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isogeometric boundary element method for axisymmetric steady-state heat transfer

ENGINEERING ANALYSIS WITH boundary elementS 2024年 160卷 89-105页

作者： Zang, Quansheng Liu, Jun Ye, Wenbin Lin, Gao Zhengzhou Univ Sch Water Conservancy & Transportat Zhengzhou 450001 Peoples R China Natl Local Joint Engn Lab Major Infrastructure Tes Zhengzhou 450001 Peoples R China Dalian Univ Technol Sch Infrastruct Engn Dept Hydraul Engn Dalian 116024 Peoples R China

isogeometric analysis (IGA) utilizes the Non -Uniform Rational B-Splines (NURBS) basis functions, which are commonly employed in Computer Aided Design (CAD), to both construct the problem's geometry and approximate the field variables. In axisymmetric scenarios, the 3D problem can be simplified to 2D, requiring only the discretization of the 1D curve boundary for the boundary element method (BEM). This study proposes an isogeometric boundary element method (IGABEM) to simulate steady -state heat transfer in axisymmetric domains. Both the precise geometry of the boundary and the physical variables are approximated with the same NURBS basis functions, yielding higher-order continuity, superior accuracy per degree of freedom (DOF), and continuous nodal gradients with fewer DOFs than the traditional BEM. Additionally, a zoning method is introduced to handle heterogeneities. Five cases including a solid cylinder, a revolution hyperboloid with a coaxial cylindrical tube, an ellipsoid with a spherical cavity, a bimaterial ellipsoid and a complex geometry with a toroidal tube validate the accuracy, convergence, computational efficiency of IGABEM, and the applicability in addressing multiply-connected domains. The method outperforms Finite element method (FEM) and conventional BEM in accurately handling steady -state axisymmetric heat transfer issues under Dirichlet, Neumann, and Robin boundary conditions.

关键词： NURBS isogeometric boundary element method Axisymmetric geometry Heat transfer Bimaterial

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Evaluation of heat flux intensity factor for a V-notched structure by the isogeometric boundary element method

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ENGINEERING FRACTURE MECHANICS 2025年 314卷

作者： Wang, Feiyang Cheng, Changzheng Li, Tengyue Liu, Jingwen Han, Zhilin Hefei Univ Technol Dept Engn Mech Hefei 230009 Peoples R China Donghua Univ Coll Phys Shanghai 201620 Peoples R China

The conventional boundary element method using piecewise polynomial interpolation cannot accurately simulate the singular heat flux field around the vertex of the V-notch. Herein, the singularity eigen-analysis combined with the isogeometric boundary element method is proposed to calculate the singular heat flux field. The V-notched structure is divided into two parts, in which one is the heat flux singularity sector near the vertex and the other is the remained structure without heat flux singularity. In the singularity sector, the asymptotic expansion of the heat flux is introduced to transform the heat conduction governing equation into ordinary differential eigen equation, from which the singularity orders and eigen angular functions can be determined, except for the amplitude coefficients in the asymptotic expansion. The boundary integral equations for the heat conduction analysis established on the remained structure are discretized by the non-uniform rational B-spline (NURBS) elements. The amplitude coefficients, which are corresponding to the heat flux intensity factors, can be yielded by coupling the isogeometric boundary integral equations with the singularity asymptotic expansion analysis. A coordinate system transformation method is then proposed to transform the heat conduction governing equations of orthotropic and anisotropic material into the one of the isotropic material, and the heat flux intensity factors are approved to be invariable before and after coordinate transformation. Since the NURBS elements are used, fewer elements are required to evaluate the heat flux intensity factors compared with the conventional boundary element method.

关键词： V-notch Heat flux intensity factor Singularity asymptotic expansion isogeometric boundary element method

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Generalized isogeometric boundary element method for uncertainty analysis of time-harmonic wave propagation in infinite domains

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APPLIED MATHEMATICAL MODELLING 2023年 114卷 360-378页

作者： Chen, Leilei Lian, Haojie Xu, Yanming Li, Shengze Liu, Zhaowei Atroshchenko, Elena Kerfriden, Pierre Huanghuai Univ Coll Architectural & Civil Engn Zhumadian Peoples R China Taiyuan Univ Technol Key Lab Insitu Property Improving Mining Minist Educ Taiyuan Shanxi Peoples R China Xinyang Normal Univ Coll Architecture & Civil Engn Xinyang Peoples R China Huanghuai Univ Henan Int Joint Lab Struct Mech & Computat Simulat Zhumadian Peoples R China Acad Mil Sci Beijing Peoples R China Hohai Univ Coll Mech & Mat Nanjing Peoples R China Univ New South Wales Sch Civil & Environm Engn Sydney NSW Australia Ctr Mat Mines Paris PSL Paris France Cardiff Univ Sch Engn Parade Cardiff CF24 3AA Wales

This paper proposes a novel generalized nth order perturbation isogeometric fast multipole boundary element method for time harmonic wave propagation in infinite domains. The non-uniform rational B-splines are employed to construct structural geometries and dis-cretize boundary integral equations. The randomness of wave number for incident plane wave is considered as the source of system uncertainty. The generalized nth order pertur-bation method is employed to model the physical field depending on the input random variable. The nth order derivatives of field functions and kernel functions in the boundary integral equations are derived by generalized nth order Taylor series expansions with a small perturbation parameter. The subtraction of singularity technique is used to evaluate the singular integrals and the fast multipole method is applied to accelerate the solution. The Monte Carlo simulations are conducted in numerical examples to demonstrate the va-lidity and correctness of the proposed algorithm.(c) 2022 Elsevier Inc. All rights reserved.

关键词： Uncertainty analysis isogeometric boundary element method Perturbation method Wave propagation Fast multipole method

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Asymptotic homogenization for effective parameters of unidirectional fiber reinforced composites by isogeometric boundary element method

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ENGINEERING ANALYSIS WITH boundary elementS 2024年 169卷

作者： Han, Zhilin Liu, Shijia Deng, Yu Luo, Chuyang Donghua Univ Coll Phys Shanghai 201620 Peoples R China Donghua Univ Shanghai Collaborat Innovat Ctr High Performance F Ctr Civil Aviat Composites & Composites Prov Minis Shanghai 201620 Peoples R China

In this paper, formulations for asymptotic homogenization method based on the boundary element method (BEM) are presented for the estimations for effective parameters of unidirectional fiber reinforced composites in the 2D plane strain case. The boundaries are discretized by shape functions of non-uniform rational Bsplines (NURBS) according to the features of isogeometric analysis and the related isogeometric boundary element method is established. The strongly and weakly singular integrals in the boundary integral equations are precisely calculated indirect schemes. Comprehensive comparisons for the obtained effective parameters by the current method are conducted with the existing ones by conventional BEM and the ones by finite element method (FEM). It is found that the estimations in present work are more accurate than the ones by conventional BEM with fewer control points and are also more accurate than the ones by FEM for fibers with more complex geometry. The outperformance of the current method shows competitive potentials in homogenization for the real 3D composites.

关键词： Asymptotic homogenization boundary integral equations isogeometric boundary element method Effective parameters

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Subdivision Surface-Based isogeometric boundary element method for Steady Heat Conduction Problems with Variable Coefficient

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Computer Modeling in Engineering & Sciences 2021年第10期129卷 323-339页

作者： Xiuyun Chen Xiaomeng Yin Kunpeng Li Ruhui Cheng Yanming Xu Wei Zhang School of Architectural Engineering Huanghuai UniversityZhumadian463003China College of Intelligent Construction Wuchang University of TechnologyWuhan430223China College of Civil Engineering and Architecture China Three Gorges UniversityYichang443000China CAS Key Laboratory of Mechanical Behavior and Design of Materials Department of Modern MechanicsUniversity of Science and Technology of ChinaHefei230026China

The present work couples isogeometric analysis(IGA)and boundary element methods(BEM)for three dimensional steady heat conduction problems with variable *** Computer-Aided Design(CAD)geometries are built by subdivision surfaces,and meantime the basis functions of subdivision surfaces are employed to discretize the boundary integral equations for heat conduction ***,the radial integration method is adopted to transform the additional domain integrals caused by variable coefficients to the boundary *** numerical examples are provided to demonstrate the correctness and advantages of the proposed algorithm in the integration of CAD and numerical analysis.

关键词： Subdivision surface isogeometric boundary element method heat conduction radial integration

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Combined shape and topology optimization for sound barrier by using the isogeometric boundary element method

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ENGINEERING ANALYSIS WITH boundary elementS 2021年 124卷 124-136页

作者： Jiang, Fuhang Zhao, Wenchang Chen, Leilei Zheng, Changjun Chen, Haibo Univ Sci & Technol China Dept Modern Mech CAS Key Lab Mech Behav & Design Mat Hefei 230027 Anhui Peoples R China Xinyang Normal Univ Coll Civil Engn Xinyang 464000 Henan Peoples R China Hefei Univ Technol Inst Sound & Vibrat Res Hefei 230009 Anhui Peoples R China

This study presents a combined shape and topology optimization method for designing sound barriers by using the isogeometric boundary element method. The objective function of combined optimization is defined as the sound pressure in reference plane. The sensitivity analysis for the combined optimization is conducted by using either the direct differentiation method or the adjoint variable method. For a shape design, the design variables are the positions of control points in isogeometric analysis, which can control the barrier shape flexibly. In the topology update, the artificial density of an integral element is selected as the design variable to find the optimal distribution of sound absorbing material (SAM) on the barrier surface. In the combined optimization process, the shape and SAM distribution of the sound barrier can be changed in each iteration process to improve the noise reduction. Four different iteration schemes for combined optimization are compared to find an effective one. Numerical tests are provided to demonstrate the validity and efficiency of the proposed methods.

关键词： Sound barrier Combined shape and topology optimization isogeometric boundary element method Sensitivity analysis Sound absorbing material distribution

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A Combined Shape and Topology Optimization Based on isogeometric boundary element method for 3D Acoustics

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Computer Modeling in Engineering & Sciences 2021年第5期127卷 645-681页

作者： Jie Wang Fuhang Jiang Wenchang Zhao Haibo Chen CAS Key Laboratory of Mechanical Behavior and Design of Materials Department of Modern MechanicsUniversity of Science and Technology of ChinaHefei230026China

A combined shape and topology optimization algorithm based on isogeometric boundary element method for 3D acoustics is developed in this *** key treatment involves using adjoint variable method in shape sensitivity analysis with respect to non-uniform rational basis splines control points,and in topology sensitivity analysis with respect to the artificial densities of sound absorption *** tool in Fortran code is adopted to improve the efficiency of *** consider the features and efficiencies of the two types of optimization methods,this study adopts a combined iteration scheme for the optimization process to investigate the simultaneous change of geometry shape and distribution of material to achieve better noise *** examples,such as sound barrier,simple tank,and BeTSSi submarine,are performed to validate the advantage of combined optimization in noise reduction,and to demonstrate the potential of the proposed method for engineering problems.

关键词： Combined shape and topology optimization isogeometric boundary element method shape sensitivity analysis topology sensitivity analysis adjoint variable method sound absorption material

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A generalized isogeometric boundary element method for the uncertain analysis of infinite domain two-dimensional acoustic problems

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FRONTIERS IN PHYSICS 2023年 11卷

作者： Yang, Yan Huo, Ruijin Yuan, Xiaohui Wu, Wenbo Huanghuai Univ Coll Architectural & Civil Engn Zhumadian Peoples R China Huanghuai Univ Henan Int Joint Lab Struct Mech & Computat Simulat Zhumadian Peoples R China Xinyang Normal Univ Coll Architecture & Civil Engn Xinyang Peoples R China Xinyang Normal Univ Henan Unsaturated Soil & Special Soil Engn Technol Xinyang Peoples R China Guangzhou Univ Sch Mech & Elect Engn Guangzhou Peoples R China

The key aim of this paper is to provide a new nth generalized order perturbed isogeometric fast multistage technique of boundary elements to compute the propagation of time harmonics in an infinite region. Structural geometry and boundary integral equations are constructed by using non-uniform rational B-splines. The source of system uncertainty is believed to be the incident plane wave number's unpredictability. The actual field, depending on the input random variables, is simulated using the extended nth-order perturbation method. The field and kernel values for boundary integral formulas are generated via the nth-order generalized series of Taylor expansions using perturbation parameters. The fast multipole method (FMM) is utilized to speed up the process. The effectiveness and correctness of the proposed algorithm are verified by Monte Carlo simulations (MCs) with numerical examples.

关键词： uncertainty analysis isogeometric boundary element method perturbation method Helmholtz formula finite difference method

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A semi-analytical treatment for nearly singular integrals arising in the isogeometric boundary element method-based solutions of 3D potential problems

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COMPUTER methodS IN APPLIED MECHANICS AND ENGINEERING 2022年 398卷 1页

作者： Han, Zhilin Pan, Wei Cheng, Changzheng Hu, Zongjun Niu, Zhongrong Donghua Univ Coll Sci Shanghai 201620 Peoples R China Hefei Univ Technol Dept Engn Mech Hefei 230009 Peoples R China

The nearly singular integral, arising in simulating thin coatings or close-boundary physical quantities, are not adequately dealt with in the isogeometric boundary element method (IGABEM), especially in 3D problems. In this paper, we propose a semi-analytical approach for the nearly singular integrals of 3D potential problems. We first expand all the kernel items by Taylor series up to second order accuracy. In order to employ the semi-analytical formulae when integrating in parametric space, coordinate (xi, eta) is further transformed to polar coordinate (rho, theta). We then use the subtraction technique to separate the integrals to near-singular parts and regular parts. For the near-singular parts, a semi-analytical treatment is performed where the integrations with respect to theta are expressed by analytical formulae recursively, while the ones related to rho are computed by Gaussian quadrature. The remaining regular integrals are treated numerically by the sinh transformation method. By adding them together, we could efficiently handle the nearly singular integrals and therefore obtain accurate close-boundary potentials and flux densities in 3D potential problems. The accuracy of the presented method for nearly singular integrals to a curved element with different orders of singularities, namely the nearly weakly, strongly and highly singular integrals, are first tested. We then further consider potential problems of three typical 3D structures. All the presented results are compared with the recently proposed improved sinh transformation method and analytical solutions. The above numerical examples fully show the efficiency and competitiveness of the presented semi-analytical schemes. (c) 2022 Elsevier B.V. All rights reserved.

关键词： 3D potential problem isogeometric boundary element method Nearly singular integrals Semi-analytical analysis sinh transformation method

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The semianalytical analysis of nearly singular integrals in 2D potential problem by isogeometric boundary element method

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INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN ENGINEERING 2020年第16期121卷 3560-3583页

作者： Han, Zhilin Huang, Yifan Cheng, Changzheng Liang, Yongcheng Hu, Zongjun Niu, Zhongrong Donghua Univ Coll Sci Shanghai Peoples R China Hefei Univ Technol Dept Engn Mech Hefei 230009 Peoples R China

Benefited from the accuracy improvement in modeling physical problem of complex geometry and integrating the discretization and simulation, the isogeometric analysis in boundary element method (IGABEM) has been drawn a great deal of attention. The nearly singular integrals of 2D potential problem in the IGABEM are addressed by a semianalytical scheme in the present work. We use the subtraction technique to separate the integrals to singular and nonsingular parts, where the singular parts can be calculated by the analytical formulae derived by utilizing a series of integration by parts, while the nonsingular parts are calculated numerically with fewer quadrature points. Comparing the present semianalytical results with the ones of exact solutions, we find that the present method can obtain precise potential and flux densities of inner points much closer to the boundary without refining the elements nearby. Sufficient comparisons with other regularization schemes, such as the exponential and sinh transformation methods, are also conducted. The results in the numerical examples show the competitiveness of the present method, especially when calculating the nearly strongly and highly singular integrals during the simulation of the flux density.

关键词： isogeometric boundary element method nearly singular integrals potential problem semianalytical analysis

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