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  • Open Access

    ARTICLE

    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 - 01 February 2020

    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 More >

  • Open Access

    ARTICLE

    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 More >

  • Open Access

    ABSTRACT

    An Isogeometric Analysis Computational Platform for Material Transport Simulation in Complex Neurite Networks

    Angran Li1, Xiaoqi Chai2, Ge Yang2,3, Yongjie Jessica Zhang1,2,*

    Molecular & Cellular Biomechanics, Vol.16, Suppl.2, pp. 66-66, 2019, DOI:10.32604/mcb.2019.07633

    Abstract Neurons exhibit remarkably complex geometry in their neurite networks. So far, how materials are transported in the complex geometry for survival and function of neurons remains an unanswered question. Answering this question is fundamental to understanding the physiology and disease of neurons. Here, we have developed an isogeometric analysis (IGA) based platform for material transport simulation in neurite networks. We modeled the transport process by reaction-diffusion-transport equations and represented geometry of the networks using truncated hierarchical tricubic B-splines (THB-spline3D). We solved the Navier-Stokes equations to obtain the velocity field of material transport in the networks. More >

  • Open Access

    ARTICLE

    An Isogeometric Analysis Computational Platform for Material Transport Simulation in Complex Neurite Networks

    Angran Li1, Xiaoqi Chai2, Ge Yang2,3, Yongjie Jessica Zhang1,2,*

    Molecular & Cellular Biomechanics, Vol.16, No.2, pp. 123-140, 2019, DOI:10.32604/mcb.2019.06479

    Abstract Neurons exhibit remarkably complex geometry in their neurite networks. So far, how materials are transported in the complex geometry for survival and function of neurons remains an unanswered question. Answering this question is fundamental to understanding the physiology and disease of neurons. Here, we have developed an isogeometric analysis (IGA) based platform for material transport simulation in neurite networks. We modeled the transport process by reaction-diffusion-transport equations and represented geometry of the networks using truncated hierarchical tricubic B-splines (THB-spline3D). We solved the Navier-Stokes equations to obtain the velocity field of material transport in the networks. More >

  • Open Access

    ARTICLE

    Computational Machine Learning Representation for the Flexoelectricity Effect in Truncated Pyramid Structures

    Khader M. Hamdia2, Hamid Ghasemi3, Xiaoying Zhuang4,5, Naif Alajlan1, Timon Rabczuk1,2,*

    CMC-Computers, Materials & Continua, Vol.59, No.1, pp. 79-87, 2019, DOI:10.32604/cmc.2019.05882

    Abstract In this study, machine learning representation is introduced to evaluate the flexoelectricity effect in truncated pyramid nanostructure under compression. A Non-Uniform Rational B-spline (NURBS) based IGA formulation is employed to model the flexoelectricity. We investigate 2D system with an isotropic linear elastic material under plane strain conditions discretized by 45×30 grid of B-spline elements. Six input parameters are selected to construct a deep neural network (DNN) model. They are the Young's modulus, two dielectric permittivity constants, the longitudinal and transversal flexoelectric coefficients and the order of the shape function. The outputs of interest are the More >

  • Open Access

    ARTICLE

    An Improved Integration for Trimmed Geometries in Isogeometric Analysis

    Jinlan Xu1, Ningning Sun1, Laixin Shu1, Timon Rabczuk2, Gang Xu1,*

    CMC-Computers, Materials & Continua, Vol.60, No.2, pp. 615-632, 2019, DOI:10.32604/cmc.2019.04464

    Abstract Trimming techniques are efficient ways to generate complex geometries in Computer-Aided Design (CAD). In this paper, an improved integration for trimmed geometries in isogeometric analysis (IGA) is proposed. The proposed method can improve the accuracy of the approximation and the condition number of the stiffness matrix. In addition, comparing to the traditional approaches, the trimming techniques can reduce the number of the integration elements with much fewer integration points, which improves the computational efficiency significantly. Several examples are illustrated to show the effectiveness of the proposed approach. More >

  • Open Access

    REVIEW

    Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review

    Yingjun Wang1,*, Zhenpei Wang2,*, Zhaohui Xia3, Leong Hien Poh2

    CMES-Computer Modeling in Engineering & Sciences, Vol.117, No.3, pp. 455-507, 2018, DOI:10.31614/cmes.2018.04603

    Abstract Isogeometric analysis (IGA), an approach that integrates CAE into conventional CAD design tools, has been used in structural optimization for 10 years, with plenty of excellent research results. This paper provides a comprehensive review on isogeometric shape and topology optimization, with a brief coverage of size optimization. For isogeometric shape optimization, attention is focused on the parametrization methods, mesh updating schemes and shape sensitivity analyses. Some interesting observations, e.g. the popularity of using direct (differential) method for shape sensitivity analysis and the possibility of developing a large scale, seamlessly integrated analysis-design platform, are discussed in More >

  • Open Access

    ARTICLE

    An Improved Isogeometric Boundary Element Method Approach in Two Dimensional Elastostatics

    Vincenzo Mallardo1, Eugenio Ruocco2

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.5, pp. 373-391, 2014, DOI:10.3970/cmes.2014.102.373

    Abstract The NURBS based isogeometric analysis offers a novel integration between the CAD and the numerical structural analysis codes due to its superior capacity to describe accurately any complex geometry. Since it was proposed in 2005, the approach has attracted rapidly growing research interests and wide applications in the Finite Element context. Only recently, in 2012, it was successfully tested together with the Boundary Element Method. The combination of the isogeometric approach and the Boundary Element Method is efficient since both the NURBS geometrical representation and the Boundary Element Method deal with quantities entirely on the More >

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