Efficient and accurate multilayer solid-shell element: Non-linear materials at finite strain

International Journal for Numerical Methods in Engineering

Volumn 63, Issue 15, 2005, Pages 2124-2170

  Tan, X G ^a,b   Vu Quoc, L ^a  

^a UNIVERSITY OF FLORIDA   (United States)

^b CFD RESEARCH CORPORATION   (United States)

Author keywords

Composite shell; Contact; Dynamic analyses; Finite strains; Incompressibility; Large deformation; Multilayer; Non linear materials; Patch tests; Plasticity; Solid shell element

Indexed keywords

APPROXIMATION THEORY; BENDING (DEFORMATION); DEGREES OF FREEDOM (MECHANICS); EIGENVALUES AND EIGENFUNCTIONS; ELASTOPLASTICITY; FINITE ELEMENT METHOD; KINEMATICS; MATHEMATICAL MODELS; MATRIX ALGEBRA; STRAIN; VECTORS;

COMPOSITE SHELL; CONTACT SURFACE; DYNAMIC ANALYSES; FINITE STRAINS; INCOMPRESSIBILITY; LARGE DEFORMATION; NONLINEAR MATERIALS; PATCH TEST; SOLID SHELL ELEMENT;

MULTILAYERS;

DYNAMIC ANALYSIS; PLASTICITY;

EID: 24044435876     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1360     Document Type: Article

References (76)

1. Simo JC, Kennedy JG. On a stress resultant geometrically exact shell model. Part V. Nonlinear plasticity. Formulation and integration algorithms. Computer Methods in Applied Mechanics and Engineering 1992; 96(2):133-171.
2. Schieck B, Pietraszkiewicz W, Stumpf H. Theory and numerical analysis of shells undergoing large elastic strains. International Journal of Solids and Structures 1992; 29(6):689-709.
3. Cho JW, Yang DY, Chung WJ. A simplified approach for incorporating thickness stress in the analysis of sheet metal forming using shell elements. International Journal for Numerical Methods in Engineering 2002; 53:2311-2327.
4. Fox DD. Transverse shear and normal stresses in nonlinear shell theory. Computers and Structures 2000; 75:313-319.
5. Chroscielewski J, Makowski J, Stumpf H. Finite element analysis of smooth, folded and multi-shell structures. Computer Methods in Applied Mechanics and Engineering 1997; 141:1-46.
6. Liao CL, Reddy JN, Engelstad SP. A solid-shell transition element for geometrically non-linear analysis of laminated composite structures. International Journal for Numerical Methods in Engineering 1988; 26(8):1843-1854.
7. Cofer WF, Will KM. A finite element technique for the ultimate strength analysis of tubular joints. Engineering Computations 1992; 9 (3):345-358.
8. ABAQUS. Version 6.2, Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, RI, 2001.
9. Vu-Quoc L, Deng H, Tan XG. Geometrically-exact sandwich shells: the static case. Computer Methods in Applied Mechanics and Engineering 2000; 189(1):167-203.
10. Simo JC, Kennedy JG, Taylor RL. Complementary mixed finite element formulations for elastoplasticity. Computer Methods in Applied Mechanics and Engineering 1989; 74(2):177-206.
11. Buchter N, Ramm E, Roehl D. Three-dimensional extension of nonlinear shell formulation based on the enhanced assumed strain concept. International Journal for Numerical Methods in Engineering 1994; 37(15):2551-2568.
12. Vu-Quoc L, Tan XG. Optimal solid shells for non-linear analyses of multilayer composites. I. Statics. Computer Methods in Applied Mechanics and Engineering 2003; 192(9-10):975-1016.
13. Miehe C. Theoretical and computational model for isotropic elastoplastic stress analysis in shells at large strains. Computer Methods in Applied Mechanics and Engineering 1998; 155(3-4):193-233.
14. Klinkel S, Gruttmann F, Wagner W. A continuum based three-dimensional shell element for laminated structures. Computers and Structures 1999; 71(1):43-62.
15. Zienkiewicz OC, Taylor RL. The Finite Element Method. Volume 2: Solid and Fluid Mechanics, Dynamics and Non-linearity (4th edn). McGraw-Hill: New York, 1991.
16. Bischoff M, Ramm E. Shear deformable shell elements for large strains and rotations. International Journal for Numerical Methods in Engineering 1997; 40(23):4427-4449.
17. MacNeal RH. A simple quadrilateral shell element. Computers and Structures 1978; 8:175-183.
18. Hughes TJR, Tezduyar TE. Finite elements based upon Mindlin plate theory with particular reference to the four-node bilinear isoparametric element. Journal of Applied Mechanics (ASME) 1981; 48: 587-596.
19. Dvorkin EN, Bathe K-J. Continuum mechanics based four-node shell element for general non-linear analysis. Engineering Computations 1984; 1(1):77-88.
20. Parisch H. A continuum-based shell theory for non-linear applications. International Journal for Numerical Methods in Engineering 1995; 38:1855-1883.
21. Sze KY, Yao LQ. A hybrid stress ANS solid-shell and its generalization for smart structure modelling. Part I - solid-shell element formulation. International Journal for Numerical Methods in Engineering 2000; 48:545-564.
22. Betsch P, Stein E. An assumed strain approach avoiding artificial thickness straining for a non-linear 4-node shell element. Communications in Numerical Methods in Engineering 1995; 11: 899-909.
23. Hughes TJR. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice-Hall: New York, 1987.
24. Belytschko T, Lin JI, Tsay CS. Explicit algorithms for the nonlinear dynamics of shells. Computer Methods in Applied Mechanics and Engineering 1984; 42:225-251.
25. Zeng Q, Combescure A. A new one-point quadrature, general nonlinear quadrilateral shell element with physical stabilization. International Journal for Numerical Methods in Engineering 1998; 42:1307-1338.
26. Vu-Quoc L, Deng H, Tan XG. Geometrically-exact sandwich shells: the dynamic case. Computer Methods in Applied Mechanics and Engineering 2001; 190(22-23):2825-2873.
27. Ogden RW. Non-linear Elastic Deformations. Ellis Horwood: Chichester, Sussex, 1984.
28. Simo JC, Hughes TJR. Computational Inelasticity. Springer: New York, 1998.
29. Simo JC. A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition: Part II. Computational aspects. Computer Methods in Applied Mechanics and Engineering 1988; 68:1-31.
30. Simo JC. Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Computer Methods in Applied Mechanics and Engineering 1992; 92:61-112.
31. Ibrahimbegovic A. Equivalent spatial and material descriptions of finite deformation elastoplasticity in principal axes. International Journal of Solids and Structures 1994; 31(22):3027-3040.
32. Betsch P, Stein E. Numerical implementation of multiplicative elasto-plasticity into assumed strain elements with application to shells at large strains. Computer Methods in Applied Mechanics and Engineering 1999; 179(3-4):215-245.
33. Miehe C. Constitutive frame of elastoplasticity at large strains based on the notion of a plastic metric. International Journal of Solids and Structures 1998; 35(30):3859-3897.
34. Felippa CA. On the original publication of the general canonical functional of linear elasticity. ASME Journal of Applied Mechanics 2000; 67:217-219.
35. Vu-Quoc L, Tan XG. Optimal solid shells for non-linear analyses of multilayer composites. II. Dynamics. Computer Methods in Applied Mechanics and Engineering 2003; 192(9-10):1017-1059.
36. Malvern LE. Introduction to the Mechanics of a Continuous Medium. Prentice-Hall: Englewood Cliffs, NJ, 1969.
37. Brillouin L. Les Tenseurs en Mécanique et en Elasticité. Dover: New York, 1946.
38. Betsch P, Stein E. A nonlinear extensible 4-node shell element based on continuum theory and assumed strain interpolations. Journal of Nonlinear Science 1996; 6:169-199.
39. Klinkel S, Wagner W. A geometrical non-linear brick element based on the EAS-method. International Journal for Numerical Methods in Engineering 1997; 40:4529-4545.
40. Belytschko T, Liu WK, Moran B. Nonlinear Finite Elements for Continua and Structures. Wiley: New York, 2000.
41. LS-DYNA. Theoretical Manual, Livermore Software Technology Corporation, Livermore, CA, 1998.
42. DYNA3D. A nonlinear, explicit, three-dimensional finite element code for solid and structural mechanics. User Manual, Lawrence Livermore National Laboratory, Livermore, CA, 1993.
43. Zhu YY, Cescotto S. Unified and mixed formulation of the 8-node hexahedral elements by assumed strain method. Computer Methods in Applied Mechanics and Engineering 1996; 129(1-2):177-209.
44. Zhu Y, Zacharia T. A new one-point quadrature, quadrilateral shell element with drilling degrees of freedom. Computer Methods in Applied Mechanics and Engineering 1996; 136(1-2):165-203.
45. Stanley GM. Continuum-based shell elements. Ph.D. Thesis, Stanford University, Stanford, CA, 1985.
46. Zienkiewicz OC, Taylor RL. The Finite Element Method. Volume 1: Basic Formulation and Linear Problems (4th edn). McGraw-Hill: New York, 1989.
47. ADINA. Version 7.5, ADINA R&D, Inc., Watertown, MA, 2002.
48. Fried I, Johnson AR. A note on elastic energy density functions for largely deformed compressible rubber solids. Computer Methods in Applied Mechanics and Engineering 1988; 69(1):53-64.
49. Zienkiewicz OC, Taylor RL. The Finite Element Method. Volume 1: The Basis (5th edn). Butterworth-Heinemann: Oxford, 2000.
50. Bathe K-J. Finite Element Procedures (2nd edn). Prentice-Hall: Englewood Cliffs, NJ, 1996.
51. Truesdell C, Noll W. The Nonlinear Field Theories of Mechanics (2nd edn). Springer: Berlin, 1992.
52. Simo JC, Taylor RL. Quasi-incompressible finite elasticity in principal stretches: continuum basis and numerical algorithms. Computer Methods in Applied Mechanics and Engineering 1991; 85:273-310.
53. Simo JC, Ortiz M. A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations. Computer Methods in Applied Mechanics and Engineering 1985; 49:221-245.
54. Simo JC. A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition: Part I. Continuum formulation. Computer Methods in Applied Mechanics and Engineering 1988; 66:199-219.
55. Eterovich AL, Bathe K-J. A hyperelastic-based large strain elasto-plastic constitutive formulation with combined isotropic-kinematic hardening using logarithmic stresses and strain measures. International Journal for Numerical Methods in Engineering 1990; 30:1099-1115.
56. Weber G, Anand L. Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solids. Computer Methods in Applied Mechanics and Engineering 1990; 79:173-202.
57. Hauptmann R, Schweizerhof K, Doll S. Extension of the 'solid-shell' concept for application to large elastic and large elastoplastic deformations. Computers and Structures, 1998, Preprint No. 98/6.
58. Simo JC, Armero, F. Geometrically nonlinear enhanced-strain mixed methods and the method of incompatible modes. International Journal for Numerical Methods in Engineering 1992; 33:1413-1449.
59. Maugin GA. The Thermomechanics of Plasticity and Fracture (1st edn). Cambridge University Press: Cambridge, 1992.
60. Karush W. Minima of functions of several variables with inequalities as side conditions. Master's Thesis, University of Chicago, Chicago, 1939.
61. Kuhn HW, Tucker AW. Nonlinear programming. In Second Berkeley Symposium on Mathematical Statistics and Probability, Neyman J (ed.). University of California Press: Berkeley, CA, U.S.A., 1951; 481-492.
62. Tapia R, Trosset M. Extension of the karush-kuhn-tucker necessity conditions to infinite programming. SIAM Review 1994; 36 (1):1-17.
63. Simo JC, Taylor RL. Consistent tangent operators for rate-independent elastoplasticity. Computer Methods in Applied Mechanics and Engineering 1985; 48:101-118.
64. Zienkiewicz OC, Taylor RL. The Finite Element Method. Volume 2: Solid Mechanics (5th edn). Butterworth-Heinemann: Oxford, 2000.
65. Tan XG. Nonlinear static and dynamic finite element analysis of multilayer shell structures. Ph.D. Thesis, University of Florida, 2002.
66. NIKE3D. A nonlinear, implicit, three-dimensional finite element code for solid and structural mechanics. User Manual, Lawrence Livermore National Laboratory, Livermore, CA, 1995.
67. Gruttmann F, Taylor RL. Theory and finite element formulation of rubberlike membrane shells using principal stretches. International Journal for Numerical Methods in Engineering 1992; 35 (5):1111-1126.
68. Li S, Hao W, Liu WK. Numerical simulations of large deformation of thin shell structures. Computational Mechanics 2000; 25 (2-3):102-116.
69. De S, Bathe K-J. Towards an efficient meshless computational technique: the method of finite spheres. Engineering Computations 2001; 18 (1-2):170-192.
70. De S, Bathe K-J. The method of finite spheres with improved numerical integration. Computers and Structures 2001; 79 (22-25):2183-2196.
71. Atluri SN, Shen S. The Meshless Local Petrov-Galerkin Method. Tech Science Press: Encino, CA, 2002.
72. Eberlein R, Wriggers P. Finite element concepts for finite elastoplastic strains and isotropic stress response in shells: theoretical and computational analysis. Computer Methods in Applied Mechanics and Engineering 1999; 171(3-4):243-279.
73. Choudhry S, Wertheimer TB. Comparison of finite strain plasticity algorithms in MARC. Technical Report, MARC Analysis Research Corporation, Palo Alto, CA, 1997.
74. Chroscielewski J, Makowski J, Stumpf H. Genuinely resultant shell finite elements accounting for geometric and material non-linearity. International Journal for Numerical Methods in Engineering 1992; 35:63-94.
75. Betsch P, Gruttmann F, Stein E. 4-node finite shell element for the implementation of general hyperelastic 3d-elasticity at finite strains. Computer Methods in Applied Mechanics and Engineering 1996; 130 (1-2):57-79.
76. Schieck B, Smolenski WM, Stumpf H. A shell finite element for large strain elastoplasticity with anisotropies - part II: constitutive equations and numerical applications. International Journal of Solids and Structures 1999; 36:5425-5451.