A performance study on configurational force and spring-analogy based mesh optimization schemes

International Journal for Computational Methods in Engineering Science and Mechanics

Volumn 7, Issue 4, 2006, Pages 241-262

  Rajagopal, A ^a   Gangadharan, R ^a   Sivakumar, S M ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

Author keywords

Discretization Error; Material Forces; R Adaption; Spring Analogy

Indexed keywords

ADAPTIVE ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; OPTIMIZATION; SPRINGS (COMPONENTS); STRAIN;

DISCRETIZATION ERROR; MATERIAL FORCES; R-ADAPTION; SPRING ANALOGY;

LOADS (FORCES);

EID: 33646267419     PISSN: 15502287     EISSN: 15502295     Source Type: Journal    
DOI: 10.1080/15502280500388169     Document Type: Article

References (24)

1. Ainsworth, M., and Oden, J. T., A Posteriori Error Estimation in Finite Element Analysis. Wiley Interscience, New York (2000).
2. Bahuska, I., and Rheinbold, W. C., "A-posteriori error estimators for the finite element method," Int. J. Numerical Methods in Engineering 12, 1597-1615 (1978).
3. Braun, M., "Configurational forces induced by finite element discretization," Proc. Estonian Acad. Sci. Phys. Math. 46, (1/2), 24-31 (1997).
4. Cook, R. D., Malkus, S. D., and Plesha, M. E., Concpts and Applications of Finite Element Analysis. Third edition, John Wiley & Sons, New York (1988).
5. Eshelby, J. D., "The elastic energy-momentum tensor," Journal of Elasticity 5(3-4), 321-335 (1975).
6. Gurtin, M. E., and PodioGuidugli, P., "On Configurational inertial forces at a phase interface," Journal of Elasticity 44, 255-269 (1996).
7. Jhon, O'Dow., A Unified Approach to the Finite Element Method and Error Analysis Procedures, Academic Press, New York (1998).
8. Jung, Ho-Cheng, "Adaptive grid optimization for structural analysis - geometry based approach," Computer Methids in Applied Mechanics and Engineering 107, 1-22 (1993).
9. Kelly, D. W., "The self-equilibration of residuals and complimentary a posteriori error estimates in finite element method," Intl Journal for Numerical Methods in Engineering 20, 1491-1506 (1984).
10. Kienzler, R., and Herrmann, G., Mechanics in Material space with Applications to Defect and Fracture Mechanics. Springer-Verlag, NY (2000).
11. Krishnamoorthy, C. S., and Mukherjee, S., "Adaptive finite element analysis with quadrilateral elements using a new h-refinement strategy," SADHANA 21(5), 623-652 (1996).
12. Maugin, G. A., "Material forces. Concepts and applications," Applied Mechanics Review 48(5), 213-245 (1995).
13. Muller, R., and Maugin, G. A., "On material forces and finite element discretization," Computational Mechanics 29, 52-60 (2002).
14. Muller, R., Kolling, S., and Gross, D., "On configurational forces in the context of the finite element method," Intl Journal for Numerical Methods in Engineering 53, 1557-1574 (2002).
15. Pierre, B., Koko, J., and Touzani, R., "Mesh r-adaption for unilateral contact problems," International Journal of Applied Mathematics and Computer Science 12, 9-16 (2002).
16. Peraire, J., Perio, J., and Morgan, K. "Adaptive remeshing for three-dimensional compressible flow computation," Journal of Computational Physics 103, 269-285 (1992).
17. Scott McRae, D. R., "Refinement grid adaptation algorithms and issues," Computational Methods in Applied Mechanics and Engineering 189, 1161-1182 (2000).
18. Thoutireddy, P., and Ortiz, M., "Variational mesh and shape optimization," Fifth World Congress on Computational Mechanics, July 7-12, Vienna. (2002).
19. Thoutireddy, P., Variational Arbitrary Lagrangian-Eulerian Method. PhD thesis. Pasadena, CA (2002).
20. Thoutireddy, P., Molinari, J. F., Repetto, E. A., and Ortiz, M. A., "Variational r-adaption and shape-optimization for finite-deformation elasticity," International Journal for Numerical Methods in Engineering 60(12), 1337-1351 (2004).
21. Thompson, J. F., Soni, B. K., and Weatherill, N. P., Handbook of Grid Generation. CRC Press, Boca Raton, FL (1999).
22. Yazdani, A. A., Gakwaya, A., and Dhatt, G., "A posteriori error estimator based on the second derivative of the displacement field for two-dimensional elastic problems," Computers and Structures 62, 317-338 (1997).
23. Zienkiewicz, O. C., and Zhu, J. Z., "A simple error estimator and adaptive procedure for practical engineering analysis," Intl Journal for Numerical Methods in Engineering 24, 337-357 (1987).
24. Zienkiewicz, O. C., and Zhu, J. Z., "Super convergence recovery techniques and a-posteriori error estimators," Intl Journal for Numerical Methods in Engineering 30, 1321-1339 (1990).