Multiobjective Topology Optimization for Preliminary Design Using Graph Theory and L-System Languages
Loading...
Date
2020-03-26
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Topology optimization is a powerful tool that, when employed at the preliminary stage of the design process, can determine potential structural configurations that best satisfy specified performance objectives. However, the use of conventional topology optimization approaches such as density-based and level set methods requires a fair amount of user knowledge of or intuition for both the design problem being considered and the desired result. While straightforward for simple structural problems with a relatively small design space, advancements in the area of smart materials and a growing interest in developing structures with increased multifunctionality may begin to render these methods as ineffective. Thus, there is a growing need for an inherently multiobjective preliminary design tool capable of exploring a vast design space to identify well-performing solutions to problems with which users have little/no intuition or experience. This work proposes the use of a heuristic alternative to conventional topology optimization approaches which couples a genetic algorithm with a parallel rewriting system known as a Lindenmayer System (L-System). The L-System encodes design variables into a string of characters that, when interpreted by a deterministic algorithm, governs the development of the topology. In particular, this work explores two distinct L-System interpretation approaches. The first is a geometry-based approach known as turtle graphics, which tracks its spatial position and orientation at all times and constructs line segments between specified coordinates. The second is a newly-developed graph-based approach referred to as Spatial Interpretation for the Development of Reconfigurable Structures (SPIDRS). This algorithm is based on the nodes, edges, and faces of a planar graph, allowing for an edge- and face-constructing agent to move more freely around the design space and introduce deliberate and natural topological modifications. This graph-based approach can also be extended to consider a three-dimensional structural design domain, the first known demonstration of 3-D L-System topology optimization. It will be demonstrated that the proposed L-System topology optimization framework effectively explores the physical design space and results in configurations comparable to both known optimal or ideal solutions as well as those found using conventional topology optimization methods, but with the advantage of straightforward multiobjective/multiphysical extension. The implementation of a sizing optimization scheme to determine optimal structural member thicknesses for SPIDRS-generated topologies will also be discussed, and several potential multiphysical design applications will be introduced.
Description
Keywords
Topology Optimization, L-System, Graph Theory, Preliminary Design, Sizing Optimization