Minimum Weight Design for Structural Eigenvalue Problems by Optimal Control Theory*, †
- 1 January 1983
- journal article
- research article
- Published by Taylor & Francis in Journal of Structural Mechanics
- Vol. 11 (4) , 491-500
- https://doi.org/10.1080/03601218308907454
Abstract
The application of optimal control theory to minimum weight design of continuous one-dimensional structural elements subject to eigenvalue constraints is discussed. If not only the value of an eigenvalue is prescribed but also its position in the sequence of the ordered eigenvalues—for example, the critical buckling load of a column—the corresponding optimal control problem is shown to include necessarily all eigenvalues. Considering the unspecified eigenvalues as free parameters, necessary conditions for minimum weight design are derived. These conditions are compared with those obtained by use of variational methods. Attention is focused on the special case of multimodal solutions.Keywords
This publication has 3 references indexed in Scilit:
- The Calculus of Variations and Optimal ControlPublished by Springer Nature ,1981
- On single and bimodal optimum buckling loads of clamped columnsInternational Journal of Solids and Structures, 1977
- A boundary value problem for a system of ordinary linear differential equations of the first orderTransactions of the American Mathematical Society, 1926