Constrained Quasiconvexity and Structural Optimization

Abstract:

We propose an approach to general structural optimization problems based on variational techniques. The analysis involves gradient Young measures in the vector case and the notion of constrained quasiconvexity, and depends on the appropriate use of stream functions in dimension two. The case of several nonlinear materials and arbitrary cost functionals depending on the gradients of the equilibrium states can also be treated. This generality is the main motivation for this work.