Wrinkling analysis of orthotropic membranes via semidefinite programming

Abstract

In this paper we propose a numerical algorithm for computing the equilibrium configuration of an orthotropic wrinkling membrane in the small deformation. We consider the minimization problem of total potential energy of orthotropic membrane structures, which is regarded as the infinite dimensional optimization problem. By introducing a tensor representing the amount of wrinkle, we reformulate this problem into an infinite-dimensional SDP problem. Throughout the numerical examples it is shown that our method can find wrinkling states, as well as the equilibrium configurations, of orthotropic membranes without any difficulty.