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The boundary element method for Ordinary State-Based Peridynamics

Computer Modeling in Engineering & Sciences 2024年第6期139卷 2807-2834页

作者： Xue Liang Linjuan Wang State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Engineering ScienceCollege of EngineeringPeking UniversityBeijing100871China CAPT-HEDPS and IFSA Collaborative Innovation Center of MoECollege of EngineeringPeking UniversityBeijing100871China School of Astronautics Beihang UniversityBeijing100191China

The peridynamics(PD),as a promising nonlocal continuum mechanics theory,shines in solving discontinuous problems.Up to now,various numerical methods,such as the peridynamic mesh-free particlemethod(PD-MPM),peridynamic finite element method(PD-FEM),and peridynamic boundary element method(PD-BEM),have been proposed.PD-BEM,in particular,outperforms other methods by eliminating spurious boundary softening,efficiently handling infinite problems,and ensuring high computational accuracy.However,the existing PD-BEM is constructed exclusively for bond-based peridynamics(BBPD)with fixed Poisson’s ratio,limiting its applicability to crack propagation problems and scenarios involving infinite or semi-infinite problems.In this paper,we address these limitations by introducing the boundary element method(BEM)for ordinary state-based peridynamics(OSPD-BEM).Additionally,we present a crack propagationmodel embeddedwithin the framework ofOSPD-BEM to simulate crack propagations.To validate the effectiveness of OSPD-BEM,we conduct four numerical examples:deformation under uniaxial loading,crack initiation in a double-notched specimen,wedge-splitting test,and threepoint bending test.The results demonstrate the accuracy and efficiency of OSPD-BEM,highlighting its capability to successfully eliminate spurious boundary softening phenomena under varying Poisson’s ratios.Moreover,OSPDBEMsignificantly reduces computational time and exhibits greater consistencywith experimental results compared to PD-MPM.

关键词： Ordinary state-based peridynamics boundary element method crack propagation fracture toughness

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Modeling tail bubble dynamics during the launch of an underwater vehicle using the boundary element method

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Journal of Hydrodynamics 2022年第3期34卷 434-443页

作者： Shao-hua Cheng Xiao-bo Quan Sai Zhang Tian-yuan Zhang Shuai Li College of Shipbuilding Engineering Harbin Engineering UniversityHarbin150001China Beijing Institute of Astronautical Systems Engineering Beijing100076China China Academy of Launch Vehicle Technology Beijing100076China

A tail bubble is generated behind a high-speed vehicle at the early stage of the underwater launch process.The tail bubble dynamic behavior involves expansion,overexpansion,contraction,pinch-off and jet formation,and it significantly influences the vehicle’s movement.However,the tail bubble dynamic behavior is an issue not very well studied.This paper establishes a numerical model for the interaction between the tail bubble and the vehicle based on the boundary element method(BEM)to gain new insight into this issue.The BEM results are compared to a computational fluid dynamics model to validate the numerical model,and good agreement is achieved.Additionally,a convergence test of the BEM model is conducted to verify its independence of the mesh size.The influence of some governing parameters on the evolution of the tail bubble is then systematically studied,focusing on its maximum radius,pinch-off time,and pinch-off position.There are two pinch-off position regimes of the tail bubble,one at the bottom and the other near the middle.

关键词： Underwater launch tail bubble bubble dynamics boundary element method

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Machine Learning Enhanced boundary element method:Prediction of Gaussian Quadrature Points

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Computer Modeling in Engineering & Sciences 2022年第4期131卷 445-464页

作者： Ruhui Cheng Xiaomeng Yin Leilei Chen College of Architecture and Civil Engineering Xinyang Normal UniversityXinyang464000China College of Intelligent Construction Wuchang University of TechnologyWuhan430223China School of Architectural Engineering Huanghuai UniversityZhumadian463000China

This paper applies a machine learning technique to find a general and efficient numerical integration scheme for boundary element methods.A model based on the neural network multi-classification algorithmis constructed to find the minimum number of Gaussian quadrature points satisfying the given accuracy.The constructed model is trained by using a large amount of data calculated in the traditional boundary element method and the optimal network architecture is selected.The two-dimensional potential problem of a circular structure is tested and analyzed based on the determined model,and the accuracy of the model is about 90%.Finally,by incorporating the predicted Gaussian quadrature points into the boundary element analysis,we find that the numerical solution and the analytical solution are in good agreement,which verifies the robustness of the proposed method.

关键词： Machine learning boundary element method Gaussian quadrature points classification problems

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Isogeometric boundary element method for Two-Dimensional Steady-State Non-Homogeneous Heat Conduction Problem

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Computer Modeling in Engineering & Sciences 2022年第8期132卷 471-488页

作者： Yongsong Li Xiaomeng Yin Yanming Xu School of Architectural Engineering Huanghuai UniversityZhumadian463000China College of Intelligent Construction Wuchang University of TechnologyWuhan430223China

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 Bezier 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.

关键词： Isogeometric analysis NURBS boundary element method heat conduction non-homogeneous radial integration method

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Topology Optimization of Sound-Absorbing Materials for Two-Dimensional Acoustic Problems Using Isogeometric boundary element method

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Computer Modeling in Engineering & Sciences 2023年第2期134卷 981-1003页

作者： Jintao Liu Juan Zhao Xiaowei Shen College of Architecture and Civil Engineering Xinyang Normal UniversityXinyang464000China College of Mechanics and Materials Hohai UniversityNanjing211100China

In this work,an acoustic topology optimizationmethod for structural surface design covered by porous materials is proposed.The analysis of acoustic problems is performed using the isogeometric boundary elementmethod.Taking the element density of porousmaterials as the design variable,the volume of porousmaterials as the constraint,and the minimum sound pressure or maximum scattered sound power as the design goal,the topology optimization is carried out by solid isotropic material with penalization(SIMP)method.To get a limpid 0–1 distribution,a smoothing Heaviside-like function is proposed.To obtain the gradient value of the objective function,a sensitivity analysis method based on the adjoint variable method(AVM)is proposed.To find the optimal solution,the optimization problems are solved by the method of moving asymptotes(MMA)based on gradient information.Numerical examples verify the effectiveness of the proposed topology optimization method in the optimization process of two-dimensional acoustic problems.Furthermore,the optimal distribution of sound-absorbingmaterials is highly frequency-dependent and usually needs to be performed within a frequency band.

关键词： boundary element method isogeometric analysis two-dimensional acoustic analysis sound-absorbing materials topology optimization adjoint variable method

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boundary element method FOR MOVING AND ROLLING CONTACT OF 2D ELASTIC BODIES WITH DEFECTS

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Acta Mechanica Sinica 2001年第2期17卷 183-192页

作者：姚振汉蒲军平金哲植 Department of Engineering Mechanics Tsinghua UniversityBeijing 100084China Pyonyang Engineering Institute PyonyangD.P.R.Korea

A scheme of boundary element method for moving contact of two-dimensional elastic bodies using conforming discretization is presented. Both the displacement and the traction boundary conditions are satisfied on the contacting region in the sense of discretization. An algorithm to deal with the moving of the contact boundary on a larger possible contact region is presented. The algorithm is generalized to rolling contact problem as well. Some numerical examples of moving and rolling contact of 2D elastic bodies with or without friction, including the bodies with a hole-type defect, are given to show the effectiveness and the accuracy of the presented schemes.

关键词： boundary element method contact problem moving contact 2D elasticity body with defects

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A boundary element method for Simulation of Deformable Objects

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Journal of Computer Science & Technology 1996年第5期11卷 497-506页

作者：徐美和唐泽圣 CADCenter DepartmentofComputerScienceTsinghuaUniversityBeijing100084 CADCenter DepartmentofComputer

In this paper, a boundary element method is first applied to real-time animation of deformable objects and to simplify data preparation. Next, the visible external surface of the object in deforming process is represented by B-spline surface, whose control points are embedded in dynamic equations of BEM. Finally, the above method is applied to anatomical simulation. A pituitary model in human brain, which is reconstructed from a set of anatomical sections, is selected to be the deformable object under action of virtual tool such as scalpel or probe. It produces fair graphic realism and high speed performance. The results show that BEM not only has less computational expense than FEM, but also is convenient to combine with the 3D reconstruction and surface modeling as it enables the reduction of the dimensionality of the problem by one.

关键词： Physically based modeling animation simulation boundary element method B-spline surface representation

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boundary element method FOR MODEL ANALYSIS OF 2-D COMPOSITE STRUCTURE

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Acta Mechanica Solida Sinica 1998年第1期11卷 63-71页

作者： Zou Jing Li Zailiang Zhong Weifang Huazhong Univ Sci & Technol Dept Mech Wuhan 430074 Peoples R China

The boundary element method is used for he modal analysis of freevibration of 2-D composite structures in this paper. Since theparticular solution method is used to treat the terms of body forces(inertial forces) in the equation of motion, only static fundamentalsolutions are needed in solving the problem. For an isotropiccantilever beam, the numerical results obtained by using the BEMpresented in this paper are in good agreement, with those of usingFEM or other BEM, but this BEM can also be used to analyze problemsfor anisotropic materials.

关键词： composite structure boundary element method particular solution method

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boundary element method FOR CALCULATING ACOUSTIC RADIATION FROM CLOSED SURFACE WITH PRESCRIBED VELOCITY DISTRIBUTION

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Chinese Journal of Acoustics 1989年第2期8卷 111-120页

作者： Zhao, Jian Wang, Hongzhen Zhu, Wuhua Zhong Shan Univ

The application of BEM to calculate acoustic radiation from closed surface in an infinite acoustic medium has the advantages of less memory space, higher accuracy and faster calculating speed. However, the singular integrals and the nonuniqueness problem of surface helmholtz equation at characteristic frequencies should be dealt with. It is suggested in this paper that combination of the interior Helmholtz equation and its derivatives with respect to the coordinate components of an interior point forms an extra equation, in order to solve the problems of acoustic radiation at various frequencies with surface Helmholtz equation; on the area which includes singular point, the singular integrals are converted to ordinary ones by polar coordinate transformation. As an example, the acoustic radiation field of closed axisymmetric surfaces with prescribed surface velocity distribution is calculated in this paper.

关键词： Computers Applications Mathematical Models Mathematical Techniques boundary element method

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boundary element method FOR ARBITRARY ELASTIC THIN SHELL

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Acta Mechanica Sinica 1992年第4期8卷 355-362页

作者：郑国英嵇醒 Southeast University Nanjing 210018China Tongji UniversityShanghai 200092China

In this paper,a boundary element scheme for arbitrary elastic thin shells is elaborated,Based on BEM of 3D linear elasticity and Kirchhoff's hypothesis,boundary integral equations for shells are deduced. As a result,only Kelvin's solution is used,the difficulty,in finding a fundamental solution of arbitrary shells is successfully avoided.

关键词： arbitrary shells boundary element method Kelvin's solution

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