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  • Open Access


    Geometric Multigrid Method for Isogeometric Analysis

    Houlin Yang1, Bingquan Zuo1,2,*, Zhipeng Wei1,2, Huixin Luo1,2, Jianguo Fei1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.3, pp. 1033-1052, 2021, DOI:10.32604/cmes.2021.014493

    Abstract The isogeometric analysis method (IGA) is a new type of numerical method solving partial differential equations. Compared with the traditional finite element method, IGA based on geometric spline can keep the model consistency between geometry and analysis, and provide higher precision with less freedom. However, huge stiffness matrix from the subdivision progress still leads to the solution efficiency problems. This paper presents a multigrid method based on geometric multigrid (GMG) to solve the matrix system of IGA. This method extracts the required computational data for multigrid method from the IGA process, which also can be used to improve the traditional… More >

  • Open Access


    Isogeometric Boundary Element Analysis for 2D Transient Heat Conduction Problem with Radial Integration Method

    Leilei Chen1, Kunpeng Li1, Xuan Peng2, Haojie Lian3,4,*, Xiao Lin5, Zhuojia Fu6

    CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.1, pp. 125-146, 2021, DOI:10.32604/cmes.2021.012821

    Abstract This paper presents an isogeometric boundary element method (IGABEM) for transient heat conduction analysis. The Non-Uniform Rational B-spline (NURBS) basis functions, which are used to construct the geometry of the structures, are employed to discretize the physical unknowns in the boundary integral formulations of the governing equations. B´ezier extraction technique is employed to accelerate the evaluation of NURBS basis functions. We adopt a radial integration method to address the additional domain integrals. The numerical examples demonstrate the advantage of IGABEM in dimension reduction and the seamless connection between CAD and numerical analysis. More >

  • Open Access


    Isogeometric Analysis and Shape Optimization of Holed Structures via the Patch Removing Technique

    Daoyuan Yu, Shouyu Cai*, Wenya Fan, Lan Zhang*

    CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.3, pp. 787-806, 2020, DOI:10.32604/cmes.2020.09936

    Abstract In this study, a patch removing based Isogeometric analysis (PR-IGA) method is proposed to conduct the holed structural analysis with only one parametric domain, in which there are also no trimmed elements. The theoretical foundation of this novel patch removing approach is that any holed structure can be obtained by removing sub-patches (i.e., the holes) from an intact base patch. Since the parametric domains of these patches are all meshed by rectangular grids, the elements in the resulted holed structural parametric domain could all be untrimmed rectangles under certain mapping conditions. To achieve the special condition, a systematic technique consisting… More >

  • Open Access


    Introduction to the Special Issue on Recent Developments of Isogeometric Analysis and Its Applications in Structural Optimization

    Yingjun Wang1,*, Zhenpei Wang2, Xiaowei Deng3, David J. Benson4, Damiano Pasini5, Shuting Wang6

    CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.3, pp. 783-785, 2020, DOI:10.32604/cmes.2020.013234

    Abstract This article has no abstract. More >

  • Open Access


    Three-Dimensional Isogeometric Analysis of Flexoelectricity with MATLAB Implementation

    Hamid Ghasemi1, Harold S. Park2, Xiaoying Zhuang3, 4, *, Timon Rabczuk5, 6

    CMC-Computers, Materials & Continua, Vol.65, No.2, pp. 1157-1179, 2020, DOI:10.32604/cmc.2020.08358

    Abstract Flexoelectricity is a general electromechanical phenomenon where the electric polarization exhibits a linear dependency to the gradient of mechanical strain and vice versa. The truncated pyramid compression test is among the most common setups to estimate the flexoelectric effect. We present a three-dimensional isogeometric formulation of flexoelectricity with its MATLAB implementation for a truncated pyramid setup. Besides educational purposes, this paper presents a precise computational model to illustrate how the localization of strain gradients around pyramidal boundary shapes contributes in generation of electrical energy. The MATLAB code is supposed to help learners in the Isogeometric Analysis and Finite Elements Methods… More >

  • Open Access


    A High-Accuracy Single Patch Representation of Multi-Patch Geometries with Applications to Isogeometric Analysis

    Jinlan Xu*, Ningning Sun, Gang Xu

    CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.2, pp. 627-642, 2020, DOI:10.32604/cmes.2020.010341

    Abstract This paper presents a novel approximating method to construct highprecision single-patch representation of B-spline surface from a multi-patch representation for isogeometric applications. In isogeometric analysis, multi-patch structure is not easy to achieve high continuity between neighboring patches which will reduce the advantage of isogeometric analysis in a sense. The proposed method can achieve high continuity at surface stitching region with low geometric error, and this technique exploits constructing the approximate surface with several control points are from original surfaces, which guarantees the local feature of the surface can be well-preserved with high precision. With the proposed approximating method, isogeometric analysis… More >

  • Open Access


    Analysis-Aware Modelling of Spacial Curve for Isogeometric Analysis of Timoshenko Beam

    Yang Xia*, Luting Deng, Jian Zhao

    CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.2, pp. 605-626, 2020, DOI:10.32604/cmes.2020.010204

    Abstract Geometric fitting based on discrete points to establish curve structures is an important problem in numerical modeling. The purpose of this paper is to investigate the geometric fitting method for curved beam structure from points, and to get high-quality parametric model for isogeometric analysis. A Timoshenko beam element is established for an initially curved spacial beam with arbitrary curvature. The approximation and interpolation methods to get parametric models of curves from given points are examined, and three strategies of parameterization, meaning the equally spaced method, the chord length method and the centripetal method are considered. The influences of the different… More >

  • Open Access


    Resolving Domain Integral Issues in Isogeometric Boundary Element Methods via Radial Integration: A Study of Thermoelastic Analysis

    Shige Wang1, Zhongwang Wang1, Leilei Chen1, Haojie Lian2,3,*, Xuan Peng4, Haibo Chen5

    CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.2, pp. 585-604, 2020, DOI:10.32604/cmes.2020.09904

    Abstract The paper applied the isogeometric boundary element method (IGABEM) to thermoelastic problems. The Non-Uniform Rational B-splines (NURBS) used to construct geometric models are employed to discretize the boundary integral formulation of the governing equation. Due to the existence of thermal stress, the domain integral term appears in the boundary integral equation. We resolve this problem by incorporating radial integration method into IGABEM which converts the domain integral to the boundary integral. In this way, IGABEM can maintain its advantages in dimensionality reduction and more importantly, seamless integration of CAD and numerical analysis based on boundary representation. The algorithm is verified… More >

  • Open Access


    Parametric Structural Optimization of 2D Complex Shape Based on Isogeometric Analysis

    Long Chen1, Li Xu1, Kai Wang1, Baotong Li2,*, Jun Hong2

    CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.1, pp. 203-225, 2020, DOI:10.32604/cmes.2020.09896

    Abstract The geometric model and the analysis model can be unified together through the isogeometric analysis method, which has potential to achieve seamless integration of CAD and CAE. Parametric design is a mainstream and successful method in CAD field. This method is not continued in simulation and optimization stage because of the model conversion in conventional optimization method based on the finite element analysis. So integration of the parametric modeling and the structural optimization by using isogeometric analysis is a natural and interesting issue. This paper proposed a method to realize a structural optimization of parametric complex shapes by using isogeometric… More >

  • Open Access


    IGA Based Bi-Layer Fiber Angle Optimization Method for Variable Stiffness Composites

    Chao Mei, Qifu Wang*, Chen Yu, Zhaohui Xia

    CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.1, pp. 179-202, 2020, DOI:10.32604/cmes.2020.09948

    Abstract This paper presents a topology optimization method for variable stiffness composite panels with varying fiber orientation and curvilinear fiber path. Non-uniform rational B-Splines (NURBS) based Isogeometric analysis (IGA) is utilized for the numerical computation of the general minimum compliance problem. The sensitivity analysis of the structure compliance function for the density and bi-layer orientation is conducted. The bi-layer fiber paths in the design domain are generated using streamline method and updated by divided pieces reselection method after the optimization process. Several common examples are tested to demonstrate the effectiveness of the method. The results show that the proposed method can… More >

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