Free material optimization with local stress constraints for laminated structures

In Free Material Optimization (FMO), the design variable is the elastic material tensor, which is allowed to change its values freely over the design domain resulting in both optimal material properties and optimal material distribution. Models are mostly available for two- and three-dimensional continuum structures. Recently, these models have been extended to laminated plates and shells. The goal of this article is to introduce constraints on local stresses to these new models. The associated optimization problems are highly nonlinear semidefinite programming problems that are known to be challenging for numerical tractability, and are solved by a primal–dual interior point method previously proposed for FMO problems without stress constraints. The algorithm utilizes the FMO problem structure, wherein the matrix inequality constraints involve small many block matrices. Several numerical experiments demonstrate the stress constrained models and the capability of the method to obtain solutions to these problems within a modest number of iterations.