Influence functions and goal-oriented error estimation for finite element analysis of shell structures

International Journal for Numerical Methods in Engineering

Volumn 63, Issue 5, 2005, Pages 709-736

  Grätsch, Thomas ^a   Bathe, Klaus Jürgen ^a  

^a Massachusetts Institute of Technology   (United States)

Author keywords

Goal oriented error estimation; Influence functions; MITC shell elements; Shell structures

Indexed keywords

ASYMPTOTIC STABILITY; ERROR ANALYSIS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; THICKNESS MEASUREMENT;

CANCELLATION EFFECTS; ERROR ESTIMATIONS; GOAL-ORIENTED ERROR ESTIMATIONS; MITC FINITE ELEMENT SHELL DISCRETIZATION;

SHELLS (STRUCTURES);

FINITE ELEMENT ANALYSIS;

EID: 20444462687     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1298     Document Type: Article

References (30)

1. Bathe KJ (ed.). Computational Fluid and Solid Mechanics. Elsevier: Amsterdam, 2003.
2. Chapelle D, Bathe KJ. Fundamental considerations for the finite element analysis of shell structures. Computers and Structures 1998; 66 :19-36.
3. Chapelle D, Bathe KJ. The Finite Element Analysis of Shells - Fundamentals. Springer: Berlin, 2003.
4. Çirak F, Ramm E. A posteriori error estimation and adaptivity for linear elasticity using the reciprocal theorem. Computer Methods in Applied Mechanics and Engineering 1998; 156:351-362.
5. Prudhomme S, Oden JT, Westermann T, Bass J, Botkin M. Practical methods for a posteriori error estimation in engineering applications. International Journal for Numerical Methods in Engineering 2003; 56:1193-1224.
6. Oden JT, Prudhomme S, Westermann T, Bass J, Botkin M. Error estimation of eigenfrequencies for elasticity and shell problems. Mathematical Models and Methods in Applied Sciences 2003; 13:323-344.
7. Bangerth W, Rannacher R. Adaptive Finite Element Methods for Differential Equations. Birkhäuser: Basel, 2003.
8. Becker R, Rannacher R. A feed-back approach to error control in finite element methods: basic analysis and examples. East - West Journal of Numerical Mathematics 1996; 4:237-264.
9. Rannacher R, Suttmeier FT. A feed-back approach to error control in finite element methods: application to linear elasticity. Computational Mechanics 1997; 19:434-446.
10. Bathe KJ. Finite Element Procedures. Prentice-Hall: Englewood Cliffs, NJ, 1996.
11. Hiller JF, Bathe KJ. Measuring convergence of mixed finite element discretizations: an application to shell structures. Computers and Structures 2003; 81:639-654.
12. Chapelle D, Bathe KJ. The mathematical shell model underlying general shell elements. International Journal for Numerical Methods in Engineering 2000; 48:289-313.
13. Bathe KJ, Iosilevich A, Chapelle D. An evaluation of the MITC shell elements. Computers and Structures 2000; 75:1-30.
14. Dvorkin EN, Bathe KJ. A continuum mechanics based four-node shell element for general nonlinear analysis. Engineering Computations 1984; 1:77-88.
15. Bucalem M, Bathe KJ. Higher-order MITC general shell elements. International Journal for Numerical Methods in Engineering 1993; 36:3729-3754.
16. Bathe KJ, Lee PS, Hiller JF. Towards improving the MITC9 shell element. Computers and Structures 2003; 81:1085-1097.
17. Babuška I, Strouboulis T. The Finite Element Method and its Reliability. Oxford Science Publications: Oxford, 2001.
18. Prudhomme S, Oden JT. On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors. Computer Methods in Applied Mechanics and Engineering 1999; 176:313-331.
19. Eriksson K, Estep D, Hansbo P, Johnson C. Introduction to adaptive methods for differential equations. Acta Numerica 1995; 4 :105-158.
20. Estep D. A posteriori error bounds and global error control for approximations of ordinary differential equations. SIAM Journal on Numerical Analysis 1995; 32:1-48.
21. Grätsch T, Hartmann F. Finite element recovery techniques for local quantities of linear problems using fundamental solutions. Computational Mechanics 2003; 33:15-21.
22. Oden JT, Prudhomme S. Goal-oriented error estimation and adaptivity for the finite element method. Computers and Mathematics with Applications 2001; 41:735-756.
23. Paraschivoiu M, Peraire J, Patera A. A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations. Computer Methods in Applied Mechanics and Engineering 1997; 150: 289-312.
24. Paraschivoiu M, Patera A. A hierarchical duality approach to bounds for the outputs of partial differential equations. Computer Methods in Applied Mechanics and Engineering 1998; 158:389-407.
25. Huerta A, Rodriguez-Ferran A, Diez P, Sarrate J. Adaptive finite element strategies based on error assessment. International Journal for Numerical Methods in Engineering 1999; 46:1803-1818.
26. Chapelle D, Bathe KJ. Optimal consistency errors for general shell elements. Comptes Rendus de l'Académie des Sciences. Série I-Mathématique, t. 332, 2001; 771-776.
27. Estep D, Holst M, Larson M. Generalized Green's functions and the effective domain of influence. SIAM Journal on Scientific Computing, to appear.
28. Grätsch T, Bathe KJ. A posteriori error estimation techniques in practical finite element analysis. Computers and Structures 2005; 83:235-265.
29. Lee PS, Bathe KJ. On the asymptotic behavior of shell structures and the evaluation in finite element solution. Computers and Structures 2002; 80:235-255.
30. Lee PS, Bathe KJ. Development of MITC isotropic triangular shell finite elements. Computers and Structures 2004; 82:945-962.