Natural Element Method for the Simulation of Structures and Processes

Natural Element Method for the Simulation of Structures and Processes

Volumn , Issue , 2013, Pages

  Chinesta, Francisco ^a   Cescotto, Serge ^a   Cueto, Elías ^a   Lorong, Philippe ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84891583803     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9781118616901     Document Type: Book

References (169)

1. Alfaro I., Bel D., Cueto E., Doblaré M., Chinesta F., "Three-dimensional simulation of aluminium extrusion by the alpha-shape based natural element method", Computer Methods in Applied Mechanics and Engineering, vol. 195, no. 33-36, 4269-4286, 2006.
2. Alfaro I., Yvonnet J., Cueto E., Chinesta F., Doblaré M., "Meshless methods with application to metal forming", Computer Methods in Applied Mechanics and Engineering, vol. 195, no. 48-49, 6661-6675, 2006.
3. Alfaro I., Yvonnet J., Chinesta F., Cueto E., "A study on the performance of natural neighbour-based Galerkin methods", International Journal of Numerical Methods ngineering, vol. 7, no. 12, 1436-1465, 2007.
4. Ammar A., Mokdad B., Chinesta F., Keunings R., "A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids", Journal of Non-Newtonian Fluid Mechanics, vol. 139, 153-176, 2006.
5. Ammar A., Ryckelynck D., Chinesta F., Keunings R., "On the reduction of kinetic theory models related to finitely extensible dumbbells", Journal of Non-Newtonian Fluid Mechanics, vol. 134, 136-147, 2006.
6. Ammar A., Mokdad B., Chinesta F., Keunings R., "A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. Part II: Transient simulation using space-time separated representation", Journal of Non-Newtonian Fluid Mechanics, vol. 144, 98-121, 2007.
7. Arnold D., Brezzi F., Fortin M., "A stable finite element for the Stokes equations", Calcolo, vol. 21, 337-344, 1984.
8. Atluri S., Kim H.G., Cho J.Y., "A critical assessment of the truly meshless local Petrov-Galerkin and local boundary integral equation methods", Computational Mechanics, vol. 24, 348-372, 1999.
9. Atluri S., Zhu T., "New concepts in meshless methods", International Journal for Numerical Methods in Engineering, vol. 47, 537-556, 2000.
10. Atzema E., Huétink J., "Finite element analysis of forward/backward extrusion using ALE techniques", SHEN S., DAWSON P., (Eds.), Proc. Numiform 95 Conference, Ithaca, p. 383-388, 1995.
11. Baaijens F., An iterative solver for the DEVSS/DG method with application to smooth and non-smooth flows of the upper convected Maxwell fluid", Journal of Non-Newtonian Fluid Mechanics, vol. 75, p. 119-138, 1998.
12. Babuška I., "The finite element method with Lagrange multipliers", Numerische Mathematik, vol. 20, 179-192, 1973.
13. Babuška I., Rheinboldt W., "Adaptive approaches and reliability estimations in finite element analysis", Computer Methods in Applied Mechanics and Engineering, vol. 17/18, p. 519-540, 1979.
14. Babuška I., Melenk J.M., "The partition of unity finite element method: Basic theory and applications", Computer Methods in Applied Mechanics and Engineering, vol. 4, 289-314, 1996.
15. Babuška I., Melenk J.M., "The partition of unity method", International Journal for Numerical Methods in Engineering, vol. 40, 727-758, 1997.
16. Babuška I., Banerjee U., Osborn J.E., "Survey of meshless and generalized finite element methods: A unified approach", Acta Numerica, vol. 12, 1-125, 2003.
17. Banerjee B., Taylor Impact Tests: Detailed Report, Report no. C-SAFE-CDIR-05-001. Department of Mechanical Engineering, University of Utah, Salt Lake City, November 2005.
18. Barry J., An W.C., "Duality of constrained Voronoï diagrams and delaunay triangulations", Algorithmica, vol. 9, 142-155, 1993.
19. Bathe K.J., Finite Element Procedures, Prentice-Hall, Englewood Cliffs, 1996.
20. Belytschko T., Lu Y.Y., Gu L., "Element-free Galerkin methods", International Journal for Numerical Methods in Engineering, vol. 37, 229-256, 1994.
21. Belikov V.V., Ivanov V.D., Kontorovich V.K., Korytnik S.A., Semenov .Y., "The non-Sibsonian interpolation: A new method of interpolation of the values of a function on an arbitrary set of points", Computational Mathematics and Mathematical Physics, vol. 37, no. 1, 9-15, 1997.
22. Belytschko T., Krongauz Y., Organ D., Fleming M., Krysl P., "Meshless methods: An overview and recent developments", Computer Methods in Applied Mechanics and Engineering, vol. 139, 3-47, 1998.
23. Belytschko T., Liu W.K., Singer M., "On adaptivity and error criteria for meshless methods", Advances in Adaptive Computational Methods in Mechanics, vol. 47, 217-228, 1998.
24. Belytschko T., Parimi C., Moës N., Sukumar N., Usui S., "Structured extended finite element methods for solids defined by implicit surfaces", International Journal for Numerical Methods in Engineering, vol. 56, 609-635, 2003.
25. Bertin E., Diagrammes de Voronoï 2D et 3D: applications en analyse d'images, PhD Thesis, Joseph Fourier University-Grenoble 1, TIMC-Institut IMAG, January 1994.
26. Boissonnat J.-D., Cazals F., "Smooth surface reconstruction via natural neighbour interpolation of distance functions", Computational Geometry, vol. 22, 185-203, 2002.
27. Bonet J., Lok T.-S.L., "Variational and momentum preservation aspects of smooth particle hydrodynamic formulations", Computer Methods in Applied Mechanics and Engineering, vol. 180, 97-115, 1999.
28. Bonet J., Kulasegaram S., "Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations", International Journal for Numerical Methods in Engineering, vol. 47, 1189-1214, 2000.
29. Bonito A., Picasso M., Laso M., "Numerical simulation of 3D viscoelastic flows with free surfaces", Journal of Computational Physics, vol. 215, 691-716, 2006.
30. Bowyer A., "Computing Dirichlet tesselations", The Computer Journal, vol. 24, no. 2, 162-166, 1981.
31. Brandes E., Smithells Metals Reference Book, Butterworths and Co. Ltd, London, 1983.
32. Braun J., Sambridge M., "A numerical method for solving partial differential equations on highly irregular evolving grids", Nature, vol. 376, 655-660, 1995.
33. Braun J., Sambridge M., Mcqueen H., "Geophysical parametrization and interpolation of irregular data using natural neighbours", Geophysical Journal International, vol. 122, 837-857, 1995.
34. Brezzi F., "On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers", Revue Française d'Automatique Informatique Recherche Opérationelle, Analyse Numérique, vol. 8, 129-151, 1974.
35. Büeler B., Enge A., Fukuda K., "Exact volume computation for polytopes: A practical study", Polytopes-Combinatorics and Computation, vol. 29, 131-154, 2000.
36. Buffa G., Hu J., Shivpuri R., Fratini L., "A continuum based FEM model for friction stir welding-model development", Materials Science and Engineering A, vol. 419, 389-396, 2006.
37. Buffa G., Hu J., Shivpuri R., Fratini L., "Design of the friction stir welding tool using the continuum based FEM model", Materials Science and Engineering A, vol. 419, 381-388, 2006.
38. Cai Y., Zhu H., "A local search algorithm for natural neighbours in the natural element method", International Journal of Solids and Structures, vol. 42, 6059-6070, 2005.
39. Carslaw H., Jaeger J., Conduction of Heat in Solids, Clarendon Press, Oxford, 1959.
40. Cescotto S., Li X., A natural neighbour method for linear elastic problems based on Fraeijs de Veubeke variational principle, Report AG2006-09/01, University of Liège, ArGEnCo Department, 2006.
41. Cescotto S., Li X., "A natural neighbour method for linear elastic problems based on Fraeijs de Veubeke variational principle", International Journal for Numerical Methods in Engineering, vol. 71, 1081-1101, 2007.
42. Cescotto S., Li X., Duchene L., "A natural neighbor method based on Fraeijs de Veubeke variational principle for elastoplasticity and fracture mechanics", Journal of Engineering Materials and Technology, vol. 130, 2008.
43. Chapelle D., Bathe K.J., "The inf-sup test", Computers and Structures, vol. 47, no. 4/5, p. 537-545, 1993.
44. Chen J.-S., Wu C.-T., Yoon S., You Y., "A stabilized conforming nodal integration for Galerkin mesh-free methods", International Journal for Numerical Methods in Engineering, vol. 50, 435-466, 2001.
45. Chenot J.-L., Massoni E., "Finite element modelling and control of new metal forming processes", International Journal of Machine Tools and Manufacture, vol. 46, 1194-1200, 2006.
46. Chinesta F., Cueto E., Ryckelynck D., Ammar A., "α-NEM and model reduction: Two new and powerful numerical techniques to describe flows involving short fibers suspensions", Revue Européenne des Elément Finis, vol. 14, no. 6-7, 903-923, 2005.
47. Chung H.-J., Belytschko T., "An error estimate in the EFG method", Computational Mechanics, vol. 21, 91-100, 1998.
48. Cueto E., Doblaré M., Gracia L., "Imposing essential boundary conditions in the natural element method by means of density-scaled α-shapes", International Journal for Numerical Methods in Engineering, vol. 49, no. 4, 519-546, 2000.
49. Cueto E., Martínez M.A., Doblaré M., "El método de los Elementos Naturales en Elasticidad compresible y cuasi-incompresible", Boletín Técnico del Instituto de Materiales y Modelos Estructurales, Central University of Venezuela (in Spanish), vol. 39, 2001.
50. Cueto E., Calvo B., Doblaré M., "Modeling three-dimensional piece-wise homogeneous domains using the α-shape based natural element method", International Journal for Numerical Methods in Engineering, vol. 54, 871-897, 2002.
51. Cueto E., Sukumar N., Calvo B., Martínez M.A., Cegoñino J., Doblaré M., "Overview and recent advances in natural neighbour Galerkin methods", Archives of Computational Methods in Engineering, vol. 10, no. 4, 307-384, 2003.
52. De S., Bathe K.J., "Towards an efficient meshless computational technique: The method of finite spheres", Engineering Computations, vol. 18, 170-192, 2001.
53. Delaunay B., "Sur la Sphère Vide. A la memoire de Georges Voronoï", Izvestia Akademii Nauk SSSR, Otdelenie Matematicheskii i Estestvennyka Nauk, vol. 7, 793-800, 1934.
54. Dirichlet G.L., "Über die Reduktion der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen ", Journal für die Reine und Angewandte Mathematik, vol. 40, 209-227, 1850.
55. Dolbow J., Belytschko T., "Numerical integration of the Galerkin weak form in meshfree methods", Computational Mechanics, vol. 23, 219-230, 1999.
56. Duarte C.A.M., Oden J.T., "An h-p adaptive method using clouds", Computer Methods in Applied Mechanics and Engineering, vol. 139, 237-262, 1996.
57. Duarte C.A.M., Babuška I., Oden J.T., "Generalized finite element methods for three-dimensional structural mechanics problems", Computers and Structures, vol. 77, no. 2, 215-232, 2000.
58. Edelsbrunner H., Mücke E., "Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms", ACM Transactions on Graphics, vol. 9, no. 1, 66-104, 1990.
59. Edelsbrunner H., Mücke E., "Three dimensional alpha shapes", ACM Transactions on Graphics, vol. 13, 43-72, 1994.
60. Enge A., Benno, Fukuda K., VINCI Version 1.0.5, Computing Volumes of Convex Polytopes, July 2003.
61. Farin G., Curves and Surfaces for CAGD, Morgan Kaufmann, San Francisco, CA, 2002.
62. Farin G., Splines over iterated Voronoï diagrams, Report no., Arizona State University, 2003.
63. Felippa C.A., "On the original publication of the general canonical functional of linear elasticity", Journal of Applied Mechanics, vol. 67, 217-219, 2000.
64. Fernández-Méndez S., Huerta A., Belytschko T., "Meshless methods", Encyclopaedia of Computational Mechanics, on-line edition, DOI: 10.1002/0470091355, 2004.
65. Fried I., "Influence of Poisson's ration on the condition of the finite element stiffness matrix", International Journal of Solids and Structures, vol. 10, 323-329, 1973.
66. Géradin M., Rixen D., Théorie des vibrations: application à la dynamique des structures, Masson, 1996.
67. Gigras P.G., Khomami B., "Adaptive configuration fields: A new multiscale simulation technique for reptation-based models with a stochastic strain measure and local variations of life span distribution", Journal of Non-Newtonian Fluid Mechanics, vol. 108, no. 1-3, 99-122, 2002.
68. Gonzalez D., Cueto E., Martinez M.A., Doblare M., "Numerical integration in natural neighbour Galerkin methods", International Journal for Numerical Methods in Engineering, vol. 60, no. 12, 2077-2104, 2004.
69. González D., Cueto E., Doblaré M., "Volumetric locking in natural neighbour Galerkin methods", International Journal for Numerical Methods in Engineering, vol. 61, no. 4, 611-632, 2004.
70. González D., Cueto E., Chinesta F., Doblaré M., "A natural element updated Lagrangian strategy for free-surface fluid dynamics", Journal of Computational Physics, vol. 223, no. 1, 127-150, 2007.
71. González D., Cueto E., Doblaré M., "Higher-order natural element methods: Towards an isogeometric meshless method", International Journal for Numerical Methods in Engineering, vol. 74, no. 13, 1928-1954, 2007.
72. Gonzalez D., Cueto E., Doblare M., "Higher-order natural element methods: Towards an isogeometric meshless method", International Journal for Numerical Method in Engineering, vol. 74, no. 13, 1928-1954, 2008.
73. Gosz J., Liu W.K., "Admissible approximations for essential boundary conditions in the reproducing kernel particle method", Computational Mechanics, vol. 19, 120-135, 1996.
74. Green P.J., Sibson R., "Computing dirichlet tesselations in the plane", The Computer Journal, vol. 21, 168-173, 1978.
75. Herrchen M., Öttinger H.C., "A detailed comparison of various FENE models", Journal Non-Newtonian Fluid Mechanics, vol. 68, 17-42, 1997.
76. Hiyoshi H., Sugihara K., "Two generalizations of an interpolant based on Voronoï diagrams", International Journal of Shape Modeling, vol. 5, no. 2, 219-231, 1999.
77. Hu H.C., "On some variational principles in the theory of elasticity and the theory of plasticity", Scientia Sinica, vol. 4, 33-54, 1955.
78. Hughes T.J.R., Ferencz R.M., Hallquist J.O., "Large-scale vectorized implicit calculations in solid mechanics on a Cray X-MP/48 utilizing EBE preconditioned conjugate gradients", Computer Methods in Applied Mechanics and Engineering, vol. 61, 215-248, 1987.
79. Illoul L., Mise en oeuvre de la méthode des éléments naturels contrainte en 3D-Application au cisaillage adiabatique, PhD Thesis, Ecole Nationale Supérieure d'Arts et Métiers, 2008.
80. Irons B., Razzaque A., "Experience with the patch test for convergence of finite elements", AZIZ A.K., (Ed.), The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, Academic Press, New York, 1972.
81. Ji H., Chopp D., Dolbow J., "A hybrid finite element/level set method for modeling phase transformations", International Journal for Numerical Methods, vol. 54, 1209-1233, 2002.
82. Kagan P., Fischer A., Bar-Yoseph P.Z., "Mechanically based models: Adaptive refinement of B-spline finite element", International Journal for Numerical Methods in Engineering, vol. 57, 1145-1175, 2003.
83. Keunings R., "Micro-macro methods for the multiscale simulation of viscoelastic flow using molecular models of kinetic theory", BINDING D., WALTERS K. (Eds.), Rheology Reviews 2004, British Society of Rheology, Aberystwyth, Wales, p. 67-98, 2004.
84. Keyak J.H., Meagher J.M., "Automated three dimensional finite element modelling of bone: A new method", Journal of Biomedical Engineering, vol. 12, 389-397, 1990.
85. Klaas O., Shephard M.S., "Authomatic generation of octree based threedimensional discretizations for partition of unity methods", Computational Mechanics, vol. 25, 296-304, 2000.
86. Krongauz Y., Application of meshless methods to solid mechanics, PhD Thesis, Northwestern University, Evanston, IL, 1996.
87. Krysl P., Grinspun E., Schröder P., "Natural hierarchical refinement for finite element methods", International Journal for Numerical Methods in Engineering, vol. 56, 1109-1124, 2003.
88. Ladevèze P., Non Linear Computational Structural Mechanics, Springer, New York, 1998.
89. Ladevèze P., Pelle J.-P., La Maîtrise du calcul en mécanique linéaire et nonlinéaire, Hermes/Lavoisier, 2001.
90. Van De Langkruis J., Lof J., Kool W.H., Van Der Zwaag S., Huétink J., "Comparison of experimental AA6063 extrusion trials to 3D numerical simulations, using a general solute-dependent constitutive model", Computational Materials Science, vol. 81, 381-392, 2000.
91. Laso M., Öttinger H.C., "Calculation of viscoelastic flow using molecular models: the CONNFFESSIT approach", Journal of Non-Newtonian Fluid Mechanics, vol. 47, 1-20, 1993.
92. Lawrence J., "Polytope volume computation", Mathematics of Computation, vol. 57, 259-271, 1991.
93. Lee C.K., Zhou C.E., "On error estimation and adaptive refinement for element free Galerkin method: Part I: Stress recovery and a posteriori error estimation", Computer and Structures, vol. 82, 413-428, 2003.
94. Lee C.K., Zhou C.E., "On error estimation and adaptive refinement for element free Galerkin method: Part II: Adaptive refinement", Computer and Structures, vol. 82, 429-443, 2003.
95. Lewis R.W., Navti S.E., Taylor C., "A mixed Lagrangian-Eulerian approach to modelling fluid flow during mould filling", International Journal for Numerical Methods in Engineering, vol. 25, 931-952, 1997.
96. Li X., Cescotto S., Rossi B., A natural neighbour method for materially non linear problems based on Fraeijs de Veubeke variational principle, Report AG2007-03/01, University of Liège, ArGEnCo Department, 2007.
97. Li X., Cescotto S., Rossi B., "A natural neighbour method for materially non linear problems based on Fraeijs de Veubeke variational principle", Acta Mechanica Sinica, vol. 25, 83-93, 2009.
98. Liu W.K., Jun S., Li S., Adee J., Belytschko T., "Reproducing kernel particle methods", International Journal for Numerical Methods in Engineering, vol. 38, 1655-1679, 1995.
99. Liu W.K., Uras R.A., Chen Y., "Enrichment of the finite element method with the reproducing kernel particle method", Journal of Applied Mechanics, ASME, vol. 64, 861-870, 1997.
100. Lof J., Huétink J., "Numerical simulation of the aluminium extrusion process", COVAS J. (Ed.), Proc. 2nd ESAFORM Conference on Material Forming, p. 29-32, 1999.
101. Lof J., Developments infinite element simulations of aluminium extrusion, PhD Thesis, Department of Mechanical Engineering, Applied Mechanics Section, University of Twente, The Netherlands, 2000.
102. Lof J., "Elasto-viscoplastic FEM simulation of the aluminium flow in the bearing area for extrusion of thin-walled sections", Journal of Materials Processing Technology, vol. 114, 174-183, 2001.
103. Lof J., Blokhuis Y., "FEM simulations of the extrusion of complex thin-walled aluminium sections", Journal of Materials Processing Technology, vol. 122, 344-354, 2002.
104. Lorensen W.E., Cline H.E., "Marching cubes: A high resolution 3D surface reconstruction algorithm", Computer Graphics, vol. 21, 163-169, 1987.
105. Lu H., Chen J., "Adaptive meshfree particle method", Lecture Notes in Computational Science and Engineering, vol. 26, 251-267, 2002.
106. Lynch D., O'neill K., "Continuously deforming finite elements for the solution of parabolic problems, with and without phase change", International Journal for Numerical Methods in Engineering, vol. 17, 81-96, 1981.
107. Macri M., De S., Shephard M.S., "Hierarchical tree-based discretization for the method of finite spheres", Computers and Structures, vol. 81, 789-803, 2003.
108. Martin J.C. , Moyce W.J., "Part IV: An experimental study of the collapse of liquid columns on a rigid horizontal plane", Philosophical Transactions of the Royal Society London, vol. 244, p. 312, 1952.
109. Martínez M.A., Cueto E., Doblaré M., Chinesta F., "Natural element meshless simulation of injection processes involving short fiber suspensions", Internatonal Journal of Forming Processes, vol. 4, no. 3-4, 2002.
110. Martínez M.A., Cueto E., Doblaré M., Chinesta F., "Fixed mesh and meshfree techniques in the numerical simulation of injection processes involving short fiber suspensions", Journal of Non-Newtonian Fluid Mechanics, vol. 115, 51-78, 2003.
111. Martínez M.A., Cueto E., Alfaro I., Doblare M., Chinesta F., "Updated Lagrangian free surface flow simulations with natural neighbour Galerkin methods", International Journal for Numerical Methods in Engineering, vol. 60, no. 13, 2105-2129, 2004.
112. Meagher D., "Geometric modeling using octree encoding", Computer Graphics and Image Processing, vol. 19, 129-147, 1982.
113. Merle R., Dolbow J., "Solving thermal and phase change with the extended finite element method", Computational Mechanics, vol. 28, no. 5, 339-350, 2002.
114. Mooi H.G., Huétink J., "Simulation of complex aluminium extrusion using an arbitrary Eulerian Lagrangian formulation", SHEN S.F., DAWSON P.R. (Eds.), Proc. Numiform 95 Conference, New York, p. 869-874, 1995.
115. Muecke E.P., Shapes and implementations in three-dimensional geometry, PhD Thesis, University of Illinois, Urbana-Champaign, 1993.
116. Nagashima T., Ishihara Y., Niiyima K., Makinouchi A., "Development of stress analysis method based on Voxel-type X-FEM", MANG H.A., RAMMERSTORFER F.G., EBERHARDSTEINER J., (Eds.), Proc. 5th World Congress on Compotatinal Mechanics, Vienna, IACM, 2002.
117. Nayroles B., Touzot G., Villon P., "Generalizing the finite element method: Diffuse approximation and diffuse elements", Computational Mechanics, vol. 10, 307-318, 1992.
118. Oden J.T., Duarte C.A.M., Zienkiewicz O.C., "A new cloud based hp finite element method", Computer Methods in Applied Mechanics and Engineering, vol. 153, 117-126, 1998.
119. Organ D., Fleming M., Terry T., Belytschko T., "Continuous meshless approximations for nonconvex bodies by diffraction and transparency", Computational Mechanics, vol. 18, 1-11, 1996.
120. Öttinger H.C., Stochastic Processes in Polymeric Fluids, Springer, New York, 1996.
121. Owens R.G., Phillips T.N., Computational Rheology, Imperial College Press, London, 2002.
122. Perzyna P., "Fundamental problems in visco-plasticity", Recent Advances in Applied Mechanics, Academic Press, New York, 1966.
123. Rabier S., Medale M., "Computation of free surface flows with a projection FEM in a moving mesh framework", Computer Methods in Applied Mechanics and Engineering, vol. 192, no. 41-42, 2003.
124. Ramaswamy B., Kawahara M., "Lagangian finite element analysis applied to viscous free surface fluid flow", International Journal for Numerical Methods in Engineering, vol. 7, 953-984, 1987.
125. Ranc N., Etude des champs de température et de déformation dans les matériaux métalliques sollicités à grande vitesse de déformation, PhD Thesis, University Paris X, Nanterre, December 2004.
126. Van Rietbergen B., Weinans H., Huiskes R., "Computational strategies for iterative solutions of large FEM applications employing Voxel data", International Journal for Numerical Methods in Engineering, vol. 39, 2473-2767, 1996.
127. Rossi B., Habraken A.M., Pascon F., "On the evaluation of the through thickness residual stresses distribution of cold formed profiles", Proc. 10th ESAFORM Conference on Material Forming, Zaragoza, p. 570-577, 2007.
128. Rvachev V.L., Sheiko T.I., "R-functions in boundary value problems in Mechanics", Applied Mechanics Reviews, vol. 48, 151-188, 1995.
129. Rvachev V.L., Sheiko T.I., Shapiro V., Tsukanov I., "On completeness of RFM solution structures", Computational Mechanics, vol. 25, 305-316, 2000.
130. Samet H., "The quadtree and related hierarchical data structures", Computing Surveys, vol. 16, no. 2, 187-260, 1984.
131. Samet H., "Spatial data structures", Modern Database Systems: The Object Model, Interoperability and Beyond, Addison Wesley/ACM press, Reading, MA, p. 361-385, 1995.
132. Sambridge M., Braun J., Mcqueen H., "New computational methods for natural neighbour interpolation in two and three dimensions", Computational Techniques and Applications: CTAC95, p. 685-692, 1996.
133. Schönhardt E., "Über die Zerlegung von Dreieckspolyedern in Tetraeder", Mathematische Annalen, vol. 98, 309-312, 1928.
134. Schmitt F., Borouchaki H., "Algorithme rapide de maillage de Delaunay dans Rd", Journées de Géométrie Algorithmique, p. 131-133, 1990.
135. Sellars C.M., Tegart W.J.M., "Hot workability", International Metallurgical Review, vol. 17, 1-24, 1972.
136. Shapiro V., Tsukanov I., "Meshfree simulation of deforming domains", Computer-Aided Design, vol. 31, 459-471, 1999.
137. Shewchuk J.R., "A condition guaranteeing the existence of higher-dimensional constrained delaunay triangulations", Proc. 14th Annual Symposium on Computational Geometry, Minnesota, p. 76-85, 1998.
138. Si H., Gârtner K., "Meshing piecewise linear complexes by constrained delaunay tetrahedralizations", Proc. 14th International Meshing Roundtable, San Diego, CA, p. 147-163, 2005.
139. Sibson R., "A vector identity for the dirichlet tesselation", Mathematical Proc. Cambridge Philosophical Society, vol. 87, 151-155, 1980.
140. Sibson R., "A brief description of natural neighbour interpolation", BARNETT V. (Ed.), Interpreting Multivariate Data, John Wiley, Chichester, p. 21-36, 1981.
141. Strouboulis T., Copps K., Babuška I., "The generalized finite element method", Computer Methods in Applied Mechanics and Engineering, vol. 190, 4081-4193, 2001.
142. Sukumar N., The natural element method in solid mechanics, PhD Thesis, Northwestern University, Evanston, Illinois, 1998.
143. Sukumar N., Moran B., Belytschko T., "The natural element method in solid mechanics", International Journal for Numerical Methods in Engineering, vol. 43, no. 5, 839-887, 1998.
144. Sukumar N., Chopp D.L., Moës N., Belytschko T., "Modeling holes and inclusions by level sets in the extended finite element method", Computer Methods in Applied Mechanics and Engineering, vol. 190, no. 46-47, 6183-6200, 2001.
145. Sukumar N., Moran B., Semenov A.Y., Belikov V.V., "Natural neighbor Galerkin methods", International Journal for Numerical Methods in Engineering, vol. 50, no. 1, 1-27, 2001.
146. Sukumar N., Dolbow J., Devan A., Yvonnet J., Chinesta F., Ryckelynck D., Lorong P., Alfaro I., Martínez M.A., Cueto E., Doblaré M., "Meshless methods and partition of unity finite elements", Internatonal Journal of Forming Processes, vol. 8-4, p. 409-427, 2005.
147. Thiessen A.H., Precipitation averages for large areas, Monthly Weather Report, vol. 39, p. 1082-1084, 1911.
148. Timoshenko S., Goodier J.N., Teoría de la Elasticidad, Editorial Urmo, 1972.
149. Traversoni L., "Natural neighbour finite elements", International Conference on Hydraulic Engineering Software, Hydrosoft Proceedings, Computational Mechanics publications, Southampton, p. 291-297, 1994.
150. Trunzler J., Joyot P., Chinesta F., "Discontinuous derivative enrichment in RKPM", Lecture Notes on Computational Science and Engineering, vol. 43, Springer, p. 93-108, 2005.
151. Fraeijs De Veubeke B.M., "Diffusion des inconnues hyperstatiques dans les voilures à longerons couplés", Bulletins du Service Technique de l'Aéronautique, vol. 24, 1951.
152. Voronoï G. M., "Nouvelles Applications des Paramètres Continus à la Théorie des Formes Quadratiques. Deuxième Memoire: Recherches sur les parallélloèdres Primitifs", Journal für die Reine and Angewandte Mathematic, vol. 134, 198-287, 1908.
153. Washizu K., On the variational principles of elasticity and plasticity, Aeroelastic and Structures Research Laboratory, Technical report 25-18, MIT, Cambridge, 1955.
154. Watson D., "Computing the n-dimensional delaunay tessellation with application to Voronoï polytopes", The Computer Journal, vol. 24, no. 2, 162-172, 1981.
155. Watson D.F., Compound signed decomposition, the core of natural neighbour interpolation in n-dimensional space (unpublished manuscript), c 2001 D.F. Watson, http://www.lang.org/naturalneighbour.html
156. Wells G.N., Sluys L.J., De Borst R., "A p-adaptive scheme for overcoming volumetric locking during plastic flow", Computer Methods in Applied Mechanics and Engineering, vol. 191, 3153-3164, 2002.
157. Wilkinson J.H., The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965.
158. Yerry M.A., Shephard M.S., "Automatic three-dimensional mesh generation by the modified octree technique", International Journal for Numerical Methods in Engineering, vol. 20, 1965-1990, 1984.
159. Yoo J., Moran B., Chen J.-S., "Stabilized conforming nodal integration in the natural-element method", International Journal for Numerical Methods in Engineering, vol. 60, 861-890, 2004.
160. You Y., Chen J., Lu H., "Filters, reproducing Kernel, and adaptive meshfree method", Computational Mechanics, vol. 31, 316-326, 2003.
161. Yvonnet J., Nouvelles approches sans maillage basées sur la méthode des éléments naturels pour la simulation numérique des procédés de mise en forme, PhD Thesis, Ecole Nationale Supérieure d'Arts et Métiers, 2004.
162. Yvonnet J., Ryckelynck D., Lorong P., Chinesta F., "A new extension of the natural element method for non-convex and discontinuous problems: The constrained natural element method", International Journal for Numerical Methods in Enginering, vol. 60, no. 8, 1452-1474, 2004.
163. Zhou J., Li L., Duszczyk J., "3D FEM simulation of the whole cycle of aluminium extrusion throughout the transient state and the steady state using the updated Lagrangian approach", Journal of Materials Processing Technology, vol. 134, 383-397, 2003.
164. Zienkiewicz O.C., Godbolet P.N., "Flow of plastic and visco-plastic solids with special reference to extrusion and forming processes", International Journal for Numerical Methods in Engineering, vol. 8, 3-16, 1974.
165. Zienkiewicz O.C., Oñate E., Heinrich J.C., "Plastic flow in metal forming. (I) Coupled thermal (II) Thin sheet forming", Applications of Numerical Methods to Forming Processes. AMD-vol 28, p. 107-120, 1978.
166. Zienkiewicz O.C., Pain P.C., Oñate E., "Flow of solids during forming and extrusion: Some aspects of numerical solutions", International Journal of Solids and Structures, vol. 14, 15-38, 1978.
167. Zienkiewicz O.C., "Flow formulation for numerical solution of forming processes", PITTMAN J.F.T., ZIENKIEWICZ O.C., WOOD R.D., ALEXANDER J.M. (Eds.), Numerical Analysis of Forming Processes, John Wiley and Sons, Chichester, p. 1-44, 1984.
168. Zienkiewicz O.C., Zhu J.Z., "A simple error estimator and adaptive procedure for practical engineering analysis", International Journal for Numerical Methods in Engineering, vol. 24, 337-357, 1988.
169. Zienkiewicz O., Boroomand B., Zhu J., "Recovery procedures in error estimation and adaptivity Part I: Adaptivity in linear problems", Computer Methods in Applied Mechanics Engineering, vol. 26, 111-125, 1999.