MULTIMODAL OPTIMIZATION OF STRUCTURES WITH FREQUENCY CONSTRAINTS

Optimally designed structures under eigenvalue constraints (natural fr equency or buckling loads) are likely to display multiple eigenvalues. This introduces singularity of eigenvalue derivatives with respect to the design vector, which does not allow use of the Kuhn-Tucker condit ions. The paper presents the optimality criteria which takes that sing ularity into account and, in contrast to commonly used Kuhn-Tucker con ditions, they are valid for multiple eigenvalues (the form of that cri teria is more general than the one derived from the Kuhn-Tucker condit ions). An algorithm is presented, which applies those criteria and als o uses a new method of computation of Lagrange multipliers. The algori thm allows for an arbitrary number of eigenvectors to be considered in optimality criteria, and the actual modality of the problem is determ ined automatically. Examples of optimization of truss structures model led by finite element method are included.