Bergan and C.A. Felippa (1985). A triangular membrane element with rotational degrees of freedom. Comp. Meth. Appl. Mech. Engng., 50, 25-69.
62. P.G. Bergan and M.K. Nygård (1986). Nonlinear shell analysisi using free formulation finite element. In K.J. Bathe and W. Wunderlich (Eds.), Finite Element Method for Nonlinear Problems, Springer, Heidelberg, Germany, 317-337.
63. P.G. Bergan and T.H. Soreide (1973). A comparative study of different numerical solution techniques as applied to a nonlinear structural problem. Comp. Meths. Appl. Mech. Eng., 2, 185-201.
64. M. Bernadou, P.M. Eiroa, and P. Trouvé (1994). On the convergence of a discrete Kirchhoff triangle method valid for shell of arbitrary shape. Comp. Meths. Appl. Mech. Eng., 118, 373-391.
65. M. Bernadou, P. Trouvé and Y. Ducatel (1989). Approximation of general shell problems by fiat plate elements part 1. Computation Mechanics, 5, 175-208.
66. M. Bernadou and P. Trouvé (1989). Approximation of general shell problems by flat plate elements part 2. addition of drilling degree of freedom. Computation Mechanics, 6, 359-378.
67. M.A. Biot (1965). Mechanics of Incremental Deformation. John Welly and Sons, New York.
68. J. Bonet and R.D. Wood (1997). Nonlinear continuum mechanics for finite element analysis. Cambridge University Press, Cambridge (UK).
69. A. Bout (1993). A displacement-based geometrically nonlinear constant stress element. Int. J. Num. Meth. Engng., 36, 1161-1188.
70. B. Brank, J. Korelc and A. Ibrahimbegovic (2002). Nonlinear shell problem formulation accounting for through-the-thickness stretching and its finite element implementation. Computers & Structures, 80, 699-717.
71. B. Brank, A. Ibrahimbegovic and S. Mamouri (2000). Finite rotation shell elements for nonlinear static and dynamics analysis. In The Fourth International Colloquium on Computational of Shell & Spatial Structures, Chania-Crete, Greece.
72. C. Brebbia and J.J. Connor (1969). Fundamentas of finite element techniques for structural engineers. Butterworths, London.
73. C. Brebbia and J.J. Connor (1969). Geometrical nonlinear finite element analysis. Proceeding Journal of Engineering Mechanics Division, ASME, 95, (EM2), 463-483.
74. S.C. Brenner and L.R. Scott (2002). The mathematical theory of finite element methods. Springer-Verlag, New York.
75. F. Brezzi and M. Fortin (1991). Mixed and hybrid finite element methods. Springer, New York.
76. M.L. Bucalem and K.J. Bathe (1993). Higher-order MITC general elements. Int. J. Num. Meth. Engng., 36, 3729-3754.
77. N. Buechter and E. Ramm (1992). Shell theory versus degeneration - a comparison in large rotation finite element analysis. Int. J. for Numerical Methods in Engineering, 34, 39-59.
78. J.W. Bull (ed.)(1998). Finite element analysis of thin-walled structures. Elsevier, London.
79. F.A. Carroll (1999). A primer for finite elements in elastic structures. Wiley, New York
80. C.R. Calladine (1988). The theory of thin shell structures. Proc. Instn. Mech. Engrs., 20 No. A3, 141-149.
81. N. Carpenter, H. Stolarski and T. Belytschko (1985). A flat triangular element shell element with improved membrane interpolation. Communications in Applied Numerical Methods, 1, 161-168.
82. N. Carpenter, H. Stolarski and T. Belytschko (1986). Improvement in 3-node triangular shell element. Int. J. Num. Meth. Engng., 23, 1643-1667.
83. D. Chapelle and K.J. Bathe (2003). The finite element analysis of shells: fundamentals. Springer, Berlin.
84. H.C. Chen (1992). Evaluation of Allman triangular membrane element used in general shell analyses. Computers and Structures, 43(5), 881-887.
85. K.K. Chen (1979). A triangular plate finite element for large displacement elastic plastic analysis of automobile structural components. Computers and Structures, 10, 203-215.
86. T.K. Cheung and M.F. Yeo (1979). A practical introduction to finite element analysis. Pitman, London.
87. P.G. Ciarlet (1976). Numerical analysis of the finite element method. Series "Séminaire de Mathématiques Supérieures", Vol. 59, Presses de l'University of Montréal, Montréal.
88. W.R. Clough and C.J. Jonhson (1968). A finite element approximation for the analysis of thin shells. Int. J. Num. Meth. Engng., 4, 43-60.
89. W.R. Clough and C.J. Jonhson (1970). Approximation of general shell problems by flat plate elements. In Proc. ACI Symposium on Concrete Thin Shells, 333-363.
90. R.W. Clough and E.L. Wilson (1971). Dynamic finite element analysis of arbitrary thin shells. Computers & Structures, 1, 33-56.
91. R.D. Cook (1968). On the Allman triangle and a related quadrilateral element. Computers & Structures, 22, 1065-1067.
92. R.D. Cook (1987). A plate hybrid element with rotational d.o.f. and adjustable stiffness. Int. J. Num. Meth. Engng., 24, 1499-1508.
93. R.D. Cook (1989). Concepts and Applications of Finite Element Analysis. 3rd edition, Jhon Wiley & Sons, Chichester.
94. R.D. Cook (1991). Modified formulation for nine-DOF plane triangles that includes vertex rotations. Int. J. Num. Meth. Engng., 31, 825-835.
95. R.D. Cook (1993). Further development of a three-node triangular shell element. Int. J. Num. Meth. Engng., 36, 1413-1425.
96. R.D. Cook (1995). Finite Element Modeling for Stress Analysis. Jhon Wiley & Sons, Chichester.
97. R.D. Cook, D.S. Malkus, M.E. Plesha and R.J. Witt (2001). Concepts and Applications of Finite Element Analysis. 4th edition, Wiley, New York.
98. E. Cosserat and F. Cosserat (1909). Theorie des corps deformables. In Chwolson, Traite De Physique, Paris, 2nd ed., 953-1173.
99. M.A. Crisfield (1981) A fast incremental / iterative solution proceedure that handles "snap-through" . Computers & Structures, 13, 55-62.
100. M.A. Crisfield (1983). An arc length method including line search and acceleration. Int. J. Num. Meth. Engng., 19, 1269-1289.
101. M.A. Crisfield (1990). A consistent co-rotational formulation for non-linear three-dimensional, beam elements. Comp. Meth. Appl. Mech. Engng., 81, 131-150.
102. M.A. Crisfield (1991). Non-Linear Finite Element Analysis of Solids and Structures. Vol. 1: Essentials. John Wiley & Sons, Chichester.
103. M.A. Crisfield (1997). Non-Linear Finite Element Analysis of Solids and Structures. Vol. 2: Advanced Topics. Jhon Wiley & Sons, Chichester.
104. M.A. Crisfield and G. Cole (1989). Co-rotational beam elements for two- and three-dimensional non-linear analysis. Proc. IUTAM/IACM Symp. on Discretization Methods in Structural Mechanics, 4, 115-124.
105. M.A. Crisfield and G.F. Moita (1996). A unified co-rotational framework for solids, shells and beams. Int. J. Solids Structures, 33, 2969-2992.
106. M.A. Crisfield and Peng, X. (1991). Recent research on co-rotational beam and shell elements. Proceeding of the International Conference on Nonlinear Engineering Computations, p 71.
107. M.A. Crisfield and X. Peng (1992). Efficient non-linear shell formulation with large rotations and plasticity. COMPLAS-3, Barcelona, 1979-1997.
108. M.A. Crisfield, Peng, X. and J. Shi (1994). Recent finite elemenet research on shells and nonlinear analysis. Marine Structure, 7, 307-321.
109. D.J. Dawe (1972). Shell analysis using a simple facet element. J. Strain Analysis, 7(4), 266-270.
110. B.F. De Veubeke (1976). The dynamics of flexible bodies. Int. J. Engrg. Sci., 14, 895-913.
111. B.F. De Veubeke (1974). Variational principles and the patch test. Int. J. Engrg. Sci., 8, 783-801.
112. Y. DeEskinazi, W. Soedel and T.Y. Yang (1975). Contact and inflated toroidal membrane with a flat surface as an approach to the tire deflection problem. J. Tire Sci Technol, ASME, 3, 43-61.
113. Y. DeEskinazi and T.Y. Yang, (1978). Displacement and stresses due to contact of a steel belted radial tire with a flat surface. J. Tire Sci Technol, ASME, 6, 48-70.
114. C.S. Desai and J.F. Abel (1972). Introduction to the finite element method a numerical for engineering analysis. Van Nostrand Reinhold Company, New York.
115. G.S. Dhatt (1970). An efficient triangular shells element. AIAA J., 8(11), 2100-2102.
116. G.S. Dhatt, L. Marcotte, Y. Matte and M. Talbot (1986). Two new discrete Kirchhoff plate shell elements. In Proc. 4th Symp. Numer. Meth. Engng, Atlanta, GA, 599-604.
117. L.H. Donnell (1934). A new theory for the buckling of thin cylinders under axial compression and bending. Trans. ASME-Aeronautical Div., 795-806.
118. R. Dungar, R.T. Severn and P.E. Taylor (1967). Vibration of plate and shell structures using triangular finite element. J. Strain Anal., 2, 73-83.
119. R. Dungar and R.T. Severn (1969). Triangular finite elements of variable thickness and their application of plate and shell problems. J. Strain Anal., 4, 10-21.
120. E.N. Dvorkin and K.J. Bathe (1984). A continuum mechanics based four-node shell element for general non-linear analysis. Engng. Comp., 1, 77-88.
121. N. El-Abbasi and S.A. Meguid (2000). A new shell element accounting for through-thickness deformation. Comput. Meth. Appl. Mech. Eng., 189, 841-862.
122. J.L. Ericksen C. Truesdell (1958). Exact theory of stress and strain in rods and shells. Archive for Rational Mechanics and Analysis. 1(4), 295-323.
123. A. Eriksson and C. Pacoste (2002). Element formulation and numerical techniques for stability problems in shells. Comp. Meth. Appl. Mech. Engng., 191, 3775-3810.
124. A. Ern (2004). Theory and practice of finite elements. Springer, New York.
125. L.J. Ernst (1981). A geometrically nonlinear finite element shell theory. Ph.D. Thesis, TU Delft.
126. R.M. Evan-Iwanpvski, H.M. Cheng and T.C. Loo (1962). Exprimental investigation of deformation and stability of spharical shells subjected to concetrated load at the apex. Proceeding of The Fourth U. S. National Congress of Applied Mechanics, pp. 563-575.
127. M. Fafard, G. Dhatt, and J.L. Batoz (1989). A new triangular discrete Kirchhoff plate/shell element with updated procedures. Int. J. Num. Meth. Engng., 31, 591-606.
128. C.A. Felippa (1966). Refined finite element analysis of linear and nonlinear two-dimensional structures. Report No. 66-22, Department of Civil Engineering, University of California, Nashville, Tennessee, 255-278.
129. C.A. Felippa (2003). A study of optimal membrane triangles with drilling freedom. Comp. Meth. Appl. Mech. Engng., 192, 2125-2168.
130. C.A. Felippa and S. Alexander (1992). Membrane triangles with corner drilling freedoms. III. Implementation and performance evaluation. Finite Element Anal. Des., 12, 203-239.
131. C.A. Felippa and P.G. Bergan (1987). A triangular bending element based on an energy-orthogonal free formulation. Comp. Meth. Appl. Mech. Engng., 61, 129-160.
132. C.A. Felippa and C. Militello (1992). Membrane triangles with corner drilling freedoms. II. The ANDES element. Finite Element Anal. Des., 12, 189-201.
133. F. Flores and E. Oñate, E. (1993). New shell elements for nonlinear structural analysis. Research Report, CIMNE, Barcelona.
134. F. Flores and E. Oñate (1993). A comparison of different finite elements based on Simo's shell theory, (in Spanish), Research Report, 33, CIMNE, Barcelona.
135. F. Flores and E. Oñate (1993). Dynamic analysis of shells and robs, (in Spanish), Research Report, 39, CIMNE, Barcelona.
136. F. Flores, E. Oñate, and F. Zarate (1995). New assumed strain triangles for non linear shell analysis. Computational Mechanics, 17, 107-114.
137. Y.C. Flugge (1973). Stresses In Shells, 2nd ed., Springer, Berlin.
138. B.M. Fraeijs de Veubeke (2001). Displacement and equilibrium model. In O.C. Zienkeiwicz, G. Hollister (Eds.), Stress Analysis, Wiley, London, 1965, pp. 145-197.
139. Int. J. Num. Meth. Engng., 52, 287-342 (Reprinted).
140. R. Frisch-Fay (1962). Flexible Bars. Butterworths: London.
141. W. Fung (1965). Foudation of Solid Mechanics. Prentice Hall, Englewood Cliffs, New Jersey.
142. J.E. Gal (2002). Triangular shell element for geometrically nonlinear analysis. Ph.D. Thesis, Faculty of Civil Engineering, Technion-I.I.T., Israel (in Hebrew).
143. R.H. Gallagher (1973). The finite element method in shell stability analysis. Computers & Structures, 3, 543-557.
144. R.H. Gallagher (1974). Finite element representations for thin shell instability analysis. In Buckling of Structures, (Edited by Budiansky), IUTAM Symposium, Cambridge, MA.
145. R.H. Gallagher (1975). Finite element analysis: Fundamentals. Prentice-Hall, New Jersey.
146. R.H. Gallagher (1977). Geometrically nonlinear shell analysis. In Proc. International Conference in nonlinear Solid and Structures Mechanics, Norway.
147. R.H. Gallagher (1989). Thirty years of finite element analysis - are there issue yet to be resolved?. Finite Element in Analysis and Design, 6, 1-8.
148. R.H. Gallagher, R.A. Gellatly, J. Padlog and R.H. Mallett (1967). A discrete element procedure for thin shell analysis. AIAA Journal, 5, 138-145.
149. R.H. Gallagher and J. Padlog (1963). Discrete element approach to structural stability analysis. AIAA Journal, 1(6), 1437-1439.
150. R.H. Gallagher and T.Y. Yang (1969). Elastic instability predictions for doubly curved shells. In Proc. Second Conference on Matrix Methods in Structural Mechanics, Wright-Patterson Air force Base, Dayton, OH.
151. H. Goldstein (1950). Classical Mechanics. Addison-Wesley, Tokyo.
152. C.S. Gran and T.Y. Yang (1978). NASTRAN and SAP IV applications of the seismic response of column-supported cooling towers. Computers and Structures, 8, 761-768.
153. C.S. Gran and T.Y. Yang (1980). Refined analysis of the seismic response of column-supported cooling towers. Computers and Structures, 11, 225-231.
154. H. Garnet and A. Pifko (1983). An efficient triangularplate bending finite element for crash simulation. Computers and Structures, 16, 371-379.
155. A.E. Green, R.J. Knops and N. Laws (1968). Large deformation, superimposed small deformations, and stability of elastic robs. Int. Journal of Solids and Structures, 4, 555-557.
156. B.E. Greene, D.R. Strome and R.C. Weikel (1961). Application of stiffness method to the analysis of shell structures. In Proc. Aviation Conference of ASME, Los Angeles, CA.
157. J.M. Greer and A.N. Palazotto (1997). Nonlinear finite element analysis of isotropic and composite shells by the total lagrangian decomposition scheme. Mech. Comp. Mater. Struct., 3, 241-271.
158. D.C. Hammerand and R.K. Kapania (2000). Geometrically nonlinear shell element for hygrothermorheologically simple linear viscoelastic composites. AIAA Journal, 38(12), 2305-2319.
159. J.C. Harris and P. Bartholomew (1989). Cubic triangular membrane element with drilling rotation freedom. RAE Technical Report 89042.
160. B.J. Hartz (1965). Matrix formulation of structural stability problems. Proceeding Journal of Engineering Structural Division, ASCE, 91, (ST6), Proc. Paper 4572.
161. C. Hausser and E. Ramm (1996). Efficient three-node shear deformable plate/shell elements-an almost hopeless undertaking. In Topping BHV, editor. Advances in Finite Element Technology. Edinburgh, Civil-Comp Press, 203-215.
162. L.R. Herrmann (1967). Finite element bending analysis of plates. J. Eng. Mech. Div. ASCE, 93 (EM5), 13-25.
163. L.R. Herrmann and D.M. Campbell (1968). A finite element analysis of thin shell. AIAA J., 6, 1842-1846S.
164. E. Hinton and D.R.J. Owen (1977). Finite element programming. Academic press, London.
165. P.T.S. Ho (1992). A comparison of performance of a flat faceted shell element and a degenerated superparametric shell element. Computers and Structures, 44(4), 895-904.
166. I. Holand and K. Bell (eds) (1972). Finite element methods in stress analysis. Tapir Forlag, Norway.
167. G. Horrigmoe and P.G. Bergan (1978). Nonlinear analysis of free-form shells by flat finite elements. Comp. Meth. Appl. Mech. Engng., 18, 11-35.
168. G. Horrigmoe (1976). Large displacement analysis of shells by hybrid stress finite element method. IASS World Congress on Space Enclosures, Montreal, 489-499.
169. G. Horrigmoe (1976). Nonlinear finite element models in solid mechanics. Dr. Ing. Thesis-Part 1, Div. Struct. Mech., Norwegian Ins. Tech., Trondheim, Report No. 76-2, Aug.
170. G. Horrigmoe (1977). Finite element instability analysis of free-form shells. Dr. ing. Thesis-Part 2, Div. Struct. Mech., Norwegian Ins. Tech., Trondheim, Report No. 77-2, May.
171. M.M. Hrabok and T.M. Hrudey (1984). A review and catalogue of plate bending finite elements. Computers and Structures, 19(3), 479-495.
172. K.M. Hsiao (1987). Nonlinear analysis of general shell structures by flat triangular shell element. Computers & Structures, 25, 665-675.
173. K.M. Hsiao and F.Y. Hou (1987). Nonlinear finite element analysis of elastic frames. Computers & Structures, 26, 693-701.
174. K.M. Hsiao and H.C. Hung (1989). Large-deflection analysis of shell structure by using corotational total lagrangian formulation. Comp. Meth. Appl. Mech. Engng., 73, 209-225.
175. K.H. Huebner and E.A. Thornton (1982). The finite element method for engineers. Wiley, New York.
176. T.J.R. Hughes (2000). The finite element method: linear static and dynamic finite element analysis. Dover Publication, Mineola N. Y.
177. T.J.R. Hughes and F. Brezzi (1989). On drilling degree of freedom. Comp. Meth. Appl. Mech. Engng., 72, 105-121.
178. T.J.R. Hughes and E. Hinton (eds.)(1986). Finite element methods for plate and shell structures. Element Technology, Vol. 1, Pineridge Press International, Swansea.
179. T.J.R. Hughes and E. Hinton (eds.)(1986). Finite element methods for plate and shell structures. Element Technology, Vol. 2, Pineridge Press International, Swansea.
180. T.J.R. Hughes and W.K. Lui (1981). Nonlinear finite element analysis of shells. Part I: Three-dimensional shells. Comp. Meth. Appl. Mech. Engng., 26, 331-362.
181. T.J.R. Hughes, A. Masud and I. Harary (1995a). Numerical assessment of some membrane elements with drilling degree of freedom. Computers and Structures, 55(2), 297-314.
182. T. J. R. Hughes, A. Masud and I. Harary (1995b). Dynamic analysis and drilling degree of freedom. Internat. J. Numer. Engrg., 38(19), 3193-3210.
183. A. Ibrahimbegovic (1997). Stress resultant geometrically exact shell theory for finite rotations and its finite element implementation. Appl. Mech. Rev., 50(4), 199-226.
184. A. Ibrahimbegovic (2000). Shell structures undergoing large rotations. In The Fourth International Colloquium on Computational of Shell & Spatial Structures, Chania-Crete, Greece.
185. A. Ibrahimbegovic and F. Frey (1994). Stress resultant geometrically nonlinear shell theory with drilling rotations- Part II: Computational aspects. Computer Method in Applied Mechanics and Engineering, 118, 285-308.
186. A. Ibrahimbegovic and F. Frey (1994). Stress resultant geometrically non-linear shell theory with drilling rotations. Part III: Linearized kinematics. Int J Num Meth Engng, 37, 3659-3683.
187. A. Ibrahimbegovic, R.L. Taylor and E. L. Wilson (1990). A robust quadrilateral membrane finite element with drilling degree of freedom. Int. J. Num. Meth. Engng., 30, 445-457.
188. A. Ibrahimbegovic and E.L. Wilson (1991). A unified formulation for triangular and quadrilateral flat shell finite element with six nodal degree of freedom. Communications in Applied Numerical Methods, 7, 1-9.
189. S. Idelsohn (1981). On the use of deep, shallow or flat shell finite elements for the analysis of thin shell structures. Comp. Meth. Appl. Mech. Engng., 26, 321-330.
190. B.M. Irons and S. Ahmad (1980). Techniques of finite elements. R. Horwood, Chichester (Eng).
191. B.M. Irons and A. Razzaquue (1972). Experience with the patch test for convergence of finite elements. R. Horwood, Chichester (Eng). Proc. Syrnp. On the Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, (Edited by A. K. Aziz), Baltimore, Academic Press, New York, 557-587.
192. M. Iura and Y. Suetake (2003). Accuracy of co-rotational formulation for 3-D Timoshenko's beam. Computer Modeling in Engineering and Sciences. 4, 249-258.
193. S. Jaamei (1986). Etude de différentes formulations lagrangiennes pour l'analyse non linéaire en grands déplacements et grandes rotations. Thèse de Doctorat, Université de Technologie de Compiegne.
194. P. Jetteur and F.A. Frey (1986). A four node marguerre element for nonlinear shell analysis. Eng. Comp., 3, 276-282.
195. C. Jeyachandrabose and J. Kirkhope (1985). An alternative explicit formulation for the DKT plate-bending element. Int. J. Num. Meth. Engng., 21, 1289-1293.
196. L. Jiang, W. Chernuka and N.G. Pegg (1992). A co-rotational, updated lagrangian formulation for geometrically nonlinear finite element. Proc. Int. Conf. Computational Methods in Engineering, A.A.O. Tay and K.Y. Lam (Eds.), World Scientific, Singapore.
197. L. Jiang, W. Chernuka and N.G. Pegg (1994A). A co-rotational, updated lagrangian formulation for geometrically nonlinear finite element analysis of shell structures. Finite Element in Analysis and Design, 18, 129-140.
198. L. Jiang and W. Chernuka (1994B). A simple four-noded co-rotational shell element for arbitrarily large rotations. Computers and Structures, 53(5), 1123-1132.
199. R.K. Kapania and P. Mohan (1996). Static, free vibration and thermal analysis of composite plates and shells using a fiat triangular shell element. Computational Mechanics, 17, 343-357.
200. K.K. Kapur and R. J. Hartz (1966). Stability of plate using the finite element method. Proceeding Journal of Engineering Mechanics Division, ASME, 92, (EM2).
201. S.W. Key and Z.E. Beisinger (1970). The analysis of thin shells by the finite element method. In Proc. IUTAM Symposium on High Speed Computing of Elastic Structures, Vol. 1, Univ. of Liege, Liege, Belgium.
202. J.H. Kim and Y.H. Kim (2002). A three-node CO ANS element for geometrically non-linear structural analysis. Comp. Meth. Appl. Mech. Engng., 191, 4035-4059.
203. N.F. Knight Jr. (1997). Raasch challenge for shell elements. AIAA Journal, 35(2), 375-381.
204. W.T. Koiter (1960). A consistent first approximation in the global theory of thin elastic shells. In The Theory of Thin Elastic Shells, W.T. Koiter (ed.), Proc. IUTAM Symposium, Delft 1959, North Holland Publ., Amsterdam, 12-33.
205. W. B. Krätzig (1993). Best nonlinear shell theory including transverse shearing and stretching. Comp. Meth. Appl. Mech. Engng., 103, 119-130.
206. W.B. Krätzig and E. Oñate (Eds.)(1990). Computational mechanics of nonlinear response of shells. Springer, Berlin.
207. P.S. Lee and K.J. Bathe (2002). On the asymptotic behavior of shell structures and the evaluation in finite element solutions. Int. J. Num. Method Engng., 80, 235-255.
208. P.S. Lee and K. J. Bathe (2005). Insight into finite element shell discretizations by use of the "basic shell mathematical model". Computers and Structures, 83, 69-90.
209. R. Leicester (1966). Large elastic deformations and snap-through of shallow doubly curved shells. Ph.D. Thesis, Department of Civil Engineering, University of Illinois.
210. R.H. Leicester (1968). Finite deformations of shallow shells. Proc.ASCE, 94 (EM 6), 1409-1423.
211. R. Levy, C.S. Chen, C.W. Lin and Y.B. Yang (2004). Geometric stiffness of membranes using symbolic algebra. Engineering Structures, 26, 759-767.
212. R. Levy and E. Gal (2001). Geometrically Nonlinear three-noded fiat triangular shell elements. Computers and Structures, 79, 2349-2355.
213. R. Levy and E. Gal (2003). Triangular shell element for large rotations analysis. AIAA Journal. 41(12), 2505-2508.
214. R. Levy, C.W. Lin, E. Gal and Y.B. Yang (2003). Geometric stiffness of
215. R. Levy and W.R. Spillers (2003). Analysis of Geometrically Nonlinear Structures. 2nd edition, Kluwer Academic Publishers, Dordtrecht.
216. S. Levy (1942). Bending of rectangular plates with large deflections. Tech. Notes, NACA, No. 846.
217. G.R. Liu and S.S. Quek (2003). The finite element method: A practical course. Butterworth-Heinemann, Oxford, Boston.
218. D.L. Logan (2002). A first course in the finite element method. Brooks/Cole, Pacific Grove, CA.
219. A.E.H. Love (1944). A treatise on the mathematical theory of elasticity. 4th ed., Dover, N.Y.,
220. R.H. MacNeal (1997). Perspective on finite elements for shell analysis. AIAA, Paper 97-1139, 2104-2113.
221. R.H. MacNeal and R.L. Harder (1985). A proposed standard set of problems to test finite element accuracy. Finite Elements in Analysis and Design, 1, 3-20.
222. R.H. MacNeal and R.L. Harder (1988). A refined four-noded membrane element with rotational degree of freedom. Computers & Structures, 28, 75-84.
223. E. Madenci and A. Barut (1994a). A free formulation flat shell element for non-linear analysis of thin composite structures. Int. J. Num. Method Engng., 37, 3825-3842.
224. E. Madenci and A. Barut (1994b). Pre- and post-buckling response of curved, thin, composite panels with cutouts under compression. Int. J. Num. Method Engng., 37, 1499-1510.
225. H.C. Martin (1965). On the derivation of stiffness matrices for the analysis of large deformations and stability problems. Proc. Conf. Matrix Meth. Struc. Mech., Air Force Institute of Technology, Wright-Patterson A.F.B., Ohio, 697-716.
226. H.C. Martin and G.F. Carey (1973). Introduction to finite element analysis: Theory and application. McGraw-Hill, New York.
227. C.E. Martinez, Y. Urthaler and R. Goncalves (1999). Nonlinear finite element analysis of submarine pipelines during intallation. Proceeding of the ASME pressure vessels and piping conference, 385, 187-194.
228. A. Masud and C.L. Tham (2000). Three-dimensional corotational framework for elasto-plastic analysis of multilayered composite shells. AIAA Journal, 38(12), 2320-2327.
229. A. Masud, C.L. Tham and W.K. Lui (2000). A 3D co-rotational formulation for geometrically nonlinear analysis of multi-layered composite shells. Computational Mechanics, 26(1), 1-12.
230. K. Mattiasson, A. Bengtsson and A. Samuelsson (1986). On the accuracy and efficiency of numerical algorithm for geometrically nonlinear structural analysis. In K.J. Bathe and W. Wunderlich (Eds.), Finite Element Method for Nonlinear Problems, Springer, Heidelberg, Germany, 3-23.
231. S.T. Mau, T.H.H. Pian and P. Tong (1973). Vibration analysis of laminated plates and shells by hybrid stress element. AIAA J., 11, 1450-1452.
232. J.L. Meek (2000). Nonlinear large displacement analysis of three dimensional structures-frames and shells. Proceeding IASS-IACM, Fourth International Colloquium on Computation of Shell & Spatial Structures, June 5-7, Chania, Crete, Greece.
233. J.L. Meek (2000). Structural mechanics and the natural mode method. A paper in honor of Professor John H. Argyris; the John Argyris contribution: Veni vidi vici. Proceeding IASS-IACM, Fourth International Colloquium on Computation of Shell & Spatial Structures, June 5-7, Chania, Crete, Greece.
234. J.L. Meek and H.S. Tan (1986). A faceted shell element with loof nodes. Int. J. Num. Meth. Engng., 23, 49-67.
235. J.L. Meek and H.S. Tan (1985). A discrete Kirchhoff plate bending element with loof nodes. Computers & Structures, 21, 1197-1212.
236. J.L. Meek and H.S. Tan (1986). Instability analysis of thin plates and arbitrary shells using faceted shell element with loof nodes. Comp. Meth. Appl. Mech. Engng., 57, 143-170.
237. J.L. Meek and S. Ristic (1997). Large displacement analysis of thin plates and shells using a flat facet finite element formulation. Comp. Meth. Appl. Mech. Engng., 145, 285-299.
238. J.L. Meek and Y. Wang (1998). Nonlinear static and dynamic analysis of shell structures with finite rotation. Comp. Meth. Appl. Mech. Engng., 162, 301-315.
239. J.F. Mescall (1965). Large deflections of spherical shells under concentrated loads. ASME Applied Mechanics Division, 936-938.
240. J.F. Mescall (1966). Numerical solution of nonlinear equations of shell of revolution. AIAA J., 4(11), 2041-2042.
241. R.V. Milford and W.C. Schnobrich (1986). Degenerate isoparametric finite elements using explicit integration. Int. J. Num. Meth. Engng., 23, 133-154.
242. A.K. Mohammed, B. Skallerud and J. Amdahl (2001). Simplified stress resultant plasticity on a geometrically nonlinear constant stress shell element. Computers and Structures, 79, 1723-1734.
243. P. Mohan and R.K. Kapania (1997). Geometrically nonlinear analysis of composite plates and shells using a flat triangular shell element. 38th AAIA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Kissimmee, FL, Paper 97-1233, 2347-2361.
244. R.J. Melosh (1965). A flat triangular shell element stiffness matrix. Proc. of the Conference on Matrix Methods in Structural Eng., Wright-Patterson Air Force Base, 503-514.
245. L.S.D. Morley (1971). On the constant-moment plate bending element. Journal of Strain Analysis, 6, 20-24.
246. L.S.D. Morley (1984). A facet-like shell theory. Internat. J. Numer. Engrg., 22(11/12), 1315-1327.
247. L.S.D. Morley and M.P. Mould (1987). The role of bending in the finite element analysis of thin shells. Finite Elements in Analysis and Design, 3, 213-240.
248. L.S.D. Morley (1991). Geometrically nonlinear constant moment triangle which passes the von Kármán patch test. Inter. J. Numer. Engrg., 31, 241-263.
249. S.K. Naboulsi and A.N. Palazotto (2003). Non-linear static-dynamic finite element formulation for composite shells. International Journal of Non-Linear Mechanics, 38, 87-110.
250. P.M. Naghdi (1972). The theory of shells and plates, mechanics of solids II. In Truesdel, C. (Ed.), Vol. Via/2, 425-640; Encyclopedia of Physics, Flügge, S. (Ed.), Springer, Berlin/Heildelberg/New York.
251. J.C. Nagtegaal and J.G. Slater (1981). A simple non-compatible thin shell element based on discrete Kirchhoff theory. In Nonlinear Finite Element Analysis of plates and Shells, J.R. Hughes, A Pifco and A. Jay (Eds.), ASME AMD, 48, 167-192.
252. B. Noble (1969). Applied Linear Algebra. Prentice-Hall, New Jersey.
253. A.K. Noor (1990). Bibliography of monographs and surveys on shells. Applied Mechanics Review, 43, 199-229.
254. A.K. Noor, T. Belyschko and J.K. Simo (Eds.) (1989). Analytical and Computational Models of Shells. CED-Vol3, ASME, New York.
255. A.K. Noor and H. G. McConb Jr. (Eds.) (1978). Trend in computerized structural analysis and synthesis. Pergamon press, New York.
256. D.H. Noori and G. de Vries (1973). The finite element method: Fundamentals and applications. Academic Press, New York.
257. B. Noor-Omid and C.C. Rankin (1991). Finite rotation analysis and consistent linearization using projectors. Comp. Meth. Appl. Mech. Engng., 93, 353-384.
258. M.K. Nygård (1986). The free formulation for nonlinear finite elements with applications to shells. Ph.D. Thesis, Division of Structural Mechanics, NTH, Trondheim, Norway.
259. M.K. Nygård and P.G. Bergan (1989). Advances in treating large rotations for nonlinear problems. State of the Art Survey on Computational Mechanics, A.K. Noor and J.T. Oden (Eds.), American Society of Mechanical Engineering, New York, 305-333.
260. J.T. Oden (1972). Finite elements of nonlinear continua. McGraw-HilI, New York.
261. J.T. Oden and J.N. Reddy (1976). An introduction to the mathematical theory of Finite elements. Wlley, New York.
262. J.T. Oden (1967). Numerical formulation of non-linear elasticity problems. Proceeding Journal of Engineering Structural Division, ASCE, 93,(ST3), Proc. Paper 5290.
263. J.T. Oden (1966). Calculation of geometric stiffness matrices for complex structures. AIAA J., 4(8), 1480-1482.
264. J. Oliver and E. Oñate (1984). A total lagrangian formulation for the geometrically nonlinear analysis of structures using finite element. Part I. two-dimensional problems: shell and plate structures. International Journal for Numerical Methods in Engineering, 20, 2253-2281.
265. M.D. Olson and T.W. Bearden (1979). A simple flat triangular shell element revisited. International Journal for Numerical Methods in Engineering, 14, 51-68.
266. E. Oñate, M. Cervera and F. Zarate (1995). A three node triangular shell element with translational degrees of freedom. Research Report CIMNE, Barcelona.
267. E. Oñate, E. Hinton and N. Glover (1978). Techniques for improving the performance of Ahmad shell elements. C/R/313/78, Department of Civil Engineering, University of Wales, Swansea.
268. E. Oñate, J. Pariaux and A. Samuelsson (eds.)(1991). The finite element method in the 1990's. A book dedicated to O.C. Zienkiewicz. CIMNE, Spain.
269. E. Oñate, J. Rejek and C.G. Garino (1995). NUMISTAMP: A research for assessment of finiteelement models for stamping processes. Journal of Materials Processing Technology, 50, 17-38.
270. E. Oñate, F. Zárate (2000). Rotation-free triangular plate and shell elements. International Journal for Numerical Methods in Engineering, 47, 557-603.
271. E. Oñate, F. Zárate and F. Flores (1994). A simple triangular element for thick and thin plate and shell analysis. International Journal for Numerical Methods in Engineering, 37, 2569-2582.
272. S. Oral and A. Barut (1991). A shear-flexible facet shell element for large deflection and instability analysis. Comp. Meth. Appl. Mech. Engng., 93, 415-431.
273. C. Oran (1973). Tangent stiffness in space frames. J. Eng. Mech. Div. ASCE, 99, 987-1001.
274. C. Oran and A. Kassimali (1997). Large deformations of frames structures under static and dynamic loads. Comp. Struc., 6, 539-547.
275. D.R.J. Owen and E. Hinton (1980). Finite element in plasticity: theory and practice. Pineridge Press Limited, Swansea; U.K..
276. C. Pacoste (1998). Co-rotational flat facet triangular elements for shell instability analyses. Comp. Meth. Appl. Mech. Engng., 156, 75-110.
277. P.F. Pai and M.J. Schulz (2000). Modeling of highly flexible structures. J. Spacecraft, 37(3), 419-421.
278. P.F. Pai and A.N. Palazotto (1995). Nonlinear displacement-based finite-element analysis of composite shells-a new total Lagrangian formulation. Int. J. Solids Structures, 32(20), 3047-3073.
279. S.W. Papenfuss (1959). Lateral plate deflection by stiffness matrix methods with application to a Marquee. M.S. Thesis, Department of Civil Engineering, University of Washington, Seattle.
280. H. Parisch (1978). Geometrical nonlinear analysis of shells. Comp. Meth. Appl. Mech. Engrg., 14, 159-178.
281. H. Parisch (1981). Large displacements of shells including material nonlinearities. Comp. Meth. Appl. Mech. Engng., 27, 183-214.
282. X. Peng and M.A. Crisfield (1992). A consistent co-rotational formulation for shell using the constant stress/constant moment triangle. Int. J. Num. Meth. Engng., 35, 1829-1847.
283. A. Pica and R.D. Wood (1980). Post buckling behavior of thin plates and shells using mindlin shallow shell formulation. Computers and Structures, 12, 759-768.
284. A. Pica, R.D. Wood and E. Hinton (1980). Finite element analysis of geometrically nonlinear plate behavior using a Mindlin formulation. Computers and Structures, 11, 203-215.
285. W. Pietraszkiewicz (1977). Introduction to the nonlinear theory of shells. Mitteilungen aus dem institute für Mechanik, Ruhr Universität, Bochum.
286. W. Pietraszkiewicz (1984). Lagrangian description and incremental formulation in the nonlinear theory of thin shells. Int. J. Nonlin. Mech., 19, 115-140.
287. W. Pietraszkiewicz and J. Badur (1983). Finite rotations in the description of continuum deformation. Int. J. Engrg. Sci., 21(9), 1097-1115.
288. R. Piltner and R. L. Taylor (2000). Triangular finite elements with rotational degree of freedom and enhanced strain modes. Computers and Structures, 75, 361-368.
289. P.N. Poulsen and L. Damkilde (1996). A flat triangular shell element with loof nodes. Int. J. Num. Meth. Engng., 39, 3867-3887.
290. E. Providas and M.A. Kattis (2000). An assessment of two fundamental flat triangular shell elements with drilling rotations. Computers and Structures, 77, 129-139.
291. E. Providas and M.A. Kattis (1999). A simple finite element model for the geometrically nonlinear analysis of thin shells. Computational Mechanics J., 24, 127-137.
292. S.S. Rao (1989). The finite element in engineering. Pergamon, Oxford (UK).
293. E. Ramm (1977). A plate/shell element for large deflection and rotations. In Bathe, K.J., Oden, J.T., and Wunderlich, W., (Eds.), Formulations and Computational Algorithms in Finite Element Analysis, M.I.T. Press, Cambridge, MA.
294. C.C. Rankin (1998). On choise of best possible corotational element frame. In Modeling and simulation Based Engineering, Atluri S.N., O'Donoghue P.E. (Eds.). Vol. 1, Tech Science Press: Forsyth, GA, 772-777.
295. C.C. Rankin and F.A. Brogan (1986). An element independent corotational procedure for the treatment of large rotations. Journal of Pressure Vessel Technology, 108, 165-174.
296. C.C. Rankin and B. Noor-Omid (1988). The use of projectors to improve finite element performance. Computers and Structures, 30, 257-267.
297. J.N. Reddy (1993). An introduction to the finite element method. McGraw-Hill, New York.
298. J.N. Reddy (2004). An introduction to nonlinear finite element Analysis. Oxford University press.
299. E. Reissner (1946). Stresses and small displacements of shallow spherical shells. Journal of Mathematics and Physics, 25, 80-85, 279-300.
300. E. Reissner (1950). On axisymmetric deformation of thin shells of revolution. Proc. Symp. in Appl. Math., 3, 32.
301. J. Rejek, J. Jovicevic and E. Oñate (1996). Industrial applications of sheet stamping simulation using new finite-element models. Journal of Materials Processing Technology, 60, 243-247.
302. E. Riks (1979). An incremental approach to the solution of snapping and buckling problems. Int. J. Solids Structures, 15, 529-551.
303. J. Robinson (1973). Integrated theory of finite element methods. J. Wiley, London.
304. O. Rodrigues (1840). Des lois géométriques qui régissent les deplacements d'un systéme solide dans l'espace et de la variation des coordinnées provenant de ces déplacements considéres indépendment des causes qui peuvent les produire les produire. J. Math. Pures. Appl., 5, 380-440.
305. A.B. Sabir (1985). A rectangular and a triangular plane elasticity element with drilling degree of freedom. In Proc. 2nd Int. Conf. on Variational Methods in Engineering, Springer-Verlag, Berlin, 17-25.
306. A.B. Sabir and M.S. Djoudi (1995). Shallow shell finite element for the large deflection geometrically nonlinear analysis of shells and plates. Thin Wall Structures, 21, 253-267.
307. A.B. Sabir and A.C. Lock (1973). The application of finite elements to the large deflection geometrically nonlinear behavior of cylindrical shells. Variational Methods in Engineering, C.A. Brebia and H. Tottenham (Eds.), Southampton Univ. press, Southampton, 7/66-7/75.
308. A. Samanta and M. Mukhopadhyay (1999). Finite element large deflection static analysis of shallow and deep stiffened shells. Finite Elementsin Analysis and Design, 33, 187-208.
309. G. Sander and P. Becker (1975). Delinquent finite Elements for Shell idealization. In Proc. World Congress on Finite Element Method in Structural Mechanics, Vol. 2, Bournemouth, U.K..
310. J.L. Sanders (1959). An improved first-approximation theory for thin shells. NASA Tech. Report R-24.
311. J.L. Sanders (1963). Nonlinear theories for thin shells. Quarterly of Applied Mathematics, 21, 21-36.
312. H. Schoop (1989) A simple nonlinear flat element for large displacement structures. Computers and Structures, 32(2), 379-385.
313. H. Schoop (1986A). Oberflächennorientierte endlicher Verdchiebungen", Ing. Arch., 56, 427-437.
314. H. Schoop (1986B). Postbuckling and snap through of thin elastic shells with a double surface theory. In Postbuckling of Elastic Structures, J. Szabó (Ed.), 321-337, Elsevier, Amsterdam.
315. A.C. Scordelis and K.S. Lo (1964). Computer analysis of cylindrical shells. Journal of The American Concrete Institute, 539-560.
316. L.J. Segerlind (1984). Applied finite element analysis. Wiley, New York.
317. J.C. Simo and D.D. Fox (1989A). On a stress resultant geometrically exact shell model. Part I: formulation and optimal parameterization. Computer Method in Applied Mechanics and Engineering, 72, 267-304.
318. J.C. Simo and D.D. Fox (1989B). On a stress resultant geometrically exact shell model Part II: the linear theory; computational aspects. Computer Method in Applied Mechanics and Engineering, 73, 53-92.
319. J.C. Simo, D.D. Fox and M.S. Rifai (1990a). On a stress resultant geometrically exact shell model. Part III: computational aspects of the nonlinear theory. Computer Method in Applied Mechanics and Engineering, 79, 21-70.
320. J.C. Simo, M.S. Rifai and D.D. Fox (1990b). On a stress resultant geometrically exact shell model. Part IV: variable thickness shells with through the thickness stretching. Computer Method in Applied Mechanics and Engineering, 81, 91-126.
321. J.C. Simo and J.G. Kennedy (1992). On a stress resultant geometrically exact shell model. Part V: nonlinear plasticity: formulation and integration algorithms. Computer Method in Applied Mechanics and Engineering, 96, 133-171.
322. W.R. Spillers, A. Saadeghvaziri and A. Luke (1993). An example of three-dimensional frame buckling. Computers and Structures, 47, 483-486.
323. H. Stolarsky and T. Belytschko (1983). Shear and membrane locking in curved c0 elements. Computer Method in Applied Mechanics and Engineering, 41, 279-296.
324. G. Strang (1972). Variational crimes in the finite element method. R. Horwood, Chichester (Eng). Proc. Symp. On the Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, A.K. Aziz (Ed.), Baltimore, Academic Press, New York, 689-710.
325. G. Strang and G.J. Fix (1973). An analysis of the finite element method. Prentice-Hall, New Jersey.
326. J.A. Stricklin, W. Haisler, P. Tisdale and R. Gunderson (1969). A rapidly converging triangular plate element. AIAA J., 7(1), 180-181.
327. J.A. Stricklin and J.E. Martinez (1969). Dynamic buckling of clamped spherical caps under step pressure loading. AIAA Journal, 7, 1212-1213.
328. K.S. Surana (1983). Geometrically nonlinear formulations for the curved shell elements. Int. J. Num. Meth. Engng., 19, 353-386.
329. B. Szabo and I. Babuska (1991). Finite element analysis. Wiley, New York.
330. L.A. Taber (1982). Large deflection of a fluid-filled shell under a point load. J. Appl. Mech., 49, 121-128.
331. M. Talbot (1986). Comparaison de deux élément de coques triangulires plats utilisant une formulation lagrangiennes actualisée. Master Thesis, Civil Engineering Department, Laval University, Quebec.
332. R.T. Taylor and J.C. Simo (1985). Bending and membrane elements for analysis of thick and thin shells. NUMETA 85 Numerical Methods in Engineering: Theory and Applications, Pande G.N. and Middelton J. (Eds.), Rotterdam, 587-591.
333. A. Tessler and T.J.R. Hughes (1985). A three-node Mindlin plate element with improved transverse shear. Comp. Meth. Appl. Mech. Engng., 50, 71-101.
334. G.A. Thurston (1961). A numerical solution of nonlinear equations of axisymmetrical bending of shallow spherical shells. Journal of Applied Mechanics, ASME, 83, 557-568.
335. G.A. Thurston (1969). Continuation of Newton's method through bifurcation points. Journal of Applied Mechanics, ASME, 425-430.
336. H.S. Tsien (1942). A theory for the buckling of thin shells. J. Aeronautical Sciences, 9, 373-384.
337. M.J. Turner, R.W. Clough, H.C. Martin and L.J. Topp (1956). Stiffness and deflection analysis of complex structures. J. Aeronaut. Sci., 23, 805-824.
338. S. Utku and R.J. Melosh (1967). Behavior of triangular shell element stiffness matrices associated with polyhedron deflection distributions. AIAA paper No. 67-114, AIAA 5th Aerospace Sciences Meeting, New York.
339. T. von Kármán (1910), Festigkeits probleme im maschinebau. In Encyklopadie der Mathematischen Wissenschaften, Vol. IV/4, c, Leipzig, 311-385.
340. T. von Kármán and H.S. Tsien (1941). The buckling of thin cylindrical shells under axial compression. J. Aeronautical Sciences, 8, 302-312.
341. F. Van Keulen and J. Booij (1996). Refined consistent formulation of a curved triangular finite rotation shell element. Int. J. Num. Meth. Engng., 39, 2803-2820.
342. F. Van Keulen, A. Bout and L. Ernst (1993). Nonlinear thin shell analysis using a curved triangular element. Comput. Methods Appl. Mech. Engng., 104, 315-343.
343. W.W. Wall, M. Gee and E. Ramm (2000). The challenge of a three-dimensional shell formulation-the conditioning problem. The Fourth International Colloquium on Computational of Shell and Spatial Structures, Chania-Crete, Greece.
344. L. Wang and G. Thierauf (1999). Finite rotations in non-linear analysis and design of elastic shells. The Fifth International Conference on Computational Structures Technology, Oxford, U.K., 223-232.
345. L. Wang and G. Thierauf (2001). Finite rotations in non-linear analysis of elastic shells. Computers and Structures, 79, 2357-2367.
346. Jr. W. Weaver and P.C. Johnson (1984). Finite element for structural analysis. Prentice-Hall, Englewood Cliffs.
347. G. Wempner (1969). Finite Elements, Finite rotations and small strains of flexible shells. Int. J. Solids Struct., 5, 117-153.
348. G. Wempner (1989). Mechanics and finite element of shells. Applied Mechanics Review, ASME, 42, 129-142.
349. J.R. Whiteman (editor) (1973). The mathematics of finite elements and applications. Academic press, New York.
350. J.R. Whiteman (editor) (1973). The mathematics of finite elements and applications II. Academic press, New York.
351. F. Wright (2001). Computing with MAPLE. Chapman & Hall/CRC, Boca Raton.
352. H.T.Y. Yang (1969). A finite element formulation for stability analysis of doubly curved thin shell structures. PH.D. Thesis, Cornell University.
353. H.T.Y. Yang (1975). Finite Element Structural Analysis. Prentice Hall, Englewood Cliffs, N.J.
354. H.T.Y. Yang, S. Saigal and D.G. Liaw (1990). Advances of thin shell finite elements and some applications-version I. Computers and Structures, 35, 481-504.
355. H.T.Y. Yang, S. Saigal, A. Masud and R.K. Kapania (2000). A survey of recent shell finite element. Int. J. Num. Meth. Engng., 47, 101-127.
356. Y.B. Yang and J.T. Chang (1998). Derivation of a geometric nonlinear triangular plate element by rigid-body concept. Bulletin of The International Association for Shell and Spatial Structures, 39, n. 127, 77-84.
357. Y.B. Yang, J.T. Chang and J.D. Yau (1999). A simple nonlinear analysis plate element and strategies of computation for nonlinear analysis. Comput. Methods Appl. Mech. Engng., 178, 307-321.
358. Y.B. Yang and S.R. Kuo (1994). Theory and Analysis of Nonlinear Frame Structures. Prentice Hall, Singapore.
359. Y.B. Yang and M.S. Shieh (1990). Solution Method for Nonlinear Problems with Multiple Critical Points. AIAA Journal, 28, 2110-2116.
360. Y. Yoshida (1974). A hybrid stress element for thin shell analysis. In Proc. International Conference on Finite Element Method in Engineering. Univ. of N.S.W., Australia.
361. O.C. Zienkiewicz (1977). The finite element method. 3rd edition, McGraw-Hill, New Jersey.
362. O.C. Zienkiewicz and Y.K. Cheung (1965). Finite element procedures in the solution of plate and shell problems. In Stress Analysis, Zienkiewicz, O.C. and Holister G.S. (Eds.), Ch. 8, John Weley, New York.
363. O.C. Zienkiewicz and K. Morgan (1983). Finite element and approximation. Wiley, New York.
364. O.C. Zienkiewicz, C.J. Parikh and I.P. King (1968). Arch Dam Analysis by a Linear Finite Element Shell Solution Program. In Proc. Symposium on Arch Dams, I.C.E., London, 19-22.
365. O.C. Zienkiewicz and R.L. Taylor (1989). The Finite element method Vol. I. IV Edition, McGraw-Hill, New Jersey.
366. O.C. Zienkiewicz and R.L. Taylor (1991). The Finite element method Vol. II. IV Edition, McGraw-Hill, New Jersey.
367. O.C. Zienkiewicz and R.L. Taylor (2000). The Finite element method. V Edition, Batterworth Heinemann, Oxford (UK).
368. O.C. Zienkiewicz, R.L. Taylor and J.M. Too (1971). Reduced Integration techniques in general analysis of plates and shells. Int. J. Num. Meth. Engng., 3, 275-290.
369. O.C. Zienkiewicz, R.L. Taylor, P. Papadopoulos and E. Oñate (1990). Plate bending elements with discrete constrains: new triangular element. Int. J. Num. Meth. Engng., 35, 505-522.