Multi-objective topology optimization of multi-component continuum structures via a Kriging-interpolated level set approach

This paper explores a framework for topology optimization of multi-component sheet metal structures, such as those often used in the automotive industry. The primary reason for having multiple components in a structure is to reduce the manufacturing cost, which can become prohibitively expensive otherwise. Having a multi-component structure necessitates re-joining, which often comes at sacrifices in the assembly cost, weight and structural performance. The problem of designing a multi-component structure is thus posed in a multi-objective framework. Approaches to solve the problem may be classified into single and two stage approaches. Two-stage approaches start by focusing solely on structural performance in order to obtain optimal monolithic (single piece) designs, and then the decomposition into multiple components is considered without changing the base topology (identical to the monolithic design). Single-stage approaches simultaneously attempt to optimize both the base topology and its decomposition. Decomposition is an inherently discrete problem, and as such, non-gradient methods are needed for single-stage and second stage of two-stage approaches. This paper adopts an implicit formulation (level-sets) of the design variables, which significantly reduces the number of design variables needed in either single or two stage approaches. The number of design variables in the formulation is independent from the meshing size, which enables application of non-gradient methods to realistic designs. Test results of a short cantilever and an L-shaped bracket studies show reasonable success of both single and two stage approaches, with each approach having different merits.