Abstract
A class of distributed-parameter optimal design problems is treated, in which the design variable appears as a coefficient in a partial differential operator. Formal sensitivity analysis techniques that are in common use in the engineering literature are studied and made technically precise. Operator theoretic techniques and Frechet differentiation theory are employed to develop a rigorous sensitivity analysis for static and vibrating elastic structures. Two examples involving fourth-order ordinary and partial differential operators, commonly encountered in treating beam and plate elements, are analyzed.
Similar content being viewed by others
References
Prager, W.,Optimal Design of Statically Determinate Beams for a Given Deflection, International Journal of Mechanical Science, Vol. 13, pp. 893–895, 1971.
Sheu, C. Y., andPrager, W.,Recent Development in Optimal Structural Design, Applied Mechanics Reviews, Vol. 21, pp. 985–992, 1968.
Komkov, V., andColeman, N.,An Analytic Approach to Some Problems of Optimal Design, Archives of Mechanics, Vol. 24, pp. 565–575, 1975.
Haug, E. J., Pan, K. C., andStreeter, T. D.,A Computational Method for Optimal Structural Design, Part II, International Journal for Numerical Methods in Engineering, Vol. 9, pp. 649–667, 1975.
Haug, E. J., Arora, J. S., andMatsui, K.,A Steepest-Descent Method for Optimization of Mechanical Systems, Journal of Optimization Theory and Applications, Vol. 19, pp. 401–424, 1976.
Haug, E. J., andFeng, T. T.,Optimization of Distributed Parameter Structures Under Dynamic Loads, Control and Dynamic Systems, Vol. 13, Edited by C. T. Leondes, Academic Press, New York, New York, 1976.
Farshad, M.,Variations of Eigenvalues and Eigenfunctions in Continuum Mechanics, AIAA Journal, Vol. 12, pp. 560–561, 1974.
Vainberg, M. M.,Variational Methods for the Study for Nonlinear Operators, Holden Day, San Fransicso, California, 1964.
Nashed, M. Z.,Differentiability and Related Properties of Nonlinear Operators, Nonlinear Functional Analysis and Applications, Edited by L. B. Rall, Academic Press, New York, New York, pp. 103–309, 1971.
Kato, T.,Perturbation Theory for Linear Operators, Springer-Verlag, New York, New York, 1966.
Tapia, R. A.,The Differentiation and Integration of Nonlinear Operators, Nonlinear Functional Analysis and Applications, Edited by L. B. Rall, Academic Press, New York New York, pp. 45–102, 1971.
Komkov, V.,On Variational Formulation of Problems in the Classical Continuum Mechanics of Solids, International Journal of Engineering Science, Vol. 6, pp. 695–720, 1968.
Beltrami, E. J.,An Algorithmic Approach to Approach to Nonlinear Analysis and Optimization, Academic Press, New York, New York, 1970.
Miele, A.,Recent Advances in Gradient Algorithms for Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 17, pp. 361–430, 1975.
Author information
Authors and Affiliations
Additional information
Communicated by C. T. Leondes
Rights and permissions
About this article
Cite this article
Haug, E.J., Komkov, V. Sensitivity analysis in distributed-parameter mechanical system optimization. J Optim Theory Appl 23, 445–464 (1977). https://doi.org/10.1007/BF00933452
Issue Date:
DOI: https://doi.org/10.1007/BF00933452