Semidefinite Programming for Finite Element Analysis of Isotropic Materials with Unilateral Constitutive Laws

A unified approach based on convex optimization is proposed for finding equilibrium configurations of structures consisting of no-tension or no-compression isotropic material in small strain and deformation. The semidefinite programming (SDP) problem is formulated so as to give the same optimizer as that of the minimization problem of total potential energy. An equilibrium configuration is obtained as an optimal solution of the SDP problem by using the primal-dual interior-point method. It is shown, in numerical examples, that equilibrium configurations are obtained without a priori knowledge of crack or wrinkling patterns.