Improved semi-analytical sensitivity analysis using a secant stiffness matrix for geometric nonlinear shape optimization

Computers and Structures

Volumn 146, Issue , 2015, Pages 143-151

  Wang, Wenjia ^a   Clausen, Peter M ^b   Bletzinger, Kai Uwe ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b FE DESIGN GmbH   (Germany)

Author keywords

Correction term; Exact semi analytical sensitivity analysis; Finite difference approximation; Geometric nonlinearity; Nonparametric shape optimization; Secant stiffness matrix

Indexed keywords

CORRECTION TERMS; FINITE DIFFERENCE APPROXIMATIONS; GEOMETRIC NON-LINEARITY; NON-PARAMETRIC; SECANT STIFFNESS MATRIXES; SEMI-ANALYTICAL;

EID: 84908541446     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2014.08.008     Document Type: Article

References (25)

1. Haftka RT, Adelman HM. Recent developments in structural sensitivity analysis. Struct Optim 1989;1(3):137-51.
2. Choi KK, Kim NH. Structural sensitivity analysis and optimization 1: linear system. New York: Springer Science + Business Media, Inc.; 2005.
3. van Keulen F, Haftka RT, Kim NH. Review of options for structural design sensitivity analysis. Part 1: linear systems. Comput Meth Appl Mech Eng 2005;194(30-33):3213-43.
4. Barthelemy B, Chon CT, Haftka RT. Accuracy problems associated with semi-analytical derivatives of static response. Finite Elem Anal Des 1988;4(3):249-65.
5. Pedersen P, Cheng G, Rasmussen J. On accuracy problems for semi-analytical sensitivity analysis. Mech Struct Mach 1989;17(3):373-84.
6. Cheng G, Olhoff N. Rigid body motion test against error in semi-analytical sensitivity analysis. Comput Struct 1993;46(3):515-27.
7. Bletzinger KU, Firl M, Daoud F. Approximation of derivatives in semi-analytical structural optimization. Comput Struct 2008;86(13-14):1404-16.
8. Olhoff N, Rasmussen J, Lund E. A method of "exact" numerical differentiation for error elimination in finite-element-based semi-analytical shape sensitivity analyses. Mech Struct Mach 1993;21(1):1-66.
9. van Keulen F, de Boer H. Rigorous improvement of semi-analytical design sensitivities by exact differentiation of rigid body motions. Int J Numer Meth Eng 1998;42(1):71-91.
10. de Boer H, van Keulen F. Refined semi-analytical design sensitivities. Int J Solids Struct 2000;37(46-47):6961-80.
11. Crisfield MA. Non-linear finite element analysis of solids and structures. Essentials, vol. 1. New York: John Wiley & Sons, Inc.; 1991.
12. Oñate E. On the derivation and possibilities of the secant stiffness matrix for non linear finite element analysis. Comput Mech 1995;15(6):572-93.
13. Pedersen P. Analytical stiffness matrices with Green-Lagrange strain measure. Int J Numer Meth Eng 2005;62(3):334-52.
14. Oñate E, Oliver J, Miquel J, Suárez B. A finite element formulation for geometrically non linear problems using a secant matrix. In: Yagawa G, Atluri SN, editors. Computational mechanics '86. Tokyo: Springer-Verlag; 1986. p. 563-70.
15. Oñate E. Formulation of a secant stiffness matrix for geometrically nonlinear finite element analysis. In: Bićanić N, editor. Nonlinear engineering computations. Swansea, UK: Pineridge Press; 1991. p. 87-95.
16. Chen WF, Goto Y. Stability design of semi-rigid frames, vol. 1. New York: John Wiley & Sons, Inc.; 1996.
17. Burns SA. Recent advances in optimal structural design. ASCE Publications; 2002.
18. Kroplin B, Dinkler D. A material law for coupled load yielding and geometric instability. Eng Comput 1988;5(3):210-6.
19. Kroplin B, Wilhelm M, Herrmann M. Unstable phenomena in sheet metal forming processes and their simulation. In: VDI Berichte 894. Düsseldorf: VDI Verlag; 1990. p. 137-52.
20. Pedersen P. Analytical stiffness matrices for tetrahedral elements. Comput Meth Appl Mech Eng 2006;196(1-3):261-78.
21. Pedersen P. The basic matrix approach for three simple finite elements (working print); 2008.
22. Jones E, Oliphant E, Peterson P, et al. SciPy: open source scientific tools for python; 2001 〈http://www.scipy.org〉.
23. Le C, Bruns T, Tortorelli D. A gradient-based, parameter-free approach to shape optimization. Comput Meth Appl Mech Eng 2010;200(9-12):985-96.
24. Arnout S, Firl M, Bletzinger KU. Parameter free shape and thickness optimization considering stress response. Struct Multidiscip Optim 2012;45(6):801-14.
25. Werner M. Reduction models for stress sensitivities in industrial structural shape optimization, Master thesis. Department of Computational Engineering, TU Darmstadt; 2012.