Remarks on variational shape sensitivity analysis based on local coordinates

Engineering Analysis with Boundary Elements

Volumn 32, Issue 11, 2008, Pages 971-985

  Barthold, F J ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Continuum mechanics; Convected coordinates; Differentiable manifolds; Fictitious load; Intrinsic concept; Intrinsic coordinates; Local coordinates; Pseudo load; Sensitivity analysis; Shape optimisation; Singular value decomposition

Indexed keywords

BIOMECHANICS; BOUNDARY ELEMENT METHOD; COMPUTATIONAL MECHANICS; CONTINUUM MECHANICS; DIFFERENTIAL EQUATIONS; ELASTICITY; FINITE ELEMENT METHOD; INVERSE PROBLEMS; MATERIALS SCIENCE; MATHEMATICAL PROGRAMMING; MECHANICS; NONLINEAR PROGRAMMING; NUMERICAL ANALYSIS; NUMERICAL METHODS; SEPARATION; SINGULAR VALUE DECOMPOSITION; STRUCTURAL DESIGN; STRUCTURAL OPTIMIZATION;

CONVECTED COORDINATES; DIFFERENTIABLE MANIFOLDS; FICTITIOUS LOAD; INTRINSIC CONCEPT; INTRINSIC COORDINATES; LOCAL COORDINATES; PSEUDO LOAD; SHAPE OPTIMISATION;

SENSITIVITY ANALYSIS;

EID: 53249149575     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2007.09.007     Document Type: Article

References (59)

1. Griewank A. Evaluating derivatives: principles and techniques of algorithmic differentiation. In: Frontiers in applied mathematics, vol. 19. Philadelphia, PA: SIAM; 2000.
2. Kleiber M., Antúnez H., Hien T., and Kowalczyk P. Parameter sensitivity in nonlinear mechanics: theory and finite element computations (1997), Wiley, Chichester
3. Haug E., Choi K., and Komkov V. Design sensitivity analysis of structural systems (1986), Academic Press, Orlando
4. Arora J. An exposition of the material derivative approach for structural shape sensitivity analysis. Comput Meth Appl Mech Eng 105 (1993) 41-62
5. Haber R. A new variational approach to structural shape design sensitivity analysis. In: Mota Soares C. (Ed). Computer aided optimal design vol. 27 (1987), Springer, New York 573-587
6. Tortorelli D., and Wang Z. A systematic approach to shape sensitivity analysis. Int J Solids Struct 30 9 (1993) 1181-1212
7. Kamat M, editor. Structural optimization: status and promise. In: Progress in astronautics and aeronautics, vol. 150. Washington, DC: AIAA; 1993.
8. Choi K, Kim N-H. Structural sensitivity analysis and optimization 1-linear systems. In: Mechanical Engineering Series. Berlin: Springer; 2005.
9. Choi K, Kim N-H. Structural sensitivity analysis and optimization 2-nonlinear systems and applications. In: Mechanical Engineering Series. Berlin: Springer; 2005.
10. Truesdell C., and Noll W. The nonlinear field theories of mechanics. In: Flügge S. (Ed). Handbuch der Physik III/3 (1965), Springer, Berlin
11. Truesdell C., and Noll W. The nonlinear field theories of mechanics. 3rd ed. (2004), Springer, Berlin
12. Zienkiewicz O., and Taylor T. The finite element method. 6th ed. (2005), Butterworth-Heinemann
13. Brebbia C. The boundary element method for engineers (1978), Pentech Press, London
14. Brebbia C. Boundary element methods (1981), Springer, Berlin
15. Hartmann F. Introduction to boundary element. Theory and applications (1989), Springer, Berlin
16. Farin G, Hoschek J, Kim M-S, editors. Handbook of computer aided geometric design. Amsterdam: Elsevier; 2002.
17. Maugin G, Steinmann P, editors. Mechanics of material forces. Berlin: Springer; 2005.
18. Murray J. Mathematical biology I: an introduction. 3rd ed. (2002), Springer, Berlin
19. Murray J. Mathematical biology II: spatial methods and biomedical applications. 3rd ed. (2003), Springer, Berlin
20. Noll W. A new mathematical theory of simple materials. Arch Ration Mech Anal 48 1 (1972) 1-50
21. Barthold F.-J., and Stein E. A continuum mechanical based formulation of the variational sensitivity analysis in structural optimization. Part I: analysis. Struct Optim 11 1/2 (1996) 29-42
22. Noll W. Five contributions of natural philosophy. Part 3: updating the nonlinear field theories of mechanics. Technical report, Carnegie Mellon University, published on internet: 〈www.math.cmu.edu/∼wn0g/noll/FC.pdf〉; 2004.
23. Noll W. A frame-free formulation of elasticity. J Elasticity 83 3 (2006) 291-307
24. Barthold F-J. Theorie und Numerik zur Berechnung und Optimierung von Strukturen aus isotropen, hyperelastischen Materialien. Dissertation, Institut für Baumechanik und Numerische Mechanik, Universität Hannover; 1993. URL: 〈http://hdl.handle.net/2003/24388〉.
25. Barthold F.-J., and Stein E. Variational sensitivity analysis and optimal design in finite elasticity-with applications to rubber materials. In: Olhoff N., and Rozvany G. (Eds). Proceedings of the first world congress on structural and multidisciplinary optimization (1995), Pergamon, Oxford 413-420
26. Barthold F.-J., and Stein E. Implementing variational design sensitivity analysis. In: Gutkowski W., and Mróz Z. (Eds). Proceedings of the second world congress on structural and multidisciplinary optimization vol. 1 (1997), Institute of Fundamental Technological Research, Polish Academy of Science, Warschau 181-186
27. Barthold F.-J. Remarks on linear and nonlinear variational design sensitivity analysis. In: Mota Soares C., Mota Soares C., and Freitas M. (Eds). Mechanics of composite materials and structures (1999), Kluwer Academic Publishers, Dordrecht 331-339
28. Barthold F-J. Zur Kontinuumsmechanik inverser Geo metrieprobleme, Habilitation, Braunschweiger Schriften zur Mechanik 44-2002, TU Braunschweig; 2002. URL: 〈http://hdl.handle.net/2003/23095〉.
29. Barthold F.-J. Continuum mechanics and inverse problems. In: Toropov V., Sienz J., and Querin O. (Eds). Proceedings of the 5th ASMO UK/ISSMO conference on engineering design optimization (2004)
30. Barthold F-J. A short guide to variational design sensitivity analysis. In: Herskovits J, Mazorche S, Canelas A, editors. WCSMO 6-CDROM proceedings, ISSMO; 2005.
31. Marsden J., and Hughes T. Mathematical foundations of elasticity (1983), Prentice-Hall, Englewood Cliffs
32. Bertram A. Axiomatische Einführung in die Konti-nuumsmechanik (1989), BI-Wissenschaftsverlag, Mannheim
33. Abraham R., Marsden J., and Ratiu T. Manifolds, tensor analysis, and applications (1983), Addison-Wesley, Reading
34. Krawietz A. Materialtheorie. Mathematische Beschrei-bung des phänomenologischen thermomechanischen Verhaltens (1986), Springer, Berlin
35. Bertram A. Elasticity and plasticity of large deformations (2005), Springer, Berlin
36. Hughes T., and Pister K. Consistent linearization in mechanics of solids and structures. Comput Struct 8 (1978) 391-397
37. Maugin G.A. Material inhomogeneities in elasticity (1993), Chapman & Hall, London
38. Gurtin M. Configurational forces as basic concepts of continuum physics (2000), Springer, New York
39. Kienzler R., and Hermann G. Mechanics in material space (2000), Springer, Berlin
40. Barthold F.-J., and Mesecke S. Remarks on computing the energy release rate and its sensitivities. In: Mota Soares C., Mota Soares C., and Freitas M. (Eds). Mechanics of composite materials and structures (1999), Kluwer Academic Publishers, Dordrecht 341-350
41. Barthold F.-J. A structural optimization viewpoint on configurational mechanics. Proc Appl Math Mech 3 1 (2003) 246-247
42. Barthold F.-J. On structural optimization and configurational mechanics. In: Maugin G., and Steinmann P. (Eds). Mechanics of material forces (2005), Springer, Berlin 219-228
43. Barthold F-J. Remarks on the application of design sensitivity analysis to fracture mechanics. In: Proceedings of the international congress fracture (ICF 11); 2005.
44. Materna D., and Barthold F.-J. Coherence of structural optimization and configurational mechanics. Proc Appl Math Mech 6 1 (2006) 245-246
45. Materna D, Barthold F-J. Relations between structural optimization and configurational mechanics with applications to mesh optimization. In: Sienz J, Querin O, Toropov V, Gosling P, editors. Proceedings of the 6th ASMO-UK/ISSMO conference on engineering design optimization. University of Leeds, UK; 2006. p. 173-81.
46. Materna D, Barthold F-J. On variational sensitivity analysis and configurational mechanics. Comput Mech 2008;41(5):661-81.
47. Materna D, Barthold F-J. Variational design sensitivity analysis in the context of structural optimization and configurational mechanics. J Fract 2007;147(1-4):133-55.
48. Barthold F-J, Wiechmann K. A comparison of displacement and mixed finite element formulations for variational design sensitivity analysis. In: Mota Soares, CA, et al, editors. III European conference on computational mechanics. Paper no. 2003. 2006.
49. Barthold F-J, Materna D. Remarks on different strategies for variational design sensitivity analysis. In: 7th world congress on structural and multidisciplinary optimization. Paper no. A0463. 2007; p. 1348-57.
50. Barthold F.-J., and Firuziaan M. Optimization of hyperelastic materials with isotropic damage. Struct Optim 20 1 (2000) 12-21
51. Barthold F.-J., and Wiechmann K. Variational design sensitivity for inelastic deformations. In: Owen D., Oñate E., and Hinton E. (Eds). Computational plasticity-fundamentals and applications (1997), CIMNE, Barcelona 792-797
52. Wiechmann K., Barthold F.-J., and Stein E. Optimization of elasto-plastic structures using the finite element method. In: Gutkowski W., and Mróz Z. (Eds). Proceedings of the second world congress on structural and multidisciplinary optimization vol. 2 (1997), Institute of Fundamental Technological Research, Polish Academy of Science, Warschau 1013-1018
53. Wiechmann K, Barthold F-J. Remarks on variational design sensitivity analysis of structures with large elastic-plastic deformations. In: 7th AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization. Paper No. AIAA-1998-4752. 1998. p. 349-58.
54. Wiechmann K. Theorie und Numerik zur Berechnung und Optimierung von Strukturen mit elastoplastischen Deformationen. Dissertation, Institut für Baumechanik und Numerische Mechanik, Universität Hannover; 2000.
55. Wiechmann K., Barthold F.-J., and Stein E. Shape optimization of shakedown analysis problems. In: Weichert D., and Maier G. (Eds). Inelastic analysis of structures under variable loads: theory and engineering applications, solid mechanics and its applications vol. 83 (2000), Kluwer Academic Publisher, Dordrecht 49-68
56. Stieghan J. Variationelle Sensitivitätsanalyse in der Theorie poröser Medien Clemens Eichhorn, Verlag für Hochschulschriften, Braunschweig, 2008.
57. Barthold F-J, Stieghan J. On sensitivity analysis in the theory of porous media. In: 7th world congress on structural and multidisciplinary optimization. Paper No. A0100. 2007. p. 2449-58.
58. Golub G., and Van Loan C. Matrix computations (1983), John Hopkins University Press, Baltimore
59. Ersoy H., and Mugan A. Design sensitivity analysis of structures based upon the singular value decomposition. Comput Meth Appl Mech Eng 191 (2002) 3459-3476