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  • Open Access


    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 strain in the stress direction… More >

  • Open Access


    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 boundary of the problem. Actually,… More >

  • Open Access


    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 >

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