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  • Open Access


    Isogeometric Boundary Element Method for Two-Dimensional Steady-State Non-Homogeneous Heat Conduction Problem

    Yongsong Li1, Xiaomeng Yin2, Yanming Xu1,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.2, pp. 471-488, 2022, DOI:10.32604/cmes.2022.020201

    Abstract The isogeometric boundary element technique (IGABEM) is presented in this study for steady-state inhomogeneous heat conduction analysis. The physical unknowns in the boundary integral formulations of the governing equations are discretized using non-uniform rational B-spline (NURBS) basis functions, which are utilized to build the geometry of the structures. To speed up the assessment of NURBS basis functions, the B´ezier extraction approach is used. To solve the extra domain integrals, we use a radial integration approach. The numerical examples show the potential of IGABEM for dimension reduction and smooth integration of CAD and numerical analysis. More >

  • Open Access


    Numerical Aspects of Isogeometric Boundary Element Methods: (Nearly) Singular Quadrature, Trimmed NURBS and Surface Crack Modeling

    Xuan Peng1,*, Haojie Lian2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.1, pp. 513-542, 2022, DOI:10.32604/cmes.2022.017410

    Abstract This work presents some numerical aspects of isogeometric boundary element methods (IGABEM). The behavior of hyper-singular and nearly-singular integration is first explored on the distorted NURBS surface. Several numerical treatments are proposed to enhance the quadrature in the framework of isogeometric analysis. Then a numerical implementation of IGABEM on the trimmed NURBS is detailed. Based on this idea, the surface crack problem is modeled incorporation with the phantom element method. The proposed method allows the crack to intersect with the boundary of the body while preserving the original parametrization of the NURBS-based CAD geometry. More >

  • Open Access


    Adaptive Extended Isogeometric Analysis for Steady-State Heat Transfer in Heterogeneous Media

    Weihua Fang1, Tiantang Yu2,*, Yin Yang3

    CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.3, pp. 1315-1332, 2021, DOI:10.32604/cmes.2021.014575

    Abstract Steady-state heat transfer problems in heterogeneous solid are simulated by developing an adaptive extended isogeometric analysis (XIGA) method based on locally refined non-uniforms rational B-splines (LR NURBS). In the XIGA, the LR NURBS, which have a simple local refinement algorithm and good description ability for complex geometries, are employed to represent the geometry and discretize the field variables; and some special enrichment functions are introduced into the approximation of temperature field, thus the computational mesh is independent of the material interfaces, which are described with the level set method. Similar to the approximation of temperature field, a temperature gradient recovery… 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


    Mathematical Interpolation and Correction of Three-Dimensional Modelling of High-Speed Railway

    Jun Gao1,2,*, Xiao Lin3

    Intelligent Automation & Soft Computing, Vol.26, No.5, pp. 1023-1034, 2020, DOI:10.32604/iasc.2020.010134

    Abstract Three-dimensional (3D) modelling of high-speed railways, bad geology, and special geotechnical engineering inferences may involve problems, such as inaccurate geological data, hidden underground geological phenomena, and complex geological processes. In this study, surface geological boundaries, drainage, transportation networks, covers, lenses, and small geological units are established using topographic surveying and mapping data, geological data, and geological exploration data acquisition. The 3D model of the karst system combines geological and mathematical interpolation curved surface 3D model simulation analysis, trend surface fitting, and interpolation of the NURBS surface and correct analysis. The model is used to describe the properties of objects, including… More >

  • Open Access


    NURBS Modeling and Curve Interpolation Optimization of 3D Graphics

    Hao Zhu1,*, Mulan Wang2, Kun Liu2, Weiye Xu3

    CMC-Computers, Materials & Continua, Vol.66, No.2, pp. 1799-1811, 2021, DOI:10.32604/cmc.2020.012706

    Abstract In order to solve the problem of complicated Non-Uniform Rational B-Splines (NURBS) modeling and improve the real-time performance of the high-order derivative of the curve interpolation process, the method of NURBS modeling based on the slicing and layering of triangular mesh is introduced. The research and design of NURBS curve interpolation are carried out from the two aspects of software algorithm and hardware structure. Based on the analysis of the characteristics of traditional computing methods with Taylor series expansion, the Adams formula and the Runge-Kutta formula are used in the NURBS curve interpolation process, and the process is then optimized… More >

  • Open Access


    Inverse Construction Methods of Heterogeneous NURBS Object Based on Additive Manufacturing

    Ting Zang1, Dongbin Zhu2,*, Guowang Mu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.125, No.2, pp. 597-610, 2020, DOI:10.32604/cmes.2020.09965

    Abstract According to the requirement of heterogeneous object modeling in additive manufacturing (AM), the Non-Uniform Rational B-Spline (NURBS) method has been applied to the digital representation of heterogeneous object in this paper. By putting forward the NURBS material data structure and establishing heterogeneous NURBS object model, the accurate mathematical unified representation of analytical and free heterogeneous objects have been realized. With the inverse modeling of heterogeneous NURBS objects, the geometry and material distribution can be better designed to meet the actual needs. Radical Basis Function (RBF) method based on global surface reconstruction and the tensor product surface interpolation method are combined… 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


    Reusing the Evaluations of Basis Functions in the Integration for Isogeometric Analysis

    Zijun Wu1, Shuting Wang2, Wenjun Shao3, *, Lianqing Yu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.122, No.2, pp. 459-485, 2020, DOI:10.32604/cmes.2020.08697

    Abstract We propose a new approach to reuse the basis function evaluations in the numerical integration of isogeometric analysis. The concept of reusability of the basis functions is introduced according to their symmetrical, translational and proportional features on both the coarse and refined levels. Based on these features and the parametric domain regularity of each basis, we classify the bases on the original level and then reuse them on the refined level, which can reduce the time for basis calculations at integration nodes. By using the sum factorization method and the mean value theorem for the integrals, a new integration method… More >

  • Open Access


    Analysis of Unsteady Heat Transfer Problems with Complex Geometries Using Isogeometric Boundary Element Method

    Weihua Fang1, Zhilin An2, Tiantang Yu2, *, Tinh Quoc Bui3, 4, *

    CMC-Computers, Materials & Continua, Vol.62, No.2, pp. 929-962, 2020, DOI:10.32604/cmc.2020.05022

    Abstract Numerical analysis of unsteady heat transfer problems with complex geometries by the isogeometric boundary element method (IGABEM) is presented. The IGABEM possesses many desirable merits and features, for instance, (a) exactly represented arbitrarily complex geometries, and higher-order continuity due to nonuniform rational B-splines (NURBS) shape functions; (b) using NURBS for both field approximation and geometric description; (c) directly utilizing geometry data from computer-aided design (CAD); and (d) only boundary discretization. The formulation of IGABEM for unsteady heat transfer is derived. The domain discretization in terms of IGABEM for unsteady heat transfer is required as that in traditional BEM. The internal… More >

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