Simple finite element model for the geometrically nonlinear analysis of thin shells

Computational Mechanics

Volumn 24, Issue 2, 1999, Pages 127-137

  Providas, E ^a   Kattis, M A ^a  

^a UNIVERSITY OF THESSALY   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PLATES (STRUCTURAL COMPONENTS); STIFFNESS MATRIX;

VON KARMAN THEORY;

STRUCTURAL ANALYSIS;

EID: 0032598825     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004660050445     Document Type: Article

References (35)

1. Allman DJ (1982) Improved finite element models for the large displacement bending and post buckling analysis of thin plates. Internat. J. Solids Structures 18(9):737-762
2. Allman DJ (1989) On the general theory of the stability of equilibrium of discrete conservative systems. Aeronautical J.:29-35
3. Bäcklund J (1973) Finite element analysis of nonlinear structures. Ph.D. thesis. Göteborg: Chalmers Tekniska Högskola
4. Bischoff M, Ramm E (1997) Shear deformable shell elements for large strains and rotations. Internat. J. Numer. Methods Engrg. 40:4427-4449
5. Bout A (1993) A displacement-based geometrically nonlinear constant stress element. Internat. J. Numer. Methods Engrg. 36:1161-1188
6. Chen KK (1979) A triangular plate finite element for large-displacement elastic-plastic analysis of automobile structural components. Comput. Struct. 10:203-215
7. Chróscielewski J, Makowski J, Stumpf H (1997) Finite element analysis of smooth, folded and multi-shell structures. Comput. Methods Appl. Mech. Engrg. 141:1-46
8. Dawe DJ (1972) Shell analysis using a simple facet element. J. Strain Analysis 7(4):266-270
9. Hellan K (1967) Analysis of elastic plates in flexure by a simplified finite element method. Civ. Engrg. Bldg. Construction Ser. No. 46. Acta Polytechnica Scandinavica
10. Herrmann LR (1967) Finite-element bending analysis of plates. J. Engrg. Mech. Div. ASCE 93 (EM5):13-26
11. Herrmann LR, Campbell DM (1968) A finite-element analysis for thin shells. AIAA J. 6(10):1842-1847
12. Hibbitt HD, Karlsson B, Sorensen EP (1995) ABAQUS Theory Manual HKS Inc.
13. Irons BM, Razzaque A (1972) Experience with the patch test for convergence of finite elements. In: Aziz AK (ed.) Mathematical foundations of the finite element method with applications to partial differential equations, New York: Academic Press 557-587
14. von Kármán T (1910) Festigkeitsprobleme im maschinenbau. In: Encyklopadie der mathematischen wissenschaften, vol. IV/4, c, Leipzig 311-385
15. van Keulen F, Booij J (1996) Refined consistent formulation of a curved triangular finite rotation shell element. Internat. J. Numer. Methods Engrg. 39:2803-2820
16. van Keulen F, Bout A, Ernst L (1993) Nonlinear thin shell analysis using a curved triangular element. Comput. Methods Appl. Mech. Engrg. 103:315-343
17. Koiter WT (1945) Over de stabiliteit van het elastisch evenwicht. Amsterdam: H. J. Paris
18. Leicester RH (1968) Finite deformations of shallow shells. J. Engrg. Mech. Div. ASCE 94:1409-1423
19. Levy S (1942) Bending of rectangular plates with large deflections, NASA Technical Note No. 846
20. Matsui T, Matsuoka O (1976) A new finite element scheme for instability analysis of thin shells. Internat. J. Numer. Methods Engrg. 10:145-170
21. Meek JL, Tan HS (1986) Instability analysis of thin plates and arbitrary shells using a faceted shell element with loof nodes. Comput. Methods Appl. Mech. Engrg. 57:143-170
22. Morley LSD (1971) The constant-moment plate-bending element. J. Strain Analysis 6(1):20-24
23. Morley LSD (1991) Geometrically nonlinear constant moment triangle which passes the von Kármán patch test. Internat. J. Numer. Methods Engrg. 31:241-263
24. Morley LSD, Morris AJ (1978) Conflict between finite elements and shell theory. Royal Aircraft Establishment Report London
25. Morley LSD, Mould MP (1987) The role of bending in the finite element analysis of thin shells. Finite Elements in Analysis and Design 3:213-240
26. Murray DW, Wilson EL (1969) Finite element large deflection analysis of plates. J. Engrg. Mech. Div. ASCE 95 (1):143-165
27. Peng X, Crisfield MA (1992) A consistent co-rotational formulation for shells using the constant stress/constant moment triangle. Internat. J. Numer. Methods Engrg. 35:1829-1847
28. Pica A, Wood RD (1980) Postbuckling behaviour of plates and shells using a Mindlin shallow shell formulation. Comput. Struct. 12:759-768
29. Providas E (1990) On the geometrically nonlinear constant moment triangle (with a note on drilling rotations). Ph.D. thesis, London: Brunel University
30. Providas E (1991) The patch test in the von Kármán geometrically nonlinear theory. In: Whiteman JR (ed.) The mathematics of finite elements and applications VII, London: Academic Press 413-423
31. Sabir AB, Lock AC (1972) The application of finite elements to the large deflection geometrically nonlinear behaviour of cylindrical shells. In: Brebbia CA, Tottenham H, (eds) Variational methods in engineering, Southampton: Southampton University Press 7/66-7/75
32. Turner MJ, Clough RW, Martin HC, Topp LJ (1956) Stiffness and deflection analysis of complex structures. J. Aeronaut. Sci. 23:805-824
33. Yang HTY, Saigal S, Liaw DG (1990) Advances of thin shell finite elements and some applications-Version I. Comput. Struct. 35:481-504
34. Zhu Y, Zacharia T (1996) A new on-point quadrature, quadrilateral shell element with drilling degrees of freedom. Comput. Methods Appl. Mech. Eng. 136:165-203
35. Zienkiewicz OC, Taylor RL (1991) The Finite Element Method, vol. 2: Solid and Fluid Mechanics, Dynamics and Non-linearity, 4th edn, New York:McGraw-Hill