Explicit structural topology optimization based on moving morphable components (MMC) with curved skeletons

Guo, Xu; Zhang, Weisheng; Zhang, Jian; Yuan, Jie

doi:10.1016/j.cma.2016.07.018

Cited by 284 publications

(98 citation statements)

References 37 publications

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“…It is worth noting that the X‐FEM approaches and body‐fitted adaptive mesh techniques can be also employed in this study to remove the artificial weak material and further improve the accuracy of the stress calculation since the clear boundaries of the structure can be explicitly described in the PLSM.…”

Section: Numerical Implementationmentioning

confidence: 99%

A level set–based method for stress‐constrained multimaterial topology optimization of minimizing a global measure of stress

Chu

Xiao

Gao

et al. 2018

Numerical Meth Engineering

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Summary In multimaterial topology optimization of minimizing a global measure of stress, the maximum stresses in different materials may not satisfy the strength design requirements simultaneously if stress constraints for different materials are not considered. In this paper, a level set–based method is presented to handle the stress‐constrained multimaterial topology optimization of minimizing a global stress measure. Specifically, a multimaterial level set model is adopted to describe the structural topology, and a stress interpolation scheme is introduced for stress evaluation. Then, a stress penalty‐based topology optimization model is presented. Meanwhile, an adaptive adjusting scheme of the stress penalty factor is employed to improve the control of the local stress level. To solve the stress‐constrained multimaterial topology optimization problem minimizing the global measure of stress, the parametric level set method is employed, and the sensitivity analysis is carried out. Numerical examples are provided to demonstrate the effectiveness of the presented method. Results indicate that multimaterial structures with optimized global stress can be gained, and stress constraints for different materials can be satisfied simultaneously.

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Section: Numerical Implementationmentioning

confidence: 99%

A level set–based method for stress‐constrained multimaterial topology optimization of minimizing a global measure of stress

Chu

Xiao

Gao

et al. 2018

Numerical Meth Engineering

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“…Kang and Wang and Wang et al first introduced design variables (orientation and position variables) defining the layout of embedded components into the level set‐based geometrical representation in topology optimization problems . Recently, several other explicit geometry‐based parameterization schemes have also been studied –. In these methods, the structural geometry is determined by the intersection of some geometry components and is optimized by updating the parameters representing the layout and the shape of these components.…”

Section: Introductionmentioning

confidence: 99%

A velocity field level set method for shape and topology optimization

Wang

Kang

2018

Numerical Meth Engineering

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Summary In this paper, we propose a new implementation of the level set shape and topology optimization, the velocity field level set method. Therein, the normal velocity field is constructed with specified basis functions and velocity design variables defined on a given set of points that are independent of the finite element mesh. A general mathematical programming algorithm can be employed to find the optimal normal velocities on the basis of the sensitivity analysis. As compared with conventional level set methods, mapping the variational boundary shape optimization problem into a finite‐dimensional design space and the use of a general optimizer makes it more efficient and straightforward to handle multiple constraints and additional design variables. Moreover, the level set function is updated by the Hamilton‐Jacobi equation using the normal velocity field; thus, the inherent merits of the implicit representation is retained. Therefore, this method combines the merits of both the general mathematical programming and conventional level set methods. Integrated topology optimization of structures with embedded components of designable geometries is considered to show the capability of this method to deal with general design variables. Several numerical examples in 2D or 3D design domains illustrate the robustness and efficiency of the method using different basis functions.

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“…New strategies have been implemented in the topology optimization method to solve the Hamilton-Jacobi-type equation [24][25][26][27], aiming at improving the computational efficiency and enhancing the numerical stability [28][29][30]. Recently, Guos group made great progress in parametric level set topology optimization methods, which significantly reduced the number of the design variables and in turn tremendously increase the computational efficiency [31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Topology Description Function Method Based on Modified Sigmoid Function

Yang

Liu

Yang

et al. 2018

Mathematical Problems in Engineering

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Optimal geometries extracted from traditional element-based topology optimization outcomes usually have zigzag boundaries, leading to being difficult to fabricate. In this study, a fairly accurate and efficient topology description function method (TDFM) for topology optimization of linear elastic structures is developed. By employing the modified sigmoid function, a simple yet efficient strategy is presented to tackle the computational difficulties because of the nonsmoothness of Heaviside function in topology optimization problem. The optimization problem is to minimize the structural compliance, with highest stiffness, while satisfying the volume constraint. The design problem is solved by a Sequential Linear Programming method. Convergent, crisp, and smooth final layouts are obtained, which can be fabricated without postprocessing, demonstrated by a series of numerical examples. Further, the proposed method has a rather higher accuracy and efficiency compared with traditional TDFM, when the classical topology optimization methods, such as bidirectional evolutionary structural optimization (BESO) and solid isotropic material with penalization (SIMP) method, are taken as benchmark.

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Explicit structural topology optimization based on moving morphable components (MMC) with curved skeletons

Cited by 284 publications

References 37 publications

A level set–based method for stress‐constrained multimaterial topology optimization of minimizing a global measure of stress

A level set–based method for stress‐constrained multimaterial topology optimization of minimizing a global measure of stress

A velocity field level set method for shape and topology optimization

An Efficient Topology Description Function Method Based on Modified Sigmoid Function

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