Optimal design of cellular structures under random fields

Abstract

Uncertainties in material properties, geometry, manufacturing processes, and operational environments are clearly critical at all scales (nano-, micro-, meso-, and macro-scale). The incorporation of reliability analysis is critical in designing material structures when material properties are uncertain. The concept of mesostructured or cellular materials is motivated by the desire to put material only where it is needed for a specific application. Typically, the cellular materials have superior structural compliant performance per weight than parts with bulk material or foams. This research develops a reliability-based synthesis method to design cellular material structures under random fields. The efficiency of the proposed framework is achieved with the combination of topology optimisation and stochastic local regression by utilising polynomial chaos expansion and Karhunen–Loeve transform. The effectiveness of the proposed framework is demonstrated with two examples including a ground truss structure and an automotive component which is composed of cellular material.