Finite Elements in Optimal Structural Design
The optimization of a structure modeled by finite elements can proceed in two diametrically opposed directions. The first direction is that of interfacing a finite element software package with an optimization package where both packages are treated primarily as black boxes. The second direction is the intimate integration of the finite element analysis and optimization processes. Many research structural optimization programs followed the second path for reasons of efficiency and convenience to the researchers who wrote these programs. However, in production codes the tendency is to follow the more modular first direction. The integrated approach is probably justified only when it reflects algorithmic integration of the analysis and optimization processes. This type of integration is presently at the research stage.
KeywordsDesign Variable Truncation Error Adjoint Method AIAA Journal Feasible Domain
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- 1.Prasad, B. and Haftka, R.T., “Structural Optimization with Plate Finite Elements,” Journal of the Structural Division, ASCE, Vol. 105, No. ST11, pp. 2367–2382, 1979.Google Scholar
- 2.Braibant, V., Fleury, C. and Beckers, P., “Shape Optimal Design. An Approach Matching CAD and Optimization Concepts,” Report SAH09, Aerospace Laboratory of the University of Liege, Belgium, 1983.Google Scholar
- 4.Iott, J., Haftka, R.T. and Adelman, H.M., “Selecting Step Sizes in Sensitivity Analysis by Finite Differences,” NASA TM 86382, 1985.Google Scholar
- 5.Camarda, C.J. and Adelman, H.M., “Static and Dynamic Structural-Sensitivity Derivative Calculation in the Finite-Element-Based Engineering Analysis Language (EAL) System,” NASA TM-85743, 1984.Google Scholar
- 6.Barthelemy, B.M., Chon, C.T. and Haftka, R.T., “Accuracy of Finite- Difference Approximations to Sensitivity Derivatives of Static Structural Response,” paper presented at the First World Congress on Computational Mechanics, Austin, Texas, S.Google Scholar
- 12.Plaut, R.H., Johnson, L.W. and Olhoff, N., “Bimodal Optimization of Compressed Columns of Elastic Foundations,” Journal of Applied Mechanics, 1986.Google Scholar
- 19.Fox, R.L. and Kapoor, M.P., “A Minimization Method for the Solution of Eigenproblem Arising in Structural Dynamics,” Proceedings of the Second Conference on Matrix Methods in Structural Mechanics, Wright-Patterson AFB, Ohio, AFFDL-TR-68-150, 1968.Google Scholar
- 22.Hughes, T.J.R., Winget, J., Levit, I. and Tezduyar, T.E., “New Alternating Direction Procedures in Finite Element Analysis Based on EBE Approximate Factorization,” Computer Methods for Nonlinear Solids and Structural Mechanics, (S. Atluri and N. Perrone, editors), AMD, Vol. 54, pp. 75–109, 1983.Google Scholar
- 24.Haftka, R.T. and Kamat, M.P., “Simultaneous Nonlinear Analysis and Design,” presented at the ASME Design Automation Conference, Cincinnati, Ohio, September 1985.Google Scholar
- 27.Powell, M.J.D., “A Fast Algorithm for Nonlinearity Constrained Optimization Calculations,” Proceedings of the 1977 Dundee Conference on Numerical Analysis, Lecture Notes in Mathematics, Vol. 630, pp. 144–157, Springer-Verlag, Berlin, 1978.Google Scholar
- 28.Lasdon, L.S. and Warren, A.D., “Generalized Reduced Gradient Software for Linearly and Nonlinearly Constrained Problems,” Design and Implementation of Optimization Software, (H. Greenberg, ed.) Sijthoff and Nordhoff Pub., 1979.Google Scholar