Insight into finite element shell discretizations by use of the "basic shell mathematical model"

Computers and Structures

Volumn 83, Issue 1, 2005, Pages 69-90

  Lee, Phill Seung ^a   Bathe, Klaus Jürgen ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

Basic shell mathematical model; MITC shell elements; Shell structures

Indexed keywords

ELASTICITY; GEOMETRY; KINEMATICS; MATHEMATICAL MODELS; PROBLEM SOLVING; STRAIN; TENSORS; VECTORS;

BASIC SHELL MATHEMATICAL MODEL; FINITE ELEMENTS; MITC SHELL ELEMENTS; SHELL STRUCTURES;

FINITE ELEMENT METHOD;

EID: 10044234851     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2004.07.005     Document Type: Article

References (27)

1. Bathe KJ. Finite element procedures. New York: Prentice Hall; 1996.
2. Chapelle D, Bathe KJ. The finite element analysis of shells-fundamentals. Berlin: Springer-Verlag; 2003.
3. Chapelle D, Bathe KJ. The mathematical shell model underlying general shell elements. Int J Numer Methods Eng 2000;48:289-313.
4. Chapelle D, Bathe KJ. Fundamental considerations for the finite element analysis of shell structures. Comput Struct 1998;66:19-36. 711-2.
5. Lee PS, Bathe KJ. On the asymptotic behavior of shell structures and the evaluation in finite element solutions. Comput Struct 2002;80:235-55.
6. Bathe KJ, Chapelle D, Lee PS. A shell problem 'highly sensitive' to thickness changes. Int J Numer Methods Eng 2003;57:1039-52.
7. Pitkäranta J, Sanchez-Palencia E. On the asymptotic behaviour of sensitive shells with small thickness. CR Acad Sci II 1997;325:127-34.
8. Baiocchi C, Lovadina C. A shell classification by interpolation. Math Mod Methods Appl Sci 2002;12:1359-80.
9. Dvorkin EN, Bathe KJ. A continuum mechanics based four-node shell element for general nonlinear analysis. Eng Comput 1984;1:77-88.
10. Bathe KJ, Dvorkin EN. A formulation of general shell elements - the use of mixed interpolation of tensorial components. Int J Numer Methods Eng 1986;22:697-722.
11. Bucalem ML, Bathe KJ. Higher-order MITC general shell elements. Int J Numer Methods Eng 1993;36:3729-54.
12. Lee PS, Bathe KJ. Development of MITC isotropic triangular shell finite elements. Comput Struct 2004;82: 945-62.
13. Bathe KJ, Iosilevich A, Chapelle D. An inf-sup test for shell finite elements. Comput Struct 2000;75:439-56.
14. Bathe KJ, Iosilevich A, Chapelle D. An evaluation of the MITC shell elements. Comput Struct 2000;75:1-30.
15. Bathe KJ. The inf-sup condition and its evaluation for mixed finite element methods. Comput Struct 2001;79: 243-52. 971.
16. Killer JF, Bathe KJ. Measuring convergence of mixed finite element discretizations: an application to shell structures. Comput Struct 2003;81:639-54.
17. Noor AK, Belytschko T, Simo JC. editors. Analytical and computational models of shells. ASME CED-Vol 3; 1989.
18. Büchter N, Ramm E. Shell theory versus degeneration - a comparison in large rotation finite element analysis. Int J Numer Methods Eng 1992;34:39-59.
19. Bernadou M. Finite element methods for thin shell problems. Chichester: Wiley; 1996.
20. Destuynder P, Salaün M. A mixed finite element for shell model with free edge boundary conditions. Part 3. Numerical aspects. Comput Methods Appl Mech Eng 1996;136:273-92.
21. Ibrahimbegović A. Stress resultant geometrically exact shell theory for finite rotations and its finite element implementation. Appl Mech Rev 1997;50:199-226.
22. Başar Y, Krätzig WB. Theory of shell structures. 2nd ed. Düsseldorf: Fortschritts-Berichte VDI; 2001.
23. Krätzig WB, Jun D. On 'best' shell models - from classical shells, degenerated and multi-layered concepts to 3D. Arch Appl Mech 2003;73:1-25.
24. Cho M, Roh HY. Development of geometrically exact new shell elements based on general curvilinear co-ordinates. Int J Numer Methods Eng 2003;56:81-115.
25. Chapelle D, Oliveira DL, Bucalem ML. MITC elements for a classical shell model. Comput Struct 2003;81:523-33.
26. Bathe KJ, Lee PS, Killer JF. Towards improving the MITC9 shell element. Comput Struct 2003;81:477-89.
27. Chapelle D, Ferent A, Bathe KJ. 3D-shell elements and their underlying mathematical model. Math Models Methods Appl Sci 2004;14:105-42.