Optimality Conditions of the Hybrid Cellular Automata for Structural Optimization

Tovar, Andrés; Patel, Neal M.; Kaushik, Amit; Renaud, John E.

doi:10.2514/1.20184

Cited by 35 publications

(13 citation statements)

References 36 publications

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“…Outstanding heuristic approaches for multimaterial topology optimization are the bi-directional evolutionary structural optimization (BESO) method [35,36], the Discrete Material Optimization (DMO) method [37,38], and the Hybrid Cellular Automaton (HCA) method [39,40]. For instance, HCA can be efficient in problems involving a large number of design variables in nonlinear multimaterial structures [41]; however, heuristic methods are not applicable to general structural optimization problems.…”

Section: Introductionmentioning

confidence: 99%

Optimal Design of Nonlinear Multimaterial Structures for Crashworthiness Using Cluster Analysis

Liu

Detwiler

Tovar

2017

Journal of Mechanical Design

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This study presents an efficient multimaterial design optimization algorithm that is suitable for nonlinear structures. The proposed algorithm consists of three steps: conceptual design generation, clustering, and metamodel-based global optimization. The conceptual design is generated using a structural optimization algorithm for linear models or a heuristic design algorithm for nonlinear models. Then, the conceptual design is clustered into a predefined number of clusters (materials) using a machine learning algorithm. Finally, the global optimization problem aims to find the optimal material parameters of the clustered design using metamodels. The metamodels are built using sampling and cross-validation, and sequentially updated using an expected improvement function until convergence. The proposed methodology is demonstrated using examples from multiple physics and compared with traditional multimaterial topology optimization method. The proposed approach is applied to nonlinear, multi-objective design problems for crashworthiness.

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Section: Introductionmentioning

confidence: 99%

Optimal Design of Nonlinear Multimaterial Structures for Crashworthiness Using Cluster Analysis

Liu

Detwiler

Tovar

2017

Journal of Mechanical Design

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“…In order to avoid numerical instabilities, the algorithm defines an effective mechanical stimulusS (or effective state variable) as the average value of the cell and its neighboring cells. In Tovar et al (2007), several examples are presented in which HCA converges to different final designs for different control parameters and neighborhood sizes. Even though it is claimed that these final designs are optimal, this is not true in a precise mathematical sense.…”

Section: Observations From Tovar's Hcamentioning

confidence: 99%

“…These rules drive the evolution of the material distribution, which is the outcome of the remodeling process. In Tovar's work, control based rules and a ratio based rule, following the principles of fully stressed design, are presented (Tovar et al, 2007). This work will only focus on the proportional, integral, and derivative (PID) control strategy.…”

Section: Optimality Of Hca Solutionsmentioning

confidence: 99%

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Convergence analysis of hybrid cellular automata for topology optimization

Penninger

Watson

Tovar

et al. 2009

Struct Multidisc Optim

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The hybrid cellular automaton (HCA) algorithm was inspired by the structural adaptation of bones to their ever changing mechanical environment. This methodology has been shown to be an effective topology synthesis tool. In previous work, it has been observed that the convergence of the HCA methodology is affected by parameters of the algorithm. As a result, questions have been raised regarding the conditions by which HCA converges to an optimal design. The objective of this investigation is to examine the conditions that guarantee convergence to a Karush-Kuhn-Tucker (KKT) point. In this paper, it is shown that the HCA algorithm is a fixed point iterative scheme and the previously reported KKT optimality conditions are corrected. To demonstrate the convergence properties of the HCA algorithm, a simple cantilevered beam example is utilized. Plots of the spectral radius for projections of the design space are used to show regions of guaranteed convergence.

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“…It is based on the concept of progressively removing inefficient material from a structure so that it evolves into an optimal design. Another approach that requires non-gradient information is the hybrid cellular automaton (HCA) method [34].…”

Section: Topology Optimized Structures Under Impact Loadsmentioning

confidence: 99%

Optimization of Functionally Graded Materials Considering Dynamical Analysis

Ramírez-Gil

Murillo-Cardoso

Silva

et al. 2016

Advanced Structured Materials

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Functionally graded materials (FGMs) are a new class of bio-inspired composite materials made from different material phases, in which their volume fraction changes gradually towards a particular direction. Accordingly, continuous changes in the composition, microstructure and porosity of the graded materials results in material properties gradients; for this reason, the material properties move smoothly and continuously from one surface to another, eliminating the interface problem. Hence, with appropriate design, FGMs can develop better properties than their homogeneous counterpart due to their better designability. One potential employment of FGMs is as damper or energy absorber in dynamic applications, in which optimization techniques such as the topology optimization method (TOM) can contribute to a better performance in relation to a non-optimized design. In this chapter, functionally graded structures are designed with and without the TOM in order to explore the advantages of the FGM concept in low-velocity impact condition, which is a special case in the world of dynamic analysis, and has interest for designing machinery parts and components.

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Optimality Conditions of the Hybrid Cellular Automata for Structural Optimization

Cited by 35 publications

References 36 publications

Optimal Design of Nonlinear Multimaterial Structures for Crashworthiness Using Cluster Analysis

Optimal Design of Nonlinear Multimaterial Structures for Crashworthiness Using Cluster Analysis

Convergence analysis of hybrid cellular automata for topology optimization

Optimization of Functionally Graded Materials Considering Dynamical Analysis

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