Reliability-based topology optimization under shape uncertainty modeled in Eulerian description

Abstract

This paper presents a reliability-based topology optimization method under geometrical uncertainties. First, we briefly introduce the concept of topology optimization. Then, we explain how shape uncertainty is modeled in Eulerian description, using an advection equation and a Karhunen-Loeve expansion. Based on the shape uncertainty modeling, we formulate a reliability measure for the shape uncertainty, briefly introducing the inverse reliability method. Two optimization problems, a minimum mean compliance problem and an optimum design problem for a compliant mechanism, are then formulated using the proposed shape uncertainty modeling. The design sensitivity analysis for the reliability analysis and optimization procedure, performed using the adjoint variable method, is then explained. A two-level optimization algorithm is constructed next, in which the inner iteration is used for reliability analysis and the outer is used for updating design variables. Finally, three numerical examples are provided to demonstrate the validity and the utility of the proposed method.