Jiaxiang Luo^1,2, Yu Li², Weien Zhou², Zhiqiang Gong², Zeyu Zhang¹, Wen Yao^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.3, pp. 823-848, 2021, DOI:10.32604/cmes.2021.016737

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 constraints. Since the calculation of… More >

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

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 during the parallelization. Furthermore, we… More >

Baoshou Liu^1,2, Xiaolei Yan¹, Yangfan Li³, Shiwei Zhou⁴, Xiaodong Huang^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.2, pp. 523-540, 2021, DOI:10.32604/cmes.2021.017211

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 convergent element-based solution, the multiple… More >

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

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 are transformed to distortion energy… More >

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

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 makes it convenient to use.… More >

Ellie Vineyard¹, Xin-Lin Gao^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.3, pp. 819-854, 2021, DOI:10.32604/cmes.2021.015688

Abstract 2-D and 3-D micro-architectured multiphase thermoelastic metamaterials are designed and analyzed using a parametric level set method for topology optimization and the finite element method. An asymptotic homogenization approach is employed to obtain the effective thermoelastic properties of the multiphase metamaterials. The -constraint multi-objective optimization method is adopted in the formulation. The coefficient of thermal expansion (CTE) and Poisson’s ratio (PR) are chosen as two objective functions, with the CTE optimized and the PR treated as a constraint. The optimization problems are solved by using the method of moving asymptotes. Effective isotropic and anisotropic CTEs and stiffness constants are obtained… More >

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

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 investigate the simultaneous change of… More >

Xinqing Li¹, Qinghai Zhao^1,*, Hongxin Zhang¹, Tiezhu Zhang², Jianliang Chen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.2, pp. 683-704, 2021, DOI:10.32604/cmes.2021.015685

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 by individually optimizing each preset… More >

Yuan Zhu^{1, 2}, Xin Ning^{1, 2}, Yao Zhang^{1, 2}, Yuwan Yin^{1, 2}

The International Conference on Computational & Experimental Engineering and Sciences, Vol.23, No.1, pp. 11-12, 2021, DOI:10.32604/icces.2021.08311

Abstract High performance of the spacecraft structure is required in the special environment, it includes mechanical performance and operational performance, etc. When performing tasks, the spaceborne equipment requires high precision. Therefore, the design of lightweight, high stability and high reliability structure is essential for spacecraft. Topology optimization is widely used in structural design. However, there are some problems in the structure after macro topology optimization, such as checkerboard, local optimal solution and other phenomena. Despite a long calculation period, the obtained structure is often not smooth enough and hard to manufacture. Aiming to this issue, this paper proposes a combined method… More >

Fusheng Qiu^1,*, Hongliang Liu^1,*, Hongjuan Zhao²

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.1, pp. 43-57, 2021, DOI:10.32604/cmes.2021.014530

Abstract This paper presents a feature modeling approach to address the 3D structural topology design optimization with feature constraints. In the proposed algorithm, various features are formed into searchable shape features by the feature modeling technology, and the models of feature elements are established. The feature elements that meet the design requirements are found by employing a feature matching technology, and the constraint factors combined with the pseudo density of elements are initialized according to the optimized feature elements. Then, through controlling the constraint factors and utilizing the optimization criterion method along with the filtering technology of independent mesh, the structural… More >