Abstract
The second-order sensitivity analysis for a domain optimization problem is studied for a linear elastic structure. In the primary elastic structure considered, the surface traction, a part of the boundary conditions, depends not only on the position but also on the shape of the structure. The first variation and the second variation of the objective functional are calculated in terms of the solution, the first variation of the solution for the primal elastic system, and of the adjoint variable introduced. Moreover, the first-order and the second-order necessary optimality conditions are derived for the structure under a hydrostatic pressure. As an illustrative problem, a mean compliance design is treated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Masanao, T., andFujii, N.,Second-Order Necessary Conditions for Domain Optimization Problems in Elastic Structures, Part 1: Surface Traction Given as a Field, Journal of Optimization Theory and Applications, Vol. 72, pp. 355–382, 1992.
Dems, K., andMróz, D.,Variational Approach by Means of Adjoint Systems to Structural Optimization and Sensitivity Analysis, Part 2: Structure Shape Variation, International Journal of Solids and Structures, Vol. 20, pp. 527–552, 1984.
Fujii, N.,Second Variation and Its Applications in a Domain Optimization Problem, Proceedings of the 4th IFAC Symposium on Control of Distributed Parameter Systems, Los Angeles, California, pp. 431–436, 1986.
Fujii, N.,Second-Order Necessary Conditions in a Domain Optimization Problem, Journal of Optimization Theory and Applications, Vol. 65, pp. 223–244, 1990.
Goto, Y., Fujii, N., andMuramatsu, Y.,Second-Order Necessary Optimality Conditions for Domain Optimization Problem with a Neumann Problem, Proceedings of the 13th IFIP Conference on Systems Modelling and Optimization, Tokyo, Japan, pp. 259–268, 1988.
Goto, Y., Fujii, N., andMuramatsu, Y.,Second-Order Necessary Optimality Conditions for Domain Optimization Problem of the Neumann type, Journal of Optimization Theory and Applications, Vol. 65, pp. 431–445, 1990.
Goto, Y., andFujii, N.,Second-Order Numerical Method for Domain Optimization Problems, Journal of Optimization Theory and Applications, Vol. 67, pp. 533–550, 1990.
Fung, Y. C.,Foundations of Solid Mechanics, Prentice-Hall, Englewood Cliffs, New Jersey, 1965.
Mróz, Z.,Variational Approach to Shape Sensitivity Analysis and Optimal Design, The Optimum Shape: Automated Structural Design, Edited by J. A. Bennet and M. E. Botkin, Plenum Press, New York, 1986.
Timoshenko, S. P., andGoodier, J. N.,Theory of Elasticity, 3rd Edition, McGraw-Hill, Singapore, Republic of Singapore, 1982.
Banichuk, N. V.,Problems and Methods of Optimal Structural Design, Translated by V. Komkov and E. J. Haug, Plenum Press, New York, New York, 1983.
Dems, K., andHaftka, R. T.,Two Approaches to Sensitivity Analysis for Shape Variation of Structures, Mechanical Structures and Machines, Vol. 16, pp. 501–522, 1989.
Fujii, N.,Existence of an Optimal Domain in a Domain Optimization Problem, Proceedings of the 13th IFIP Conference on Systems Modelling and Optimization, Tokyo, Japan, pp. 251–258, 1988.
Author information
Authors and Affiliations
Additional information
Communicated by N. V. Banichuk
Rights and permissions
About this article
Cite this article
Masanao, T., Fujii, N. Second-order necessary conditions for domain optimization problems in elastic structures, part 2: Surface traction dependent on the shape. J Optim Theory Appl 72, 383–401 (1992). https://doi.org/10.1007/BF00940524
Issue Date:
DOI: https://doi.org/10.1007/BF00940524