Nested approach to structural optimization in nonsmooth mechanics

Abstract

This work applies the nested approach of structural optimization, in the form of the method of moving asymptotes (MMA), to some typical problems of nonsmooth mechanics. Namely, the state problems that arise when mechanical structures, in this case, trusses, are subjected to frictionless contact constraints and/or the constraints arising due to supporting cables that are rigid in tension but do not admit compression. In these problems the state as a function of the design is not everywhere differentiable and since MMA is developed for smooth problems, it is not clear that it is an admissible solution method. However, from the series of test problems in this paper we conclude that it is indeed a valid method: it shows convergence to a solution for all cases except for a class of problems with strict conditions on the magnitude of the contact (cable) forces, but these difficulties could be removed by the introduction of a small modification of MMA in the form of simple move limits.