Design Optimization of Lightweight Structures for Additive Manufacturing

Abstract

Lightweight structures have many applications in different engineering areas, such as automotive, aerospace, or medical industries, among many others. Optimal design of lightweight structures deals with finding the most economical distribution of the material in the design domain. This concept becomes even more important when additive manufacturing (AM) is considered for fabrication of the parts, since it allows for exceptional freedom in the design process. In this dissertation, we consider the design optimization problem for additively manufactured planar frame structures. We specifically consider three different optimization approaches in tackling the problem of finding lightest planar frames which can withstand the external loads. We apply exact optimization methods in Chapter 3, where we propose a novel mixed integer quadratically constrained optimization model for the problem and compare its performance to the existing models from the literature. We then propose a problem-specific heuristic method in Chapter 4, which is capable of solving large-scale problems that couldn’t be handled by exact optimization methods. This heuristic method is a combination of a member-node adding approach and nonlinear optimization, in which the solving process starts from a version of ground structure with a minimal number of elements and then gradually includes elements with the most promising contribution in reducing the stress in the structure. In Chapter 5 we test the ability of metaheuristics, specifically Genetic Algorithm (GA) to solve this mathematical optimization problem. In the proposed hybrid approach, we combine GA with nonlinear optimization. To this end, we designed a new encoding of the candidate solutions together with the GA operators that in addition to the stochastic nature of the GA in solving combinatorial problems, combined with the deterministic exactness of nonlinear optimization provides a novel way to solve the design problem. We conclude the dissertation by providing the main findings and future research in Chapter 6.