The first optimal design problem for an elastic column subject to buckling was formulated by Lagrange over 200 years ago. However, rapid development of structural optimization under stability constraints occurred only in the last twenty years. In numerous optimal structural design problems the stability phenomenon becomes one of the most important factors, particularly for slender and thin-walled elements of aerospace structures, ships, precision machines, tall buildings etc. In engineering practice stability constraints appear more often than it might be expected; even when designing a...

Optimal design of structures leads, as a rule, to slender and thin-walled shapes of the elements, and such elements are subject to the loss of stability. Hence the constraints of structural optimization usually include stability constraints, expressed by some eigenvalues. Optimal design under vibration constraints belongs also to optimization with respect to eigenvalues. The present volume gives a short introduction to structural optimization and then pays particular attention to multimodal optimization under stability and vibration constraints, both in elastic and inelastic range. One part...