Peridynamics-informed effect of micro-cracks on topology optimization of lightweight structures

Abstract

Most structures are preferred to be light-weighted when they are used in industrial applications such as automotive, aerospace, and naval structures. Classical continuum mechanics (CCM) formulations are commonly adopted to solve the topology optimization problems. However, CCM brings about some restrictions to the modeling, analysis, and solution of complex structures with structural discontinuities, defects, and micro/macro damages. Unlike CCM, peridynamic theory provides a wider range of analysis options because of its nonlocal integration nature, which can eliminate the need for partial derivatives in the equation of motion, thereby being suitable for effective modeling of cracks, damages, etc. This paper presents an application of peridynamics based topology optimization (PD-TO) to study the effect of micro-damages for designing lightweight engineering structures. The PD-TO algorithm used herein is based on the coupling of bond-based method and Optimality Criteria (OC) topology optimization method. The structure is designed by locating various microcracks for investigating the microdamage effect on the optimal topologies. To this end, the PD-TO model is implemented using an in-house MATLAB code, and strain energy density distributions are compared between different topologies. As a result, the importance of including damage regions within the lightweight design optimization stage is revealed.