In contrast to the previous two chapters, which detailed L-system topology optimization approaches that interpret gene-informed rules into a complex set of layout-building instructions, this chapter introduces a grammar-to-layout approach known as the Arrangement L-system (ALS). Here, developmental operations that mimic the processes of cellular division, growth, and movement are directly informed by the genes and then iteratively applied to an iteratively changing topological layout that, once complete, represents an individual. The differences between formulations of the L-system, parameterized L-system, and ALS are discussed; examples of how the cellular division processes are used to develop a topological layout are provided; and extensions to the ALS such as directed search cellular dynamics and cellular division via the two-point topological derivative are detailed. The applicability of the ALS to a variety of structural design problems will be demonstrated, and it will be shown that this approach compares favorably with both conventional topology optimization methods discussed throughout this work as well as the graph-based SPIDRS approach introduced in the previous chapter.

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. This chapter explores both the different classifications of topology optimization methodologies and their implementation within the design process, specifically highlighting potential areas where such techniques may fall short. This motivates a discussion on the relevance of a bioinspired approach to topology optimization known as EvoDevo, where topologies developed by interpreting instructions from a Lindenmayer system (L-system) encoding are evolved using a genetic algorithm. Such an approach can lend itself well to multiobjective design problems with a vast design space and for which users have little/no experience or intuition.

To this point, the proposed L-system topology optimization methods have been considered in the context of benchmark structural topology optimization problems, as such problems afford an opportunity for comparison to both other topology optimization methodologies and mathematically proven optimal or ideal solutions. However, the motivation behind the development of these approaches stems from the need for preliminary design method capable of considering complex multiobjective problems involving multiple physics for which the user may not have an intuition. This chapter briefly summarizes several multiphysical problems that have been approached using L-system topology optimization, including fluid transport, heat transfer, electrical, and aeroelastic applications. By no means an exhaustive survey, these examples are intended to provide an overview of potential applications and hopefully provoke opportunities for future efforts.

To address the need for an inherently multiobjective preliminary design tool, this chapter introduces a heuristic alternative to the conventional topology optimization approaches discussed in the previous chapter. Specifically, a parallel rewriting system known as a Lindenmayer system (L-system) is used to encode a limited number of design variables into a string of characters which, when interpreted using a deterministic algorithm, governs the development of a topology. The general formulation of L-systems is provided before discussing how L-system encodings can be interpreted using a graphical method known as turtle graphics. Turtle graphics constructs continuous, straight line segments by tracking the spatial position and orientation of a line-constructing agent, leading to the creation of branched structures that mimic those found in numerous natural systems. The performance of the proposed method is then assessed using simple, well-known topology optimization problems and comparisons to mathematically known optimal or ideal solutions as well as those generated using conventional topology optimization methodologies.

While the L-system approach introduced in the previous chapter exhibits potential for topology optimization applications, the modeling power of the turtle graphics interpretation is severely limited due to its reliance on limited parameters and its inability to guarantee the deliberate formation of load paths. Based on these characteristics, this chapter introduces a graph-based interpretation approach known as Spatial Interpretation for the Development of Reconfigurable Structures (SPIDRS) that uses principles of graph theory to allow an edge-constructing agent to introduce deliberate topological modifications. Furthermore, SPIDRS operates using instructions generated by a parametric L-system, which enhances modeling power and affords greater design freedom. This approach can also be extended to consider a three-dimensional structural design domain. It will be demonstrated that this interpretation approach results in configurations comparable to known optimal/ideal solutions as well as those found using conventional topology optimization methods, especially when coupled with a sizing optimization scheme to determine optimal structural member thicknesses.

To place the proposed bioinspired approach in the proper context, this chapter provides a review of the topology optimization problem and a general overview and demonstration of existing topology optimization techniques. Four different classes of methodologies are discussed: (1) pixel/voxel representations, (2) ground structure-based representations, (3) boundary representations, and (4) emerging methods. For each class, we consider both the established approach and, if applicable, any extension(s) to the established approach or new methodology that utilizes the same underlying principles; each method is demonstrated using a common structural optimization problem, allowing for direct comparison. Where possible, we offer observations regarding the strengths and weaknesses of each approach and recommendations as to how and where each approach should be employed.