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Novel Methods of Topology Optimization and Engineering Applications

Submission Deadline: 31 May 2021 (closed) View: 178

Guest Editors

Prof. Kai Long, North China Electric Power University, China
Prof. Xiaodong Huang, Swinburne University of Technology, Australia
Dr. Quhao Li, Shandong University, China
Dr. Xuan Wang, Hefei University of Technology, China
Prof. Zunyi Duan, Northwestern Polytechnical University, China

Summary

As a promising design tool, topology optimization has experienced tremendous progress. Aiming to allocate the available material to maximize system performance while satisfying multiple constraints, a number of branches have come into emergence, e.g. homogenization method, Solid Isotropic Material with Penalization (SIMP), Evolutionary Structural Optimization (ESO) and Bi-directional Evolutionary Structural Optimization (BESO), level set method (LSM), phase field method, moving morphable components or voids (MMC, MMV) method. In recent years, several novel methods on topology optimization have emerged, such as parametric level set method, moving morphable components method, new bubble method and the combination with traditional technique.

 

We initiate this special issue to highlight the new developments of topology optimization methods and their applications, with particular focus on theory developments, numerical implementations and potential applications.

 

Potential topics include but are not limited to:

(1) New topology optimization method, theory, numerical technique and its engineering application

(2) Metamaterial material design, bionics design, multi-scale design by topology optimization method

(3) Topology optimization method related to nonlinearity, buckling, stress, fatigue and multiple physical problems

(4) Topology optimization combined with large-scale computation or reliability

Keywords

Topology optimization, multi-scale design, bionics design, nonlinear topology optimization

Published Papers

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  • Open Access

    EDITORIAL

    Introduction to the Special Issue on Novel Methods of Topology Optimization and Engineering Applications

    Kai Long, Xiaodong Huang, Zunyi Duan, Xuan Wang, Quhao Li
    CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.1, pp. 27-29, 2022, DOI:10.32604/cmes.2022.020822
    （This article belongs to the Special Issue: Novel Methods of Topology Optimization and Engineering Applications)
    Abstract This article has no abstract. More >

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    2057

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    1248

  • Open Access

    ARTICLE

    Topology Optimization with Aperiodic Load Fatigue Constraints Based on Bidirectional Evolutionary Structural Optimization

    Yongxin Li, Guoyun Zhou, Tao Chang, Liming Yang, Fenghe Wu
    CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.1, pp. 499-511, 2022, DOI:10.32604/cmes.2022.017630
    （This article belongs to the Special Issue: Novel Methods of Topology Optimization and Engineering Applications)
    Abstract Because of descriptive nonlinearity and computational inefficiency, topology optimization with fatigue life under aperiodic loads has developed slowly. A fatigue constraint topology optimization method based on bidirectional evolutionary structural optimization (BESO) under an aperiodic load is proposed in this paper. In view of the severe nonlinearity of fatigue damage with respect to design variables, effective stress cycles are extracted through transient dynamic analysis. Based on the Miner cumulative damage theory and life requirements, a fatigue constraint is first quantified and then transformed into a stress problem. Then, a normalized termination criterion is proposed by approximate More >

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    2560

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    1296

  • Open Access

    ARTICLE

    An XBi-CFAO Method for the Optimization of Multi-Layered Variable Stiffness Composites Using Isogeometric Analysis

    Chao Mei, Qifu Wang, Chen Yu, Zhaohui Xia
    CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.2, pp. 627-659, 2021, DOI:10.32604/cmes.2021.017704
    （This article belongs to the Special Issue: Novel Methods of Topology Optimization and Engineering Applications)
    Abstract This paper presents an effective fiber angle optimization method for two and multi-layered variable stiffness composites. A gradient-based fiber angle optimization method is developed based on isogeometric analysis (IGA). Firstly, the element densities and fiber angles for two and multi-layered composites are synchronously optimized using an extended Bi-layered continuous fiber angle optimization method (XBi-CFAO). The densities and fiber angles in the base layer are attached to the control points. The structure response and sensitivity analysis are accomplished using the non-uniform rational B-spline (NURBS) based IGA. By the benefit of the B-spline space, this method is More >

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    1914

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    1467

  • Open Access

    ARTICLE

    Fail-Safe Topology Optimization of Continuum Structures with Multiple Constraints Based on ICM Method

    Jiazheng Du, Ying Zhang, Fanwei Meng
    CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.2, pp. 661-687, 2021, DOI:10.32604/cmes.2021.017580
    （This article belongs to the Special Issue: Novel Methods of Topology Optimization and Engineering Applications)
    Abstract Traditional topology optimization methods may lead to a great reduction in the redundancy of the optimized structure due to unexpected material removal at the critical components. The local failure in critical components can instantly cause the overall failure in the structure. More and more scholars have taken the fail-safe design into consideration when conducting topology optimization. A lot of good designs have been obtained in their research, though limited regarding minimizing structural compliance (maximizing stiffness) with given amount of material. In terms of practical engineering applications considering fail-safe design, it is more meaningful to seek… More >

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    2273

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    1236

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    ARTICLE

    An Improved Data-Driven Topology Optimization Method Using Feature Pyramid Networks with Physical Constraints

    Jiaxiang Luo, Yu Li, Weien Zhou, Zhiqiang Gong, Zeyu Zhang, Wen Yao
    CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.3, pp. 823-848, 2021, DOI:10.32604/cmes.2021.016737
    （This article belongs to the Special Issue: Novel Methods of Topology Optimization and Engineering Applications)
    Abstract Deep learning for topology optimization has been extensively studied to reduce the cost of calculation in recent years. However, the loss function of the above method is mainly based on pixel-wise errors from the image perspective, which cannot embed the physical knowledge of topology optimization. Therefore, this paper presents an improved deep learning model to alleviate the above difficulty effectively. The feature pyramid network (FPN), a kind of deep learning model, is trained to learn the inherent physical law of topology optimization itself, of which the loss function is composed of pixel-wise errors and physical More >

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    2870

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    2125

  • Open Access

    ARTICLE

    An Improved Graphics Processing Unit Acceleration Approach for Three-Dimensional Structural Topology Optimization Using the Element-Free Galerkin Method

    Haishan Lu, Shuguang Gong, Jianping Zhang, Guilan Xie, Shuohui Yin
    CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.3, pp. 1151-1178, 2021, DOI:10.32604/cmes.2021.016165
    （This article belongs to the Special Issue: Novel Methods of Topology Optimization and Engineering Applications)
    Abstract We proposed an improved graphics processing unit (GPU) acceleration approach for three-dimensional structural topology optimization using the element-free Galerkin (EFG) method. This method can effectively eliminate the race condition under parallelization. We established a structural topology optimization model by combining the EFG method and the solid isotropic microstructures with penalization model. We explored the GPU parallel algorithm of assembling stiffness matrix, solving discrete equation, analyzing sensitivity, and updating design variables in detail. We also proposed a node pair-wise method for assembling the stiffness matrix and a node-wise method for sensitivity analysis to eliminate race conditions More >

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    2143

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    1638

  • Open Access

    ARTICLE

    Thermoelastic Structural Topology Optimization Based on Moving Morphable Components Framework

    Jun Yan, Qi Xu, Zhirui Fan, Zunyi Duan, Hongze Du, Dongling Geng
    CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.3, pp. 1179-1196, 2021, DOI:10.32604/cmes.2021.016950
    （This article belongs to the Special Issue: Novel Methods of Topology Optimization and Engineering Applications)
    Abstract This study investigates structural topology optimization of thermoelastic structures considering two kinds of objectives of minimum structural compliance and elastic strain energy with a specified available volume constraint. To explicitly express the configuration evolution in the structural topology optimization under combination of mechanical and thermal load conditions, the moving morphable components (MMC) framework is adopted. Based on the characteristics of the MMC framework, the number of design variables can be reduced substantially. Corresponding optimization formulation in the MMC topology optimization framework and numerical solution procedures are developed for several numerical examples. Different optimization results are More >

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    2076

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    1626

  • Open Access

    ARTICLE

    Functionally Graded Cellular Structure Design Using the Subdomain Level Set Method with Local Volume Constraints

    Lianxiong Chen, Hui Liu, Xihua Chu, Jiao Wang
    CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.3, pp. 1197-1218, 2021, DOI:10.32604/cmes.2021.016894
    （This article belongs to the Special Issue: Novel Methods of Topology Optimization and Engineering Applications)
    Abstract Functional graded cellular structure (FGCS) usually shows superior mechanical behavior with low density and high stiffness. With the development of additive manufacturing, functional graded cellular structure gains its popularity in industries. In this paper, a novel approach for designing functionally graded cellular structure is proposed based on a subdomain parameterized level set method (PLSM) under local volume constraints (LVC). In this method, a subdomain level set function is defined, parameterized and updated on each subdomain independently making the proposed approach much faster and more cost-effective. Additionally, the microstructures on arbitrary two adjacent subdomains can be More >

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    2382

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    1586

    Cited by

    1

  • Open Access

    ARTICLE

    Multi-Material Topology Optimization of Structures Using an Ordered Ersatz Material Model

    Baoshou Liu, Xiaolei Yan, Yangfan Li, Shiwei Zhou, Xiaodong Huang
    CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.2, pp. 523-540, 2021, DOI:10.32604/cmes.2021.017211
    （This article belongs to the Special Issue: Novel Methods of Topology Optimization and Engineering Applications)
    Abstract This paper proposes a new element-based multi-material topology optimization algorithm using a single variable for minimizing compliance subject to a mass constraint. A single variable based on the normalized elemental density is used to overcome the occurrence of meaningless design variables and save computational cost. Different from the traditional material penalization scheme, the algorithm is established on the ordered ersatz material model, which linearly interpolates Young's modulus for relaxed design variables. To achieve a multi-material design, the multiple floating projection constraints are adopted to gradually push elemental design variables to multiple discrete values. For the More >

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    2569

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    1756

  • Open Access

    ARTICLE

    A Parameter-Free Approach to Determine the Lagrange Multiplier in the Level Set Method by Using the BESO

    Zihao Zong, Tielin Shi, Qi Xia
    CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.1, pp. 283-295, 2021, DOI:10.32604/cmes.2021.015975
    （This article belongs to the Special Issue: Novel Methods of Topology Optimization and Engineering Applications)
    Abstract A parameter-free approach is proposed to determine the Lagrange multiplier for the constraint of material volume in the level set method. It is inspired by the procedure of determining the threshold of sensitivity number in the BESO method. It first computes the difference between the volume of current design and the upper bound of volume. Then, the Lagrange multiplier is regarded as the threshold of sensitivity number to remove the redundant material. Numerical examples proved that this approach is effective to constrain the volume. More importantly, there is no parameter in the proposed approach, which More >

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    2261

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    1382

  • Open Access

    ARTICLE

    Fatigue Topology Optimization Design Based on Distortion Energy Theory and Independent Continuous Mapping Method

    Hongling Ye, Zonghan Li, Nan Wei, Pengfei Su, Yunkang Sui
    CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.1, pp. 297-314, 2021, DOI:10.32604/cmes.2021.016133
    （This article belongs to the Special Issue: Novel Methods of Topology Optimization and Engineering Applications)
    Abstract Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications, which often occurs with no obvious signal. The maximum structural stress is far below the allowable stress when the structures are damaged. Aiming at the lightweight structure, fatigue topology optimization design is investigated to avoid the occurrence of fatigue failure in the structural conceptual design beforehand. Firstly, the fatigue life is expressed by topology variables and the fatigue life filter function. The continuum fatigue optimization model is established with the independent continuous mapping (ICM) method. Secondly, fatigue life constraints More >

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    2551

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    1672

  • Open Access

    ARTICLE

    A Combined Shape and Topology Optimization Based on Isogeometric Boundary Element Method for 3D Acoustics

    Jie Wang, Fuhang Jiang, Wenchang Zhao, Haibo Chen
    CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.2, pp. 645-681, 2021, DOI:10.32604/cmes.2021.015894
    （This article belongs to the Special Issue: Novel Methods of Topology Optimization and Engineering Applications)
    Abstract A combined shape and topology optimization algorithm based on isogeometric boundary element method for 3D acoustics is developed in this study. The key treatment involves using adjoint variable method in shape sensitivity analysis with respect to non-uniform rational basis splines control points, and in topology sensitivity analysis with respect to the artificial densities of sound absorption material. OpenMP tool in Fortran code is adopted to improve the efficiency of analysis. To consider the features and efficiencies of the two types of optimization methods, this study adopts a combined iteration scheme for the optimization process to More >

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    2698

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    1872

  • Open Access

    ARTICLE

    Robust Topology Optimization of Periodic Multi-Material Functionally Graded Structures under Loading Uncertainties

    Xinqing Li, Qinghai Zhao, Hongxin Zhang, Tiezhu Zhang, Jianliang Chen
    CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.2, pp. 683-704, 2021, DOI:10.32604/cmes.2021.015685
    （This article belongs to the Special Issue: Novel Methods of Topology Optimization and Engineering Applications)
    Abstract This paper presents a robust topology optimization design approach for multi-material functional graded structures under periodic constraint with load uncertainties. To characterize the random-field uncertainties with a reduced set of random variables, the Karhunen-Loève (K-L) expansion is adopted. The sparse grid numerical integration method is employed to transform the robust topology optimization into a weighted summation of series of deterministic topology optimization. Under dividing the design domain, the volume fraction of each preset gradient layer is extracted. Based on the ordered solid isotropic microstructure with penalization (Ordered-SIMP), a functionally graded multi-material interpolation model is formulated More >

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    2667

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    1616

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    1

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