Finite deformation plate theory and large rigid-body motions

International Journal of Non-Linear Mechanics

Volumn 39, Issue 7, 2004, Pages 1093-1109

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

^a TAMBOV STATE TECHNICAL UNIVERSITY   (Russian Federation)

Author keywords

Finite deformations; Finite element method; First order multilayered plate theory; Large rigid body motions

Indexed keywords

FINITE ELEMENT METHOD; LAGRANGE MULTIPLIERS; PLATES (STRUCTURAL COMPONENTS); SHEAR DEFORMATION; STRAIN;

NEWTON-RAPHSON METHOD; RIGID-BODY MOTION;

NONLINEAR SYSTEMS;

EID: 0344308469     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7462(03)00099-4     Document Type: Article

References (36)

1. Dawe D.J. Rigid-body motions and strain-displacement equations of curved shell finite elements. Int. J. Mech. Sci. 14:1972;569-578.
2. Kulikov G.M., Plotnikova S.V. Efficient mixed Timoshenko-Mindlin shell elements. Int. J. Numer. Methods Eng. 55:2002;1167-1183.
3. Kulikov G.M., Plotnikova S.V. Simple and effective elements based upon Timoshenko-Mindlin shell theory. Comput. Methods Appl. Mech. Eng. 191:2002;1173-1187.
4. Noor A.K., Burton W.S. Assessment of shear deformation theories for multilayered composite plates. Appl. Mech. Rev. 42(1):1989;1-12.
5. Hodges D.H., Atilgan A.R., Danielson D.A. A geometrically nonlinear theory of elastic plates. Trans. ASME J. Appl. Mech. 60:1993;109-116.
6. Kulikov G.M. Refined global approximation theory of multilayered plates and shells. J. Eng. Mech. 127:2001;119-125.
7. Kulikov G.M. Analysis of initially stressed multilayered shells. Int. J. Solids Struct. 38:2001;4535-4555.
8. Kulikov G.M., Plotnikova S.V. Finite element formulation of straight composite beams undergoing finite rotations. Trans. Tambov State Tech. Univ. 7:2001;617-633.
9. Kulikov G.M., Plotnikova S.V. Investigation of locally loaded multilayered shells by mixed finite-element method. Part 1. Geometrically linear statement. Mech. Compos. Mater. 38:2002;397-406
10. Kulikov G.M., Plotnikova S.V. Investigation of locally loaded multilayered shells by mixed finite-element method. Part 2. Geometrically nonlinear statement. Mech. Compos. Mater. 38:2002;539-546.
11. Parisch H. A continuum-based shell theory for non-linear applications. Int. J. Numer. Methods Eng. 38:1995;1855-1883.
12. Park H.C., Cho C., Lee S.W. An efficient assumed strain element model with six DOF per node for geometrically non-linear shell. Int. J. Numer. Methods Eng. 38:1995;4101-4122.
13. Bathe K.J. Finite Element Procedures. 1996;Prentice-Hall, Englewood Cliffs, NJ.
14. Betsch P., Stein E. An assumed strain approach avoiding artificial thickness straining for a nonlinear 4-node shell element. Commun. Numer. Methods Eng. 11:1995;899-909.
15. Büchter N., Ramm E. Shell theory versus degeneration - a comparison in large rotation finite element analysis. Int. J. Numer. Methods Eng. 34:1992;39-59.
16. Kreja I., Schmidt R., Reddy J.N. Finite elements based on a first-order shear deformation moderate rotation shell theory with applications to the analysis of composite structures. Int. J. Non-Linear Mech. 32:1997;1123-1142.
17. Li M., Zhan F. The finite deformation theory for beam, plate and shell. Part IV. The FE formulation of Mindlin plate and shell based on Green-Lagrangian strain. Comput. Methods Appl. Mech. Eng. 182:2000;187-203.
18. Palmerio A.F., Reddy J.N., Schmidt R. On a moderate rotation theory of elastic anisotropic shells. Part I. Theory. Int. J. Non-Linear Mech. 25:1990;687-700
19. Palmerio A.F., Reddy J.N., Schmidt R. On a moderate rotation theory of elastic anisotropic shells. Part II. FE analysis. Int. J. Non-Linear Mech. 25:1990;701-714.
20. Simo J.C., Rifai M.S., Fox D.D. On a stress resultant geometrically exact shell model. Part IV. Variable thickness shells with through-the-thickness stretching. Comput. Methods Appl. Mech. Eng. 81:1990;91-126.
21. Vu-Quoc L., Deng H., Tan X. Geometrically exact sandwich shells. the static case Comput. Methods Appl. Mech. Eng. 189:2000;167-203.
22. Hughes T.J.R., Tezduyar T.E. Finite elements based upon Mindlin plate theory with particular reference to the four-node bilinear isoparametric element. Trans. ASME J. Appl. Mech. 48:1981;587-596.
23. Wempner G., Talaslidis D., Hwang C.M. A simple and efficient approximation of shell via finite quadrilateral elements. Trans. ASME J. Appl. Mech. 49:1982;115-120.
24. Basar Y., Itskov M., Eckstein A. Composite laminates. nonlinear interlaminar stress analysis by multi-layer shell elements Comput. Methods Appl. Mech. Eng. 185:2000;367-397.
25. Bischoff M., Ramm E. On the physical significance of higher order kinematic and static variables in a three-dimensional shell formulation. Int. J. Solids Struct. 37:2000;6933-6960.
26. Klinkel S., Gruttmann F., Wagner W. A continuum based three-dimensional shell element for laminated structures. Comput. Struct. 71:1999;43-62.
27. Kulikov G.M. Non-linear analysis of multilayered shells under initial stress. Int. J. Non-Linear Mech. 36:2001;323-334.
28. Washizu K. Variational Methods in Elasticity and Plasticity. 3rd Edition:1982;Pergamon Press, Oxford.
29. Crivelli L.A., et al. A three-dimensional non-linear Timoshenko beam based on the core-congruential formulation. Int. J. Numer. Methods Eng. 36:1993;3647-3673.
30. Li M. The finite deformation theory for beam, plate and shell. Part I. The two-dimensional beam theory. Comput. Methods Appl. Mech. Eng. 146:1997;53-63.
31. Hsiao K.M. Nonlinear analysis of general shell structures by flat triangular elements. Comput. Struct. 25:1987;665-675.
32. Barut A., Madenci E., Tessler A. Nonlinear analysis of laminates through a Mindlin-type shear deformable shallow shell element. Comput. Methods Appl. Mech. Eng. 143:1997;155-173.
33. Minguet P., Dugundji J. Experiments and analysis for composite blades under large deflections. Part I. Static Behavior. AIAA J. 28:1990;1573-1579.
34. Pai P.F., Anderson T.J., Wheater E.A. Large-deformation tests and total-Lagrangian finite-element analyses of flexible beams. Int. J. Solids Struct. 37:2000;2951-2980.
35. Rothert H., Dehmel W. Nonlinear analysis of isotropic, orthotropic and laminated plates and shells. Comput. Methods Appl. Mech. Eng. 64:1987;429-446.
36. To C.W.S., Wang B. Hybrid strain based geometrically nonlinear laminated composite triangular shell finite elements. Finite Elements Anal. Des. 33:1999;83-124.