Rapid stress analysis of geometrically complex domains using implicit meshing

Computational Mechanics

Volumn 30, Issue 5-6, 2003, Pages 460-478

  Bishop, J ^a  

^a GENERAL MOTORS CORPORATION   (United States)

Author keywords

Embedded fictitious domain; Finite element integration; Hermite; Implicit meshing; Lagrange; Weak variational form

Indexed keywords

COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; INTEGRATION; LAGRANGE MULTIPLIERS;

EMBEDDED FICTITIOUS DOMAIN; FINITE ELEMENT INTEGRATION; IMPLICIT MESHING METHOD; WEAK VARIATIONAL FORM;

STRESS ANALYSIS;

EID: 0037590085     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-003-0424-5     Document Type: Article

References (35)

1. ABAQUS/Standard Version 6.2, Hibbitt, Karlson, & Sorensen Inc., 1080 Main St., Pawtucket, Rhode Island 02860-4847
2. ABAQUS/Standard Version 6.2 (2001) ABAQUS/Standard user's manual, Version 6.1, Hibbitt, Karlson, & Sorensen Inc., 1080 Main St., Pawtucket, Rhode Island 02860-4847 Vol. 1, (4.1.2-2):(4.1.2-4)
3. Bank R, Sherman A, Weiser A (1983) Refinement algorithms and data structures for regular local mesh refinement. Scientific Computing 3: 17
4. Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P (1996) Meshless methods: An overview and recent developments. Comput. Meth. Appl. Mech. Eng. 139: 3-47
5. Belytschko T, Lu Y, Gu L (1994) Element-free Galerkin Methods. Int. J. Numer. Meth. Eng. 37: 229-256
6. Bezuszka S, Kenney M, Silvey L (1977) Tessellations: the geometry of patterns Chicago, Illinois, Creative Publications 78
7. Cordes L, Moran B (1996) Treatment of material discontinuity in the element-free Galerkin method. Comput. Meth. Appl. Mech. Eng. 139: 75-89
8. Cruchaga M, Celentano D, Tezduyar T (2001) A moving Lagrangian interface technique for flow computations over fixed meshes. Comput. Meth. Appl. Mech. Eng. 191: 525-543
9. Dolbow J, Belytschko T (1999) Numerical integration of the Galerkin weak form in meshfree methods. Comput. Mech. 23: 219-230
10. Franca L, Dutra Do Carmo E (1989) The Galerkin gradient least-squares method. Comput. Meth. Appl. Mech. Eng. 74(1): 41-54
11. Glowinski R, Pan T, Hesla T, Joseph D (1999) A distributed Lagrange multiplier/fictitious domain method for particulate flows. Int. J. Multiphase Flow 25: 755-794
12. Glowinski R, Pan T, Periaux J (1994) A fictitious domain method for Dirichlet problem and applications. Comput. Meth. Appl. Mech. Eng. 111: 283-303
13. Glowinski R, Pan T, Wells R, Zhou X (1992) Wavelet and finite element solutions for the Neumann problem using fictitious domains. Technical Report, Rice University, Computational Mathematics Laboratory
14. Haslinger J, Jedelsky D (1996) Genetic algorithms and fictitious domain based approaches in shape optimization. Struc. Optim. 12: 257-264
15. Hughes T (1987a) The finite element method: linear static and dynamic finite-element analysis. (1987) Prentice-Hall, Englewood Cliffs, New Jersey, pp. 57-108
16. Hughes T (1987b) The finite element method: linear static and dynamic finite-element analysis Prentice-Hall, Englewood Cliffs, New Jersey, p. 172
17. Hughes T, Franca L (1987) A new finite element formulation for computational fluid dynamics: VII. The Stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity/pressure spaces. Comput. Meth. Appl. Mech. Eng. 65(1): 85-96
18. Johansen H, Colella P (1998) A cartesian grid embedded boundary method for Poisson's equation on irregular domains. J. Comput. Phys. 147: 60-85
19. Ko J, Kurdila A, Wells R, Zhou X (1996) On the conditioning of numerical boundary measures in wavelet Galerkin methods. Commun. Numer. Meth. Eng. 12: 281-294
20. Kunisch K, Peichl G (2001) Numerical gradients for shape optimization based on embedding domain techniques. Comput. Optim. Appl. 18: 95-114
21. Kunoth A (2001) Wavelet techniques for the fictitious-domain-Lagrange-multiplier-approach. Numer. Algorithms 27: 291-316
22. Kurdila A, Sun T, Grama P, Ko J (1995) Affine fractal interpolation functions and wavelet-based finite elements. Comput. Mech. 17: 169-185
23. Larson R, Hostetler R (1986) Calculus with Analytic Geometry, 3rd edn. D.C. Health & Co., Lexington, Massachusetts, p. 766
24. Li S, Liu W (2002) Mesh free and particle methods and their applications. Appl. Mech. Rev. 55(91): 1-34
25. McKenney A, Greengard L, Mayo A (1995) A Fast poisson solver for complex geometries. J. Comp. Phys. 118: 348-355
26. O'Rourke J (1998a) Computational geometry in C. Cambridge University Press, Cambridge, United Kingdom, pp. 1-32
27. O'Rourke J (1998b) Computational geometry in C. Cambridge University Press, Cambridge, United Kingdom
28. Rheinboldt W, Mesztenyi C (1980) On a data structure for adaptive finite element mesh refinements. ACM Trans. Math. Software 6(2): 166-187
29. Sukumar N, Chopp D, Moes N, Belytschko T (2001) Modeling holes and inclusions by level sets in the extended finite-element method. Comput. Meth. Appl. Mech. Eng. 190: 6183-6200
30. Timoshenko S, Goodier J (1987) Theory of elasticity, 3rd edn., McGraw-Hill, New York, New York pp. 90-95
31. Unigraphics (2002) Version 18, Unigraphics Solutions Inc., 10824 Hope Street, Cypress, California 90630
32. Zienkiewicz O (1977) The Finite Element Method, 3rd edn., McGraw-Hill, London, pp. 261-262
33. Zienkiewicz O, Zhu J (1995) Superconvergence and the superconvergent patch recovery. Finite Elem. Anal. Design 19: 11-23
34. Zohdi T, Feucht M, Gross D, Wriggers P (1998) A description of macroscopic damage via microstructural relaxation. Int. J. Numer. Meth. Eng. 43: 493-507
35. Zohdi T, Wriggers P (2001) Aspects of the computational testing of the mechanical properties of microheterogeneous material samples. Int. J. Numer. Meth. Eng. 50: 2573-2599