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Providing a succinct overview of Lindenmayer system (L-system) topology optimization, this book focuses on the methods and theory underlying this novel bioinspired approach. Starting from basic principles, the book outlines how topology optimization can be utilized at the conceptual design stage and shows how it offers straightforward applicability to multi-objective and/or multi-physical industrial problems. Design strategies are clearly demonstrated using a host of case studies and real-world examples, and their potential challenges and solutions are discussed. Written from an optimization and design perspective, the authors both summarize the latest advances in this field and suggest potential avenues of research and development for future work. This will be the ideal resource for engineering practitioners, researchers, and students wanting to gain a new perspective on using topology optimization to improve product design.
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.
OBJECTIVES/GOALS: We evaluated the long-term success of tissue engineered intervertebral discs (TE-IVDs) cultured in flexible (FPLA) or stiff (PLA) support materials, hypothesizing that FPLA would maintain disc height and tissue hydration in the minipig spine. METHODS/STUDY POPULATION: TE-IVD: NP cells were encapsulated in alginate and NP plugs were placed in the center of FPLA cages. AF cells were encapsulated in type I collagen and pipetted around NP plugs. Implantation: Empty FPLA cages (n=4), and TE-IVDs cultured in FPLA (n=4) were implanted at C3-4 or C5-6 following complete discectomy (DX) in skeletally mature minipigs (n=4). Imaging and Quantification: Terminal disc height indices (DHI) were calculated from weekly x-rays using a previously described method, and results were compared to the PLA pilot study. T2 MRI scans were taken of levels treated with TE-IVDs to quantify disc hydration as previously described. RESULTS/ANTICIPATED RESULTS: FPLA cages restored DHIs to native levels until endpoint. In contrast, PLA cages fractured, and terminal DHIs were statistically similar to DX levels. Of the four levels treated with TE-IVDs, 2 were displaced from the disc space. Stabilized levels yielded DHIs which were statistically similar to native IVD and greater than displaced and DX levels. Displaced levels yielded DHIs which were significantly lower than native and stabilized levels, but greater than DX levels (P<0.05). T2 MRIs of stabilized TEIVDs revealed that levels treated with a construct maintained tissue hydration which was significantly greater than levels treated with an empty cage or DX levels (P<0.0001), but which was about half the hydration of native disc tissue. DISCUSSION/SIGNIFICANCE: Implanting TE-IVDs with FPLA support cages leads to disc height maintenance and the stabilization of hydrated tissues in the spine, enhancing the long term success of TE-IVD implants and providing a basis for clinical translation.
Infants are born predisposed to develop strong relationships to those most likely to protect them; this emotional connection from the child to the protective adult is described as attachment (Ainsworth, 1979; Bowlby, 1983; Crittenden, 2006; Spierling et al., 2019). In turn, parents’ behavioral and physiological responses prime them to respond to attachment behaviors, such as crying, with protective behaviors (Ainsworth, 1979; Bowlby, 1983; Cong et al., 2015). This emotional connection from the attachment figure to the child is described as bonding (Scatliffe et al., 2019). Parental bonding is more often studied in biological mothers, but similar processes of bonding can occur in fathers and other caregivers who act in the role of parents (Bowlby, 1983; Cong et al., 2015; Dayton, Malone, & Brown, 2020). Relationships are a dyadic experience, influenced by both the parent and the child, dynamically changing over time, and shaped by the family context (Ainsworth, 1979; Crittenden, 2006; Wilson et al., 2000). Bonding and attachment are distinct concepts, even though the labels are sometimes used interchangeably (Habib & Lancaster, 2006; McNamara, Townsend, & Herbert, 2019).
Simon Stephens is one of the most prolific playwrights in twenty-firstcentury British theater; his exuberant creative imagination is reflected in his idiosyncratic and daringly experimental approach to theater-making that has yielded highly innovative and stylistically eclectic plays which have set Stephens apart from the tradition of new writing in British theater. One of the most outstanding characteristics of his theater practice is the extent to which Stephens interrogates conventions by crossing aesthetic, dramaturgical, and cultural borders. For Stephens, taking a (geographical) distance, exploring different cultures, and drawing on them as a source of inspiration for his own work is a fundamental prerequisite not only for adopting a fresh perspective on but also for better getting to know and establishing a more intimate relationship with one's “home”—and oneself: “When we travel abroad we see our home with a clarity that we may never have been offered before.”
These border-crossings have informed his work as a playwright on multiple levels, most notably regarding the composition, development, and production of his plays. Throughout his career, Stephens has closely collaborated with European directors, for example Ivo van Hove, who has directed Stephens's Song from Far Away (2015), and Sebastian Nübling, under whose direction several of his plays premiered in Germany; indeed, many of his works have been popular outside Britain, especially on the German-speaking stage. Accordingly, for Stephens, “theater practice is not simply about staging the imagination of a playwright but a multi-authored process of collaboration, conflict, intervention and exploration.” His work as a writer is thus based on a dynamic understanding of the relationships between playwright, director, actors, and audiences. Emphasizing this spirit of interaction, he prefers to describe himself as a playwright rather than an author because the former term “is charged with connotations of life as a theater worker.” As he further explains below, notions of authority and authorial control over his texts are much less interesting to Stephens than collaboration as a source of creative inspiration.
It is in this collaborative and interactive vein that adaptation has played a defining and increasingly important role in Stephens's theater practice. His projects have ranged from turning novels into dramatic texts—most famously Stephens's adaptation of Mark Haddon's The Curious Incident of the Dog in the Night-Time (2012)—to writing new translations of plays by Henrik Ibsen, Anton Chekhov, and Bertolt Brecht.
Tree-ring chronologies encode interannual variability in forest growth rates over long time periods from decades to centuries or even millennia. However, each chronology is a highly localized measurement describing conditions at specific sites where wood samples have been collected. The question whether these local growth variabilites are representative for large geographical regions remains an open issue. To overcome the limitations of interpreting a sparse network of sites, we propose an upscaling approach for annual tree-ring indices that approximate forest growth variability and compute gridded data products that generalize the available information for multiple tree genera. Using regression approaches from machine learning, we predict tree-ring indices in space and time based on climate variables, but considering also species range maps as constraints for the upscaling. We compare various prediction strategies in cross-validation experiments to identify the best performing setup. Our estimated maps of tree-ring indices are the first data products that provide a dense view on forest growth variability at the continental level with 0.5° and 0.0083° spatial resolution covering the years 1902–2013. Furthermore, we find that different genera show very variable spatial patterns of anomalies. We have selected Europe as study region and focused on the six most prominent tree genera, but our approach is very generic and can easily be applied elsewhere. Overall, the study shows perspectives but also limitations for reconstructing spatiotemporal dynamics of complex biological processes. The data products are available at https://www.doi.org/10.17871/BACI.248.