Finite rotation geometrically exact four-node solid-shell element with seven displacement degrees of freedom

CMES - Computer Modeling in Engineering and Sciences

Volumn 28, Issue 1, 2008, Pages 15-38

  Kulikov, G M ^a   Plotnikova, S V ^a  

^a TAMBOV STATE TECHNICAL UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTITUTIVE EQUATIONS; EQUATIONS OF MOTION; LINEAR EQUATIONS; ROTATION; STIFFNESS MATRIX;

ANALYTICAL INTEGRATION; COARSE MESHES; CURVILINEAR COORDINATE SYSTEMS; DEGREES OF FREEDOM; DISPLACEMENT VECTORS; EQUIVALENT SINGLE LAYERS; FINITE ROTATIONS; FIRST ORDERS; GEOMETRICALLY NON-LINEAR; MEMBRANE LOCKING; NON-LINEAR; RIGID BODIES; SHELL ELEMENTS; TANGENT STIFFNESS MATRIX; TRANSVERSE DISPLACEMENTS; ZERO ENERGY MODES;

SHELLS (STRUCTURES);

EID: 49149128372     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (36)

1. ABAQUS (1998): ABAQUS Theory and User's Manuals, Version 5.8. Hibbitt, Karlsson & Sorensen Inc., Rawtucket, Rhode Island.
2. Atluri, S. N. (1973): On the hybrid stress finite element model for incremental analysis of large deflection problems. International Journal of Solids and Structures, vol. 9, pp. 1177-1191.
3. Atluri, S. N.; Liu, H. T.; Han, Z. D. (2006a): Meshless local Petrov-Galerkin (MLPG) mixed collocation method for elasticity problems. CMES: Computer Modeling in Engineering & Sciences, vol. 14, pp. 141-152.
4. Atluri, S. N.; Liu, H. T.; Han, Z. D. (2006b): Meshless local Petrov-Galerkin (MLPG) mixed finite difference method for solid mechanics. CMES: Computer Modeling in Engineering & Sciences, vol. 15, pp. 1-16.
5. Basar, Y.; Ding, Y.; Schultz, R. (1993): Refined shear-deformation models for composite laminates with finite rotations. International Journal of Solids and Structures, vol. 30, pp. 2611-2638.
6. Basar, Y.; Itskov, M.; Eckstein, A. (2000): Composite laminates: nonlinear interlaminar stress analysis by multi-layer shell elements. Computer Methods in Applied Mechanics and Engineering, vol. 185, pp. 367-397.
7. Basar, Y.; Kintzel, O. (2003): Finite rotations and large strains in finite element shell analysis. CMES: Computer Modeling in Engineering & Sciences, vol. 4, pp. 217-230.
8. Bathe, K. J.; Dvorkin, E. N. (1986): A formulation of general shell elements - the use of mixed interpolation of tensorial components. International Journal for Numerical Methods in Engineering, vol. 22, pp. 697-722.
9. Betsch, P.; Stein, E. (1995): An assumed strain approach avoiding artificial thickness straining for a nonlinear 4-node shell element. Communications in Numerical Methods in Engineering, vol. 11, pp. 899-909.
10. Bischoff, M.; Wall, W. A.; Bletzinger, K. U.; Ramm, E. (2004): Models and finite elements for thin-walled structures. In: E. Stein, R. de Borst, T. J. R. Hughes (eds) Encyclopedia of Computational Mechanics. Vol. 2: Solids and Structures. Willey, pp. 59-137.
11. Boland, P. L.; Pian, T. H. H. (1977): Large deflection analysis of thin elastic structures by the assumed stress hybrid finite element method. Computers and Structures, vol. 7, pp. 1-12.
12. Brank, B. (2005): Nonlinear shell models with seven kinematic parameters. Computer Methods in Applied Mechanics and Engineering, vol. 194, pp. 2336-2362.
13. Braun, M.; Bischoff, M.; Ramm, E. (1994): Nonlinear shell formulations for complete three-dimensional constitutive laws including composites and laminates. Computational Mechanics, vol. 15, pp. 1-18.
14. Cho, C.; Lee, S. W. (1996): On the assumed strain formulation for geometrically non-linear analysis. Finite Elements in Analysis and Design, vol. 24, pp. 31-47.
15. El-Abbasi, N.; Meguid, S. A. (2000): A new shell element accounting for through-thickness deformation. Computer Methods in Applied Mechanics and Engineering, vol. 189, pp. 841-862.
16. Hughes, T. J. R.; Tezduyar, T. E. (1981): Finite elements based upon Mindlin plate theory with particular reference to the four-node bilinear isoparametric element. Journal of Applied Mechanics, vol. 48, pp. 587-596.
17. Kim, Y. H.; Lee, S. W. (1988): A solid element formulation for large deflection analysis of composite shell structures. Computers & Structures, vol. 30, pp. 269-274.
18. Kulikov, G. M. (2004): Strain-displacement relationships that exactly represent large rigid-body displacements of a shell. Mechanics of Solids, vol. 39, pp. 105-113.
19. Kulikov, G. M. (2007): On the first-order seven-parameter plate theory. Trans. TSTU, vol. 13, pp. 518-528.
20. Kulikov, G. M.; Plotnikova S. V. (2002): Simple and effective elements based upon Timoshenko-Mindlin shell theory. Computer Methods in Applied Mechanics and Engineering, vol. 191, pp. 1173-1187.
21. Kulikov, G. M.; Plotnikova, S. V. (2003): Non-linear strain-displacement equations exactly representing large rigid-body motions. Part I. Timoshenko-Mindlin shell theory. Computer Methods in Applied Mechanics and Engineering, vol. 192, pp. 851-875.
22. Kulikov, G. M.; Plotnikova, S. V. (2005): Equivalent single-layer and layer-wise shell theories and rigid-body motions. Part II. Computational aspects. Mechanics of Advanced Materials and Structures, vol. 12, pp. 331-340.
23. Kulikov, G. M.; Plotnikova S. V. (2006): Non-linear strain-displacement equations exactly representing large rigid-body motions. Part II. Enhanced finite element technique. Computer Methods in Applied Mechanics and Engineering, vol. 195, pp. 2209-2230.
24. Kulikov, G. M.; Plotnikova S. V. (2007): Non-linear geometrically exact assumed stress-strain four-node solid-shell element with high coarsemesh accuracy. Finite Elements in Analysis and Design, vol. 43, pp. 425-443.
25. Lee, K.; Cho, C.; Lee, S. W. (2002): A geometrically nonlinear nine-node solid shell element formulation with reduced sensitivity to mesh distortion. CMES: Computer Modeling in Engineering & Sciences, vol. 3, pp. 339-349.
26. Pagano, N. J. (1970): Exact solutions for rectangular bidirectional composites and sandwich plates. Journal of Composite Materials, vol. 4, pp. 20-34.
27. Parisch, H. (1995): A continuum-based shell theory for non-linear applications. International Journal for Numerical Methods in Engineering, vol. 38, pp.1855-1883.
28. Park, H. C.; Cho, C.; Lee, S. W. (1995): An efficient assumed strain element model with six dof per node for geometrically nonlinear shells. International Journal for Numerical Methods in Engineering, vol. 38, pp. 4101-4122.
29. Sansour, C. (1995): A theory and finite element formulation of shells at finite deformations involving thickness change: circumventing the use of a rotation tensor. Archive of Applied Mechanics, vol. 65, pp. 194-216.
30. Schoop, H. (1986): Oberflächenorientierte Schalentheorien endlicher Verschiebungen. IngenieurArchiv, vol. 56, pp. 427-437.
31. Simo, J. C.; Rifai, M. S.; Fox, D. D. (1990): On a stress resultant geometrically exact shell model. Part IV. Variable thickness shells with throughthe-thickness stretching. Computer Methods in Applied Mechanics and Engineering, vol. 81, pp. 91-126.
32. Suetake, Y.; Iura, M.; Atluri S. N. (2003): Variational formulation and symmetric tangent operator for shells with finite rotation field, CMES: Computer Modeling in Engineering & Sciences, vol. 4, pp. 329-336.
33. Sze, K. Y. (2002): Three-dimensional continuum finite element models for plate/shell analysis. Progress in Structural Engineering and Materials, vol. 4, pp. 400-407.
34. Sze, K. Y.; Chan, W. K.; Pian, T. H. H. (2002): An eight-node hybrid-stress solid-shell element for geometric non-linear analysis of elastic shells. International Journal for Numerical Methods in Engineering, vol. 55, pp. 853-878.
35. Sze, K. Y.; Liu, X. H.; Lo, S. H. (2004): Popular benchmark problems for geometric nonlinear analysis of shells. Finite Elements in Analysis and Design, vol. 40, pp. 1551-1569.
36. Timoshenko, S. P.; Goodier, J. N. (1970): Theory of Elasticity, 3rd edition, McGraw-Hill, NewYork.