Reliability-based topology optimization for multi-material structures

Abstract

Structural optimization is a crucial aspect of engineering design, aimed at identifying the optimal configuration of a structure that meets specified constraints, such as displacement, stress, and buckling resistance, while providing optimal performance. One such optimization technique is topology optimization (TO), which can be applied in both continuum and discrete settings, and is used to determine optimal material layouts, best shape, size, and connectivity of a structure based on a set of criteria. Deterministic design optimization is a widely used method in engineering, where design parameters, such as material properties, loadings, and geometry, are treated as deterministic quantities. However, this approach may not always account for uncertainties in modeling, loads, and material properties, which could lead to unexpected failures and catastrophic damage. To address this issue, reliability-based topology optimization (RBTO) has been developed, incorporating reliability analysis to minimize the risk of unexpected failures. In the case of building structures, which often consist of complex hierarchical compositions assembled with multiple materials, it becomes challenging to achieve multiple design objectives with a single material. To overcome this limitation, multi-material RBTO is proposed, allowing for the consideration of two or more material combinations in a structure under uncertainty in loads and material properties, leading to optimal design. An optimization algorithm using gradients of objective and constraint functions has been used in this approach to efficiently update design variables and converge to feasible solutions. The efficacy of this method is demonstrated through numerical examples.