Finite Elements in Optimal Structural Design

  • Raphael T. Haftka
  • Manohar P. Kamat
Part of the NATO ASI Series book series (volume 27)


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.


Design Variable Truncation Error Adjoint Method AIAA Journal Feasible Domain 
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  1. 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. 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
  3. 3.
    Gill, P.E., Murray, W., Saunders, M.A. and Wright, M.H., “Computing Forwards-Difference Intervals for Numerical Optimization,” SIAM J. Sci. and Stat. Comput., Vol. No. 2, pp. 310–321, June 1983.MathSciNetCrossRefGoogle Scholar
  4. 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. 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. 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
  7. 7.
    Haug, E.J., Komkov, V. and Choi, K.K., Design Sensitivity Analysis of Structural Systems, Academic Press, 1986.MATHGoogle Scholar
  8. 8.
    Cardani, C. and Mantegazza, P., “Calculation of Eigenvalue and Eigenvector Derivatives for Algebraic Flutter and Divergence Eigenproblems,” AIAA Journal, Vol. 17, pp. 408–412, 1979.MATHCrossRefGoogle Scholar
  9. 9.
    Nelson, R.B., “Simplified Calculation of Eigenvector Derivatives,” AIAA Journal, Vol. 14, pp. 1201–1205, 1976.MATHCrossRefGoogle Scholar
  10. 10.
    Haftka, R.T., “Design for Temperature and Thermal Buckling Constraints Employing a Noneigenvalue Formulation,” Journal of Spacecraft, Vol. 20, pp. 363–367, 1983.CrossRefGoogle Scholar
  11. 11.
    Hwang, J.T., Dougherty, E.P., Rabitz, S. and Rabitz, H., “The Green’s Function Method of Sensitivity Analysis in Chemical Kinetics,” J. Chem. Phys., Vol. 69, pp. 5180–5191, 1978.MathSciNetCrossRefGoogle Scholar
  12. 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
  13. 13.
    Khot, N.S., Berke, L. and Venkayya, V.B., “Comparison of Optimality Criteria Algorithms for Minimum Weight Design of Structures,” AIAA Journal, Vol. 17, No. 2, pp. 182–189, 1979.MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Haftka, R.T. and Kamat, M.P., Elements of Structural Optimization, Martinus Nijhoff, The Netherlands, 1985.MATHGoogle Scholar
  15. 15.
    Fox, R.L. and Schmit, L.A., “An Integrated Approach to Structural Synthesis and Analysis,” AIAA Journal, Vol. 3, pp. 1104–1112, June 1965.MATHCrossRefGoogle Scholar
  16. 16.
    Fox, R.L. and Schmit, L.A., “Advances in the Integrated Approach to Structural Synthesis,” Journal of Spacecraft and Rockets, Vol. 3, pp. 858–866, June 1966.CrossRefGoogle Scholar
  17. 17.
    Schmit, L.A., Bogner, F.K. and Fox, R.L., “Finite Deflection Discrete Element Analysis Using Plate and Shell Discrete Elements,” AIAA Journal, Vol. 6, No. 5, pp. 781–791, 1968.MATHCrossRefGoogle Scholar
  18. 18.
    Fox, R.L. and Stanton, E.L., “Developments in Structural Analysis by Direct Energy Minimization,” AIAA Journal, Vol. 6, No. 6, pp. 1036–1042, 1968.MATHCrossRefGoogle Scholar
  19. 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
  20. 20.
    Kamat, M.P. and Hayduk, R.J., “Recent Developments in Quasi-Newton Methods for Structural Analysis and Synthesis,” AIAA Journal, Vol. 20, No. 5, pp. 672–679, 1982.MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Johnson, O.B., Micchelli, C.A. and Paul, G., “Polynomial Preconditioners for Conjugate Gradient Calculations,” SIAM Journal for Numerical Analysis, Vol. 20, pp. 362–376, 1983.MathSciNetMATHCrossRefGoogle Scholar
  22. 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
  23. 23.
    Haftka, R.T., “Simultaneous Analysis and Design,” AIAA Journal, Vol. 23, No. 7, pp. 1099–1103, 1985.MATHCrossRefGoogle Scholar
  24. 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
  25. 25.
    Haftka, R.T. and Starnes, J.H., Jr., “Application of a Quadratic Extended Interior Penalty Function for Structural Optimization,” AIAA Journal, Vol. 14, pp. 718–724, 1976.MATHCrossRefGoogle Scholar
  26. 26.
    Powell, M.J.D., “Restart Procedures for the Conjugate Gradient Methods,” Mathematical Progress, Vol. 11, pp. 42–49, 1976.MATHCrossRefGoogle Scholar
  27. 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. 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

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Raphael T. Haftka
    • 1
  • Manohar P. Kamat
    • 2
  1. 1.Department of Aerospace and Ocean EngineeringVirginia Polytechnic Institute and State UniversityBlacksburgUSA
  2. 2.School of Engineering Science and MechanicsGeorgia Institute of TechnologyAtlantaUSA

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