Zhaohui Xia^1,3, Baichuan Gao³, Chen Yu^2,*, Haotian Han³, Haobo Zhang³, Shuting Wang³

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.2, pp. 1103-1137, 2024, DOI:10.32604/cmes.2023.029177

Abstract This paper aims to solve large-scale and complex isogeometric topology optimization problems that consume significant computational resources. A novel isogeometric topology optimization method with a hybrid parallel strategy of CPU/GPU is proposed, while the hybrid parallel strategies for stiffness matrix assembly, equation solving, sensitivity analysis, and design variable update are discussed in detail. To ensure the high efficiency of CPU/GPU computing, a workload balancing strategy is presented for optimally distributing the workload between CPU and GPU. To illustrate the advantages of the proposed method, three benchmark examples are tested to verify the hybrid parallel strategy in this paper. The results… More > Graphic Abstract

ShiJie Luo¹, Feng Yang¹, Yingjun Wang^1,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.1, pp. 1-1, 2023, DOI:10.32604/icces.2023.09474

Abstract The isogeometric analysis Method (IGA) is an efficient and accurate engineering analysis method. However, in order to obtain accurate analysis results, the grid must be refined, and the increase of the number of refinements will lead to large-scale equations, which will increase the computational cost. Compared with the traditional equation solvers such as preconditioned conjugate gradient method (PCG), generalized minimal residual (GMRES), the advantage of multigrid method is that the convergence rate is independent of grid scale when solving large-scale equations. This paper presents an adaptive weighted Jacobi method to improve the convergence of geometric multigrid method to efficiently solve… More >

Xuhang Lin¹, Haibo Chen^1,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.1, pp. 1-1, 2023, DOI:10.32604/icces.2023.09388

Abstract As an important and useful tool for reducing noise, the sound barrier is of practical significance. The sound barrier has different noise reduction effects for different sizes, shapes and properties of the sound absorbing material. Liu et al. [1] have performed shape optimization of sound barriers by using isogeometric boundary element method and method of moving asymptotes (MMA). However, in engineering practice, it is difficult to determine some parameters accurately such as material properties, geometries, external loads. Therefore, it is necessary to consider these uncertainty conditions in order to ensure the rationality of the numerical calculation of engineering problems. In… More >

Jinlan Xu^*, Shuxin Xiao, Gang Xu, Renshu Gu

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.2, pp. 1957-1973, 2023, DOI:10.32604/cmes.2023.028665

Abstract In this paper, we propose a parameterization transfer algorithm for planar domains bounded by B-spline curves, where the shapes of the planar domains are similar. The domain geometries are considered to be similar if their simplified skeletons have the same structures. One domain we call source domain, and it is parameterized using multi-patch B-spline surfaces. The resulting parameterization is C1 continuous in the regular region and G1 continuous around singular points regardless of whether the parameterization of the source domain is C1/G1 continuous or not. In this algorithm, boundary control points of the source domain are extracted from its parameterization… More >

Jingwen Ren¹, Hongwei Lin^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 2957-2984, 2023, DOI:10.32604/cmes.2023.025983

Abstract Isogeometric analysis (IGA) is introduced to establish the direct link between computer-aided design and analysis. It is commonly implemented by Galerkin formulations (isogeometric Galerkin, IGA-G) through the use of nonuniform rational B-splines (NURBS) basis functions for geometric design and analysis. Another promising approach, isogeometric collocation (IGA-C), working directly with the strong form of the partial differential equation (PDE) over the physical domain defined by NURBS geometry, calculates the derivatives of the numerical solution at the chosen collocation points. In a typical IGA, the knot vector of the NURBS numerical solution is only determined by the physical domain. A new perspective… More > Graphic Abstract

Zhihui Xiong^*, Lei Kou, Jinjie Zhao, Hao Cui, Bo Wang

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 803-824, 2023, DOI:10.32604/cmes.2023.024833

Abstract Serious uneven settlement of the tunnel may directly cause safety problems. At this stage, the deformation of the tunnel is predicted and analyzed mainly by numerical simulation, while the commonly used finite element method (FEM) uses low-order continuous elements. Therefore, the accuracy of tunnel settlement prediction is not enough. In this paper, a method is proposed to study the vertical deformation of the tunnel by using the combination of isogeometric analysis (IGA) and Bézier extraction operator. Compared with the traditional IGA method, this method can be easily integrated into the existing FEM framework, and ensure the same accuracy. A numerical… More >

Xuan Peng^1,*, Chao Zheng^2,3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.3, pp. 1837-1853, 2023, DOI:10.32604/cmes.2022.022367

Abstract A novel continuum-based fast projection scheme is proposed for cloth simulation. Cloth geometry is described by NURBS, and the dynamic response is modeled by a displacement-only Kirchhoff-Love shell element formulated directly on NURBS geometry. The fast projection method, which solves strain limiting as a constrained Lagrange problem, is extended to the continuum version. Numerical examples are studied to demonstrate the performance of the current scheme. The proposed approach can be applied to grids of arbitrary topology and can eliminate unrealistic over-stretching efficiently if compared to spring-based methodologies. More >

Jintao Liu¹, Juan Zhao¹, Xiaowei Shen^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.2, pp. 981-1003, 2023, DOI:10.32604/cmes.2022.021641

Abstract In this work, an acoustic topology optimization method for structural surface design covered by porous materials is proposed. The analysis of acoustic problems is performed using the isogeometric boundary element method. Taking the element density of porous materials as the design variable, the volume of porous materials as the constraint, and the minimum sound pressure or maximum scattered sound power as the design goal, the topology optimization is carried out by solid isotropic material with penalization (SIMP) method. To get a limpid 0–1 distribution, a smoothing Heaviside-like function is proposed. To obtain the gradient value of the objective function, a… More >

Qingyuan Hu^1,*, Yuan Liang², Menghao Liu¹, Manfeng Hu¹, Yawen Mao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.1, pp. 459-481, 2023, DOI:10.32604/cmes.2022.020327

Abstract Topological optimization plays a guiding role in the conceptual design process. This paper conducts research on structural topology optimization algorithm within the framework of isogeometric analysis. For multi-component structures, the Nitsche’s method is used to glue different meshes to perform isogeometric multi-patch analysis. The discrete variable topology optimization algorithm based on integer programming is adopted in order to obtain clear boundaries for topology optimization. The sensitivity filtering method based on the Helmholtz equation is employed for averaging of curved elements' sensitivities. In addition, a simple averaging method along coupling interfaces is proposed in order to ensure the material distribution across… More >

Jinggang Deng^1,2, Bingquan Zuo^1,2,*, Huixin Luo^1,2, Weikang Xie^1,2, Jiashu Yang^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.3, pp. 965-990, 2022, DOI:10.32604/cmes.2022.020631

Abstract In this paper, a new computation scheme based on parallelization is proposed for Isogeometric analysis. The parallel computing is introduced to the whole progress of Isogeometric analysis. Firstly, with the help of the “tensorproduct” and “iso-parametric” feature, all the Gaussian integral points in particular element can be mapped to a global matrix using a transformation matrix that varies from element. Then the derivatives of Gauss integral points are computed in parallel, the results of which can be stored in a global matrix. And a middle layer is constructed to assemble the final stiffness matrices in parallel. The numerical example results… More >