Reliability-based topology optimization under geometrical uncertainty

Abstract

This paper presents a reliability-based topology optimization method considering the uncertainty of geometrical variations. Geometrical variations are modeled as an advection of shape, i.e. normalized density, by a random velocity field, represented by a finite number of independent normal random variables, based on the Karhunen-Loève (K-L) expansion. First, the topology optimization method used in this study, i.e. a Heaviside projection method with a partial differential equation (PDE) filter, is briefly discussed. Next, the method for modeling geometrical variations using an advection equation and a K-L expansion is described, and a reliability index for the geometrical variations is defined. The reliability-based topology optimization problem is then formulated using the reliability index, based on the concept of the performance measure approach (PMA), and the design sensitivity is obtained based on the method of Lagrange multipliers and the adjoint variable method. Finally, a numerical example is provided to confirm the validity and effectiveness of the proposed method.