Abstract
Optimization techniques are increasingly being used for performing nonlinear structural analysis. Under these circumstances the structural design problem can be viewed as a nested optimization problem. The present paper suggests that there are computational benefits to treating this nested problem as a large single optimization problem. That is, the response variables (such as displacements) and the structural parameters are all treated as design variables in a unified formulation which performs simultaneously the design and analysis. Three truss examples are used for the demonstration comparing two nested optimization procedures with two computational procedures for the simultaneous solution. The examples show that the simultaneous approach is competitive with the more traditional nested approach.
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References
Fox, R. L.; Kapoor, M. P. (1968): A minimization method for the solution of eigenproblem arising in structural dynamics. Proc. 2nd Conf. Matrix Methods Struct. Mech., Wright-Patterson AFB, Ohio, AFFDL-TR-68-150
Fox, R. L.; Schmit, L. A. (1965): An integrated approach to structural synthesis and analysis. AIAA J. 3, 1104–1112
Fox, R. L.; Schmit, L. A. (1966): Advances in the integrated approach to structural synthesis. J. Spacecr. Rockets 3, 858–866
Fox, R. L.; Stanton, E. L. (1968): Developments in structural analysis by direct energy minimization. AIAA J. 6, 1036–1042
Garrett, L. B. (1981): Interactive design and analysis of future large spacecraft concepts. NASA TP-1937
Haftka, R. T. (1985): Simultaneous analysis and design. AIAA J. 23, 1099–1103
Haftka, R.T.; Kamat, M.P. (1985): Elements of structural optimization. Amsterdam: Nijhoff
Haftka, R. T.; Starnes, J. H. Jr. (1976): Application of a quadratic extended interior penalty function for structural optimization. AIAA J. 14, 718–724
Hughes, T. J. R.; Winget, J.; Levit, I.; Tezduyar, T. E. (1983): New alternating direction procedures in finite element analysis based on EBE approximate factorization. In: Computer methods for nonlinear solids and structural mechanics (eds. Atluri, S.; Perrone, N.), pp. 75–109. ASME, New York (AMD, vol. 54)
Johnson, O. B.; Micchelli, C. A.; Paul, G. (1983): Polynomial preconditioners for conjugate gradient calculations. SIAM J. Numer. Anal. 20, 362–376
Kamat, M. P.; Hayduk, R. J. (1982): Recent developments in quasi-Newton methods for structural analysis and synthesis. AIAA J. 20, 672–679
Khot, N. S., Berke, L.; Venkayya, V. B. (1978): Comparison of optimality criteria algorithms for minimum weight design of structures. AIAA J. 17, 182–189
Lasdon, L. S.; Warren, A. D. (1979): Generalized reduced gradient software for linearly and nonlinearly constrained problems. In: Design and implementation of optimization software (ed. Greenberg, H.) Amsterdam: Sijthoff and Nordhoff
Plant, R. H.; Johnson, L. W.; Olhoff, N. (1986): Bimodal optimization of compressed columns on elastic foundations. J. Appl. Mech. 53, 130–134
Powell, M.J.D. (1976): Restart procedures for the conjugate gradient methods. Math. Progr. 11, 42–49
Powell, M. J. D. (1978): A fast algorithm for nonlinearly constrained optimization calculations. In: Numerical analysis (ed. Watson, C. A.), pp. 144–157. Proc. Biennial Cong. Dundee 1977. Berlin, Heidelberg, New York: Springer (Lecture Notes in Mathematics, vol. 630)
Schmit, L. A.; Bogner, F. K.; Fox, R. L. (1968): Finite deflection discrete element analysis using plate and shell discrete elements. AIAA J. 6, 781–791
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Haftka, R.T., Kamat, M.P. Simultaneous nonlinear structural analysis and design. Computational Mechanics 4, 409–416 (1989). https://doi.org/10.1007/BF00293046
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DOI: https://doi.org/10.1007/BF00293046