Yingjun Wang¹, Zhongyuan Liao¹, Shengyu Shi^{1, *}, Zhenpei Wang^{2, *}, Leong Hien Poh³

CMES-Computer Modeling in Engineering & Sciences, Vol.122, No.2, pp. 433-458, 2020, DOI:10.32604/cmes.2020.08680

Abstract Focusing on the structural optimization of auxetic materials using data-driven methods, a back-propagation neural network (BPNN) based design framework is developed for petal-shaped auxetics using isogeometric analysis. Adopting a NURBS-based parametric modelling scheme with a small number of design variables, the highly nonlinear relation between the input geometry variables and the effective material properties is obtained using BPNN-based fitting method, and demonstrated in this work to give high accuracy and efficiency. Such BPNN-based fitting functions also enable an easy analytical sensitivity analysis, in contrast to the generally complex procedures of typical shape and size sensitivity More >

Zijun Wu¹, Shuting Wang², Wenjun Shao^{3, *}, 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 More >

Weihua Fang¹, Zhilin An², Tiantang Yu^{2, *}, Tinh Quoc Bui^{3, 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 >

Angran Li¹, Xiaoqi Chai², Ge Yang^2,3, Yongjie Jessica Zhang^1,2,*

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 >

Yingjun Wang^1,*, Zhenpei Wang^2,*, 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 >

Angran Li¹, Xiaoqi Chai², Ge Yang^2,3, Yongjie Jessica Zhang^1,2,*

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 >

Khader M. Hamdia², Hamid Ghasemi³, Xiaoying Zhuang^4,5, Naif Alajlan¹, Timon Rabczuk^1,2,*

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 >

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 >

Jinlan Xu¹, Ningning Sun¹, Laixin Shu¹, Timon Rabczuk², Gang Xu^1,*

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 >