Reliability-Based Topology Optimization with Analytic Sensitivities

摘要

Reliability-based topology optimization has the potential to generate novel structures which are both optimal and reliable. In this research, a simple implementation of reliability-based topology optimization which utilizes the Solid-Isotropic Material with Penalization (SIMP) formulation for topology optimization is explored. Reliability is considered using the First-Order Reliability Method (FORM), however this gives the optimization problem a double-loop structure. Numeric sensitivity analysis of the nested problem is computationally intractable due to the large number of design variables, so an alternative procedure derived from the Lagrange Multiplier Theorem is used. This procedure uses a system of linear equations to obtain the sensitivities of the MPP without requiring additional solutions of the nested FORM problem. The procedure is then used to obtain topologies for a benchmark problem, a compliance-constrained cantilever structure with multiple random loads, and a deflection-constrained cantilever structure.