An EFG method for the nonlinear analysis of plates undergoing arbitrarily large deformations

Engineering Analysis with Boundary Elements

Volumn 32, Issue 6, 2008, Pages 494-511

  Tiago, Carlos ^a   Pimenta, Paulo M ^b  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Geometrically exact; Hybrid weak form; Meshfree; Moving least squares; Multi region; Plates

Indexed keywords

FINITE ELEMENT METHOD; LEAST SQUARES APPROXIMATIONS; NONLINEAR ANALYSIS; PARAMETERIZATION; STIFFNESS MATRIX;

EFG METHOD; HYBRID WEAK FORM; NONLINEAR THEORY;

DEFORMATION;

EID: 43649085676     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2007.10.014     Document Type: Article

References (44)

1. Simo J.C., and Fox D.D. On a stress resultant geometrically exact shell model. Part I: formulation and optimal parametrization. Comput Methods Appl Mech Eng 72 3 (1989) 267-304
2. Pimenta PM. On the geometrically-exact finite-strain rod model. In: Proceeding of the third Pan-American congress on applied mechanics, PACAM III. Brazil: Escola Politécnica da Universidade de São Paulo; January 4-8, 1993. p. 279-82.
3. Pimenta PM. On the geometrically-exact finite-strain shell model. In: Proceeding of the third Pan-American congress on applied mechanics, PACAM III. Brazil: Escola Politécnica da Universidade de São Paulo, January 4-8, 1993. p. 616-19.
4. Pimenta P.M., and Yojo T. Geometrically exact analysis of spatial frames. Appl Mech Rev 46 11 (1993) 118-128
5. Pimenta PM. Geometrically exact analysis of initially curved rods, In: Topping BHV, editor. Advances in computational techniques for structural engineering; 1996. p. 99-108.
6. Pimenta, PM, Campello, EMB. Geometrically nonlinear analysis of thin-walled space frames, In: Waszczyszyn Z, Stein E editors. Second European conference on computational mechanics. Cracow, Poland; 2001.
7. Campello E.M.B., Pimenta P.M., and Wriggers P. A triangular finite shell element based on a fully nonlinear shell formulation. Comput Mech 31 6 (2003) 505-518
8. Pimenta P.M., Campello E.M.B., and Wriggers P. A fully nonlinear multi-parameter shell model with thickness variation and a triangular shell finite element. Comput Mech 34 3 (2004) 181-193
9. Tiago C, Pimenta P. Geometrically exact analysis of space frames by a meshless method. In: Leitão V, Alves C, Duarte C, editors. ECCOMAS thematic conference on meshless methods. Lisbon, Portugal; 2005. p. C441-8.
10. Lu Y.Y., Belytschko T., and Gu L. A new implementation of the element free Galerkin method. Comput Methods Appl Mech Eng 113 3-4 (1994) 397-414
11. Belytschko T., Krongauz Y., Organ D., Fleming M., and Krysl P. Meshless methods: an overview and recent developments. Comput Methods Appl Mech Eng 139 1-4 (1996) 3-47
12. Li S., and Liu W.K. Meshfree and particle methods and their applications. Appl Mech Rev 55 1 (2002) 1-34
13. Belytschko T., Lu Y.Y., Gu L., and Element-free Galerkin methods. Int J Numer Methods Eng 37 2 (1994) 229-256
14. Duarte C.A., and Tinsley Oden J. H-p clouds-an h-p meshless method. Numer Methods Partial Differ Equations 12 6 (1996) 673-705
15. Argyris J. An excursion into large rotations. Comput Methods Appl Mech Eng 32 1-3 (1982) 85-155
16. Teixeira de Freitas J.A., Moitinho de Almeida J.P., and Ribeiro Pereira E.M.B. Non-conventional formulations for the finite element method. Comput Mech 23 5-6 (1999) 488-501
17. Cordes L.W., and Moran B. Treatment of material discontinuity in the element-free Galerkin method. Comput Methods Appl Mech Eng 139 1-4 (1996) 75-89
18. Tiago C., and Leitão V. Development of a EFG formulation for damage analysis of reinforced concrete beams. Comput Struct 82 17-19 (2004) 1503-1511
19. Moitinho de Almeida J.P., and Teixeira de Freitas J.A. Continuity conditions for finite element analysis of solids. Int J Numer Methods Eng 33 4 (1992) 845-853
20. Lancaster P., and Šalkauskas K. Surfaces generated by moving least squares methods. Math Comput 37 155 (1981) 141-158
21. Belytschko T., Krongauz Y., Fleming M., Organ D., and Liu W.K.S. Smoothing and accelerated computations in the element free Galerkin method. J Comput Appl Math 74 1-2 (1996) 111-126
22. Tiago C, Leitão VMA. Eliminating shear-locking in meshless methods: a critical overview and a new framework for structural theories. In: Leitão VMA, Alves C, Armando Duarte C, editors. Advances in meshfree techniques. Computational methods in applied sciences, vol. 5. Berlin: Springer; 2007. p. 123-45.
23. Garcia O., Fancello E.A., de Barcellos C.S., and Duarte C.A. Hp-clouds in Mindlin's thick plate model. Int J Numer Methods Eng 47 8 (2000) 1381-1400
24. Donning B.M., and Liu W.K. Meshless methods for shear-deformable beams and plates. Comput Methods Appl Mech Eng 152 1-2 (1998) 47-71
25. Beissel S., and Belytschko T. Nodal integration of the element-free Galerkin method. Comput Methods Appl Mech Eng 139 1-4 (1996) 49-74
26. Cho J.Y., and Atluri S.N. Analysis of shear flexible beams, using the meshless local Petrov-Galerkin method, based on a locking-free formulation. Eng Comput 18 1-2 (2001) 215-240
27. Dolbow J., and Belytschko T. Volumetric locking in the element free Galerkin method. Int J Numer Methods Eng 46 6 (1999) 925-942
28. Tiago C, Leitão V. Further developments on GMLS: plates on elastic foundation. In: Atluri SN, Tadeu AJB, editors. Advances in computational and experimental engineering and sciences. CD-ROM Proceedings. Madeira, Portugal: Tech Science Press; July 2004. p. 1378-83.
29. Tiago C, Leitão VMA. Local imposition of essential boundary conditions in meshfree methods. In: VII World congress on computational mechanics. Los Angeles, USA; July 2006.
30. Simo J.C., and Hughes T.J.R. Computational inelasticity. Interdisciplinary applied mathematics (2000), Springer, Berlin
31. Ibrahimbegović A. Stress resultant geometrically nonlinear shell theory with drilling rotations-Part I. A consistent formulation. Comput Methods Appl Mech Eng 118 3-4 (1994) 265-284
32. Cardona A., and Géradin M. A beam finite-element non-linear theory with finite rotations. Int J Numer Methods Eng 26 11 (1988) 2403-2438
33. Mann H.B. Quadratic forms with linear constraints. Am Math Mont 50 7 (1943) 430-433
34. Spring D. On the second derivative test for constrained local extrema. Am Math Mont 92 9 (1985) 631-643
35. Hassell C., and Rees E. The index of a constrained critical point. Am Math Mont 100 8 (1993) 772-778
36. Shutler P. Constrained critical points. Am Math Mont 102 1 (1995) 49-52
37. Greenberg L., Maddocks J.H., and Hoffman K.A. The bordered operator and the index of a constrained critical point. Math Nachr 219 1 (2000) 109-124
38. Qi Z., and Tianqi Y. The adaptive parameter incremental method for the analysis of snapping problems. Appl Math Mech 16 9 (1995) 851-858
39. Crisfield M.A. A fast incremental/iterative solution procedure that handles "snap-through". Comput Struct 13 1-3 (1981) 55-62
40. Schweizerhof K.H., and Wriggers P. Consistent linearization for path following methods in nonlinear FE analysis. Comput Meth Appl Mech Eng 59 3 (1986) 261-279
41. Atluri S.N., Cho J.Y., and Kim H.-G. Analysis of thin beams, using the meshless local Petrov-Galerkin method, with generalized moving least squares interpolations. Comput Mech 24 5 (1999) 334-347
42. Mattiasson K. Numerical results from large deflection beam and frame problems analysed by means of elliptic integrals. Int J Numer Meth Eng 17 1 (1981) 145-153
43. Liu X.H., Sze K.Y., and Lo S.H. Popular benchmark problems for geometric nonlinear analysis of shells. Finite Elem Anal Des 40 11 (2004) 1551-1569
44. Timoshenko S.P., and Gere J.M. Theory of elastic stability. 2nd ed. (1961), McGraw-Hill, New York