Identification of optimal topologies for crashworthiness with the evolutionary level set method

Bujny, Mariusz; Aulig, Nikola; Olhofer, Markus; Duddeck, Fabian

doi:10.1080/13588265.2017.1331493

Cited by 41 publications

(22 citation statements)

References 37 publications

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“…Mathematically, these rectangular components are described by several location and structure parameters, including center coordinates, length, thickness, and inclined angle [26]. The proposed morphable component-based method is validated by the Miniature Bending Beam example [26] and applied to a rectangular beam [27] and linear elastic cases [28]. Nonetheless, the representability of the proposed method is limited by its rectangular shape, which would be difficult to represent some large curvature shapes.…”

Section: B Level Set Methodsmentioning

confidence: 99%

Research on Evolutionary Level Set Method and Gaussian Mixture Model Based Target Shape Design Optimization Problem

et al. 2019

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Evolutionary algorithms (EAs) have been successfully used in solving many design optimization problems. However, it generally requires expensive computational resources to tune the EA hyper-parameters and validate the performance. Since a single simulation takes a long time and multiple iterations are required, using EAs to real-world design structure optimization is becoming extremely timeconsuming. Therefore, the target shape design optimization problem (TSDOP) has been proposed as a miniature model to replace real-world complex problems. There are three major components in developing EAs for TSDOP, i.e., a shape representation, a fitness evaluation, and an evolutionary strategy. For the shape representation, spline-based methods are frequently used in the research community. However, as their flexibility is dramatically limited by the fixed topology, they have difficulty in representing discontinuous shapes without adding any adjustment strategies. In addition, the spline-based methods will easily generate self-intersection (loop) problem that always increases the search difficulty and reduces the convergence speed during the evolutionary iterations. Therefore, in this paper, we first propose a level-set method integrated with a Gaussian mixture model (GMMLSM) as a shape representation method to overcome the fixed topology and loop problem in the existing spline-based methods. We also propose an improved chaotic evolution for the GMMLSM shape representation, namely, GMMLSM-CE, which integrates the ergodicity from the chaotic system and the good robustness from differential evolution (DE). To evaluate the efficiency and performance of the proposed GMMLSM-CE, experiments on two target shapes with three different EAs are conducted. The empirical results show that: 1) GMMLSM has the ability to represent continuous and discontinuous shapes and can naturally avoid self-intersection (loop) problem; 2) CE has a good performance for parameter tuning, and; 3) GMMLSM-CE has a good representation accuracy and fast convergence speed in terms of solving the TSDOP. INDEX TERMSTarget shape design optimization, level set method, Gaussian mixture model, evolutionary algorithms. GLOSSARY Chaotic evolution CE Covariance matrix adaptation evolution strategy CMA-ES CMA-ES-cooperative coevolution CMA-ES-CC Compactly-supported Radial Basis Function CSRBF Differential evolution DEThe associate editor coordinating the review of this manuscript and approving it for publication was Azwirman Gusrialdi.

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Section: B Level Set Methodsmentioning

confidence: 99%

Research on Evolutionary Level Set Method and Gaussian Mixture Model Based Target Shape Design Optimization Problem

et al. 2019

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“…In addition, a structure's specifications and manufacturability are constraints that should be satisfied [81], [80], [147], [8], [163], [164], [165], [166]. Nonlinear constraints can be handled in two ways: (1) implicitly by using repair/filtering mechanisms, e.g., [42], [80], [81], [21], [68], [73], [46], [112], [101], [37] or assigning a penalty function to the objective function value, e.g., [81], [59], [79], [25], [19], and (2) coupled explicitly with the optimization algorithm [25], [35], [95], [102], [82], [52], [44] incorporating constraint-handling techniques, e.g., [167], [154], [168], [169], [170], [171], [172].…”

Section: Optimization Algorithmsmentioning

confidence: 99%

Evolutionary Black-Box Topology Optimization: Challenges and Promises

Guirguis

Aulig

Picelli

et al. 2020

IEEE Trans. Evol. Computat.

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Black-box topology optimization (BBTO) uses evolutionary algorithms and other soft computing techniques to generate near-optimal topologies of mechanical structures. Although evolutionary algorithms are widely used to compensate the limited applicability of conventional gradient optimization techniques, methods based on BBTO have been criticized due to numerous drawbacks. In this paper, we discuss topology optimization as a black-box optimization problem. We review the main BBTO methods, discuss their challenges and present approaches to relax them. Dealing with those challenges effectively can lead to wider applicability of topology optimization, as well as the ability to tackle industrial, highly-constrained, nonlinear, many-objective and multimodal problems. Consequently, future research in this area may open the door for innovating new applications in science and engineering that may go beyond solving classical optimization problems of structural engineering. Furthermore, algorithms designed for BBTO can be added to existing software toolboxes and packages of topology optimization.

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“…In Reference 17, a set of moving morphable voids described by B-spline curves was adopted as basic building blocks for topology optimization. Due to the big potential in providing explicit geometry information, MMC/MMV has extended to solve three-dimensional problems, 18,19 shell optimization problems, 20,21 crash problems, 22 flexible multibody problems, [23][24][25] length scale control problems, 26,27 and so on. [28][29][30][31][32][33] Additionally, a similar idea to MMC has also been proposed in References 34-38 by using geometry projection technique under SIMP framework.…”

Section: Introductionmentioning

confidence: 99%

Explicit structural topology optimization using boundary element method‐based moving morphable void approach

Zhang

Jiang

Feng

et al. 2021

Numerical Meth Engineering

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This article presents an explicit topology optimization approach using boundary element method based moving morphable void (MMV). Structural analysis in the conventional MMV approach is performed on a fixed mesh over the entire design domain. However, in the proposed method structural boundaries are described using B-splines and discretized with boundary elements making explicit representation of the boundaries possible. In this regard, the proposed approach has following merits: a) the use of weak material, which is often adopted to mimic voids can be completely avoided; b) exact and explicit description of voids in MMV allows the capture of tiny structural features in a robust and effective way; c) numerical instabilities stemming from the use of fixed meshes can be naturally avoided. Several numerical examples are provided to demonstrate the effectiveness of the proposed approach.

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Identification of optimal topologies for crashworthiness with the evolutionary level set method

Cited by 41 publications

References 37 publications

Research on Evolutionary Level Set Method and Gaussian Mixture Model Based Target Shape Design Optimization Problem

Research on Evolutionary Level Set Method and Gaussian Mixture Model Based Target Shape Design Optimization Problem

Evolutionary Black-Box Topology Optimization: Challenges and Promises

Explicit structural topology optimization using boundary element method‐based moving morphable void approach

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