Abstract
The use of a homotopy method is demonstrated for optimal design of a stiffened laminated plate for maximum buckling load. Instead of obtaining a single optimum, the homotopy technique generates in a single computer execution an entire family of optimum designs with a given parameter. In the present application the parameter is set to the total structural weight, and the optimal designs are obtained as a function of the weight of the laminated plates. It is seen that the number of simultaneous buckling modes of optimum plates is increased as the total weight is increased. So for low weights the optimal design starts with unimodal design and for higher weight the optimal design becomes bimodal, trimodal, and finally it becomes tetramodal.
Similar content being viewed by others
References
Dennis, J. E., Jr. and Schnabel, R. B., 1983, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs.
Golub, G. H., Underwood, R., and Wilkinson, J. H. 1972, “The Lanczos Algorithm for the Symmetric Ax=λBx Problem,” Report STAN-CS-72-270, Department of Computer Science, Stanford University, Stanford, CA.
Jones, Robert M., 1975, Mechanics of Composite Materials, McGraw-Hill Book Company, Washington, D.C.
Scott, D. S. and Parlett, B. N., 1983, “LAS02.” NETLIB, Argonne National Lab., Argonne, IL.
Shin, Y. S., Haftka, R. T. and Plaut, R. H., 1988a, “Simultaneous Analysis and Design for Eigenvalue Maximization,” AIAA Journal, Vol. 26, No. 6, pp. 738–744.
Shin, Y. S., Haftka, R. T., Watson, L. T. and Plaut, R. H., 1988b, “Tracing Structural Optima As a Function of Available Structural Resources by a Homotopy Method,” Computer Methods in Applied Mechanics and Engineering, Vol. 70, No. 2 pp. 151–164.
Shin, Y. S., Haftka, R. T., Plaut, R. H. and Watson, L. T., 1989, “Design of Laminated Plates for Maximum Buckling Load,” Journal of Composite Materials, Vol. 23, pp. 348–369.
Watson, L. T., 1979a, “A Globally Convergent Algorithm for Computing Fixed Point of C2 Maps,” Appl. Math, Comput., Vol. 5, pp. 297–311.
Watson, L. T., 1979b, “Fixed Point of C2 Maps,” J. Comp. Appl. Math., Vol. 5, pp. 131–140.
Watson, L. T. 1986, “Numerical Linear Algebra Aspects of Globally Convergent Homotopy Methods,” SIAM Review, Vol. 28, pp. 529–545.
Yang, T. Y. 1986, Finite Element Structural Analysis, Prentice-Hall, Englewood Cliffs, N. J.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shin, YS. Optimal design of stiffened laminated plates using a homotopy method. KSME Journal 7, 399–407 (1993). https://doi.org/10.1007/BF02953209
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02953209