SIMP type topology optimization procedure considering uncertain load position

In this paper a new type of probabilistic optimal topology design method is elaborated for continuum type of structures where the points of application of the loads are given randomly. In the proposed probabilistic topology optimization method the minimum penalized weight design of the discretized structure is subjected to compliance constraint and side constraints. The compliance expression is probabilistic one. By the use of an appropriate stochastic upperbound theorem, the original stochastic mathematical programming problem is substituted by a deterministic one. The numerical procedure is based on iterative formula which is formed by the use of the first order optimality condition of the Lagrangian function. The application is illustrated by numerical example.