Energy-based r-adaptivity: A solution strategy and applications to fracture mechanics

International Journal of Fracture

Volumn 147, Issue 1-4, 2007, Pages 117-132

  Scherer, Michael ^a   Denzer, Ralf ^a   Steinmann, Paul ^b  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

Barrier method; Constrained energyminimization; Hyperelasticity; Material forces; Mesh optimization

Indexed keywords

FINITE ELEMENT METHOD; MESH GENERATION; OPTIMIZATION; POTENTIAL ENERGY;

BARRIER METHOD; ENERGY BASED R-ADAPTIVITY; HYPERELASTICITY;

FRACTURE MECHANICS;

EID: 41449100284     PISSN: 03769429     EISSN: 15732673     Source Type: Journal    
DOI: 10.1007/s10704-007-9143-9     Document Type: Conference Paper

References (29)

1. Armero F and Love E (2003). An arbitrary Lagrangian-Eulerian finite element method for finite strain plasticity. Int J Numer Meth Eng 57: 471-508
2. Askes H, Kuhl E and Steinmann P (2004). An ALE formulation based on spatial and material settings of continuum mechanics. Part 2: classification and applications. Comput Methods Appl Mech Eng 193: 4223-4245
3. Bathe KJ and Sussman TD (1983). An algorithm for the construction of optimal finite element meshes in linear elasticity. Comput Methods Nonlinear Solids Struct Mech 54: 15-36
4. Bertsekas DP (1995). Nonlinear programming. Athena Scientific, Belmont, MA
5. Braun M (1997). Configurational forces induced by finite-element discretization. Proc Estonian Acad Sci Phys Math 46: 24-31
6. Carpenter WC and Zendegui S (1982). Optimum nodal locations for a finite element idealization. Eng Optim 5: 215-221
7. Carroll WE and Barker RM (1973). A theorem for optimum finite-element idealizations. Int J Solids Struct 9: 883-895
8. Felippa CA (1976a). Numerical experiments in finite element grid optimization by direct energy search. Appl Math Model 1: 239-244
9. Felippa CA (1976b). Optimization of finite element grids by direct energy search. Appl Math Model 1: 93-96
10. Gill PE, Murray W, Wright MH (1981) Practical optimization. Academic Press
11. Holzapfel GA (2000). Nonlinear solid mechanics. Wiley, Chichester
12. Hughes TJR (1987). The finite element method. Dover Publications, New York
13. Jarre S (2004). Optimierung. Springer-Verlag, Berlin
14. Knupp PM (2000a). Achieving finite element mesh quality via optimization of the Jacobian matrix norm and associated quantities. Part I - a framework for surface mesh optimization. Int J Numer Meth Eng 48: 401-420
15. Knupp PM (2000b). Achieving finite element mesh quality via optimization of the Jacobian matrix norm and associated quantities. Part II - a framework for volume mesh optimization and the condition number of the Jacobian matrix. Int J Numer Meth Eng 48: 1165-1185
16. Kuhl E, Askes H and Steinmann P (2004). An ALE formulation based on spatial and material settings of continuum mechanics. Part 1: Generic hyperelastic formulation. Comput Methods Appl Mech Eng 193: 4207-4222
17. Luenberger DG (1973). Introduction to linear and nonlinear programming. Addison-Wesley Publishing Company, Reading
18. Marsden JE and Hughes TJR (1983). Mathematical foundations of elasticity.. over Publications, New York
19. McNeice GM and Marcal PV (1973). Optimization of finite element grids based on minimum potential energy. Trans ASME J Eng Ind 95(1): 186-190
20. Mosler J and Ortiz M (2006). On the numerical implementation of varational arbitrary Lagrangian-Eulerian (VALE) formulations. Int J Numer Meth Eng 67: 1272-1289
21. Mueller R and Maugin GA (2002). On material forces and finite element discretizations. Comput Mech 29: 52-60
22. Mueller R, Kolling S and Gross D (2002). On configurational forces in the context of the finite element method. Int J Numer Meth Eng 53: 1557-1574
23. Mueller R, Gross D and Maugin GA (2004). Use of material forces in adaptive finite element methods. Comput Mech 33: 421-434
24. Rajagopal A, Gangadharan R and Sivakumar SM (2006). On material forces and finite element discretizations. Int J Comput Meth Eng Sci Mech 7: 241-262
25. Steinmann P, Ackermann D and Barth FJ (2001). Application of material forces to hyperelastostatic fracture mechanics. Part II: Computational setting. Int J Solids Struct 38: 5509-5526
26. Sussman T and Bathe KJ (1985). The gradient of the finite element variational indicator with respect to nodal point co-ordinates: An explicit calculation and application in fracture mechanics and mesh optimization. Int J Numer Meth Eng 21: 763-774
27. Thoutireddy P (2003) Variational arbitrary Lagrangian-Eulerian method. Ph.D. Thesis, California Institute of Technology, Passadena, California
28. Thoutireddy P and Ortiz M (2004). A variational r-adaption and shape-optimization method for finite-deformation elasticity. Int J Numer Meth Eng 61: 1-21
29. Wriggers P (2001). Nichtlineare finite-element-methoden. Springer-Verlag, Berlin