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A New Formulation of the Scaled Boundary Finite Element Method for Heterogeneous Media:Application to Heat Transfer Problems
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作者 Nima Noormohammadi Nazanin Pirhaji Khouzani 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2024年第2期285-296,共12页
The solution to heat transfer problems in two-dimensional heterogeneous media is attended based on the scaled boundary finite element method(SBFEM)coupled with equilibrated basis functions(EqBFs).The SBFEM reduces the... The solution to heat transfer problems in two-dimensional heterogeneous media is attended based on the scaled boundary finite element method(SBFEM)coupled with equilibrated basis functions(EqBFs).The SBFEM reduces the model order by scaling the boundary solution onto the inner element.To this end,tri-lateral elements are emanated from a scaling center,followed by the development of a semi-analytical solution along the radial direction and a finite element solution along the circumferential/boundary direction.The discretization is thus limited to the boundaries of the model,and the semi-analytical radial solution is found through the solution of an eigenvalue problem,which restricts the methods’applicability to heterogeneous media.In this research,we first extracted the SBFEM formulation considering the heterogeneity of the media.Then,we replaced the semi-analytical radial solution with the EqBFs and removed the eigenvalue solution step from the SBFEM.The varying coefficients of the partial differential equation(PDE)resulting from the heterogeneity of the media are replaced by a finite series in the radial and circumferential directions of the element.A weighted residual approach is applied to the radial equation.The equilibrated radial solution series is used in the new formulation of the SBFEM. 展开更多
关键词 scaled boundary finite element method Equilibrated basis functions Heat transfer
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A Computational Framework for Parachute Inflation Based on Immersed Boundary/Finite Element Approach
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作者 HUANG Yunyao ZHANG Yang +3 位作者 PU Tianmei JIA He WU Shiqing ZHOU Chunhua 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2024年第4期502-514,共13页
A computational framework for parachute inflation is developed based on the immersed boundary/finite element approach within the open-source IBAMR library.The fluid motion is solved by Peskin's diffuse-interface i... A computational framework for parachute inflation is developed based on the immersed boundary/finite element approach within the open-source IBAMR library.The fluid motion is solved by Peskin's diffuse-interface immersed boundary(IB)method,which is attractive for simulating moving-boundary flows with large deformations.The adaptive mesh refinement technique is employed to reduce the computational cost while retain the desired resolution.The dynamic response of the parachute is solved with the finite element approach.The canopy and cables of the parachute system are modeled with the hyperelastic material.A tether force is introduced to impose rigidity constraints for the parachute system.The accuracy and reliability of the present framework is validated by simulating inflation of a constrained square plate.Application of the present framework on several canonical cases further demonstrates its versatility for simulation of parachute inflation. 展开更多
关键词 parachute inflation fluid-structure interaction immersed boundary method finite element method adaptive mesh refinement
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MODE III 2-D FRACTURE ANALYSIS BY THE SCALED BOUNDARY FINITE ELEMENT METHOD
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作者 Shenshen Chen Qinghua Li +1 位作者 Yinghua Liu Zhiqing Xue 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2013年第6期619-628,共10页
The scaled boundary finite element method (SBFEM) is a novel semi-analytical technique that combines the advantages of the finite element method and the boundary element method with unique properties of its own. Thi... The scaled boundary finite element method (SBFEM) is a novel semi-analytical technique that combines the advantages of the finite element method and the boundary element method with unique properties of its own. This method has proven very efficient and accurate for determining the stress intensity factors (SIFs) for mode I and mode II two-dimensional crack problems. One main reason is that the SBFEM has a unique capacity of analytically representing the stress singularities at the crack tip. In this paper the SBFEM is developed for mode III (out of plane deformation) two-dimensional fracture anMysis. In addition, cubic B-spline functions are employed in this paper for constructing the shape functions in the circumferential direction so that higher continuity between elements is obtained. Numerical examples are presented at the end to demonstrate the simplicity and accuracy of the present approach for mode Ⅲ two-dimensional fracture analysis. 展开更多
关键词 fracture mechanics scaled boundary finite element method mode stress in- tensity factors
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Increment-Dimensional Scaled Boundary Finite Element Method for Solving Transient Heat Conduction Problem 被引量:2
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作者 Li Fengzhi Li Tiantian +1 位作者 Kong Wei Cai Junfeng 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2018年第6期1073-1079,共7页
An increment-dimensional scaled boundary finite element method (ID-SBFEM) is developed to solve the transient temperature field.To improve the accuracy of SBFEM,the effect of high frequency factor on dynamic stiffness... An increment-dimensional scaled boundary finite element method (ID-SBFEM) is developed to solve the transient temperature field.To improve the accuracy of SBFEM,the effect of high frequency factor on dynamic stiffness is considered,and the first-order continued fraction technique is used.After the derivation,the SBFE equations are obtained,and the dimensions of thermal conduction,the thermal capacity matrix and the vector of the right side term in the equations are doubled.An example is presented to illustrate the feasibility and good accuracy of the proposed method. 展开更多
关键词 heat conduction scaled boundary finite element method(SBFEM) temperature field accuracy
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Application of scaled boundary finite element method in static and dynamic fracture problems 被引量:2
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作者 Zhenjun Yang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2006年第3期243-256,共14页
The scaled boundary finite element method (SBFEM) is a recently developed numerical method combining advantages of both finite element methods (FEM) and boundary element methods (BEM) and with its own special fe... The scaled boundary finite element method (SBFEM) is a recently developed numerical method combining advantages of both finite element methods (FEM) and boundary element methods (BEM) and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors (SIFs) directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods. 展开更多
关键词 scaled boundary finite element method Dynamic stress intensity factors Mixed-mode crack propagation Remeshing algorithm Linear elastic fracture mechanics
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Dynamic Crack Propagation Analysis Using Scaled Boundary Finite Element Method 被引量:2
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作者 林皋 朱朝磊 +1 位作者 李建波 胡志强 《Transactions of Tianjin University》 EI CAS 2013年第6期391-397,共7页
The prediction of dynamic crack propagation in brittle materials is still an important issue in many engineering fields. The remeshing technique based on scaled boundary finite element method(SBFEM) is extended to pre... The prediction of dynamic crack propagation in brittle materials is still an important issue in many engineering fields. The remeshing technique based on scaled boundary finite element method(SBFEM) is extended to predict the dynamic crack propagation in brittle materials. The structure is firstly divided into a number of superelements, only the boundaries of which need to be discretized with line elements. In the SBFEM formulation, the stiffness and mass matrices of the super-elements can be coupled seamlessly with standard finite elements, thus the advantages of versatility and flexibility of the FEM are well maintained. The transient response of the structure can be calculated directly in the time domain using a standard time-integration scheme. Then the dynamic stress intensity factor(DSIF) during crack propagation can be solved analytically due to the semi-analytical nature of SBFEM. Only the fine mesh discretization for the crack-tip super-element is needed to ensure the required accuracy for the determination of stress intensity factor(SIF). According to the predicted crack-tip position, a simple remeshing algorithm with the minimum mesh changes is suggested to simulate the dynamic crack propagation. Numerical examples indicate that the proposed method can be effectively used to deal with the dynamic crack propagation in a finite sized rectangular plate including a central crack. Comparison is made with the results available in the literature, which shows good agreement between each other. 展开更多
关键词 scaled boundary finite element method dynamic stress intensity factor remeshing dynamic fracture
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THE COUPLING OF BOUNDARY ELEMENT AND FINITE ELEMENT METHODS FOR THE EXTERIOR NONSTATIONARY NAVIER-STOKES EQUATIONS 被引量:2
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作者 何银年 李开泰 《Acta Mathematica Scientia》 SCIE CSCD 1991年第2期190-207,共18页
In this paper, we represent a new numerical method for solving the nonstationary Stokes equations in an unbounded domain. The technique consists in coupling the boundary integral and finite element methods. The variat... In this paper, we represent a new numerical method for solving the nonstationary Stokes equations in an unbounded domain. The technique consists in coupling the boundary integral and finite element methods. The variational formulation and well posedness of the coupling method are obtained. The convergence and optimal estimates for the approximation solution are provided. 展开更多
关键词 the COUPLING OF boundary element AND finite element methodS FOR the EXTERIOR NONSTATIONARY NAVIER-STOKES EQUATIONS
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An explicit finite element-finite difference method for analyzing the effect of visco-elastic local topography on the earthquake motion 被引量:6
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作者 李小军 廖振鹏 关慧敏 《Acta Seismologica Sinica(English Edition)》 CSCD 1995年第3期447-456,共10页
An explicit finite element-finite difference method for analyzing the effects of two-dimensional visco-elastic localtopography on earthquake ground motion is prOPosed in this paper. In the method, at first, the finite... An explicit finite element-finite difference method for analyzing the effects of two-dimensional visco-elastic localtopography on earthquake ground motion is prOPosed in this paper. In the method, at first, the finite elementdiscrete model is formed by using the artificial boundary and finite element method, and the dynamic equationsof local nodes in the discrete model are obtained according to the theory of the special finite element method similar to the finite difference method, and then the explicit step-by-step integration formulas are presented by usingthe explicit difference method for solving the visco-elastic dynamic equation and Generalized Multi-transmittingBoundary. The method has the advantages of saving computing time and computer memory space, and it is suitable for any case of topography and has high computing accuracy and good computing stability. 展开更多
关键词 VISCO-ELASTIC seismic response finite difference method explicit finite element artificial boundary
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HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS 被引量:4
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作者 Wang Tongke(王同科) 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2002年第2期213-225,共13页
In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference me... In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective. 展开更多
关键词 SECOND order ordinary differential equation TWO-POINT boundary value problem high accuracy finite volume element method error estimate.
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Scaled Boundary Finite Element Analysis of Wave Passing A Submerged Breakwater 被引量:3
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作者 曹凤帅 滕斌 《China Ocean Engineering》 SCIE EI 2008年第2期241-251,共11页
The scaled boundary finite element method (SBFEM) is a novel semi-analytical technique combining the advantage of the finite element method (FEM) and the boundary element method (BEM) with its unique properties.... The scaled boundary finite element method (SBFEM) is a novel semi-analytical technique combining the advantage of the finite element method (FEM) and the boundary element method (BEM) with its unique properties. In this paper, the SBFEM is used for computing wave passing submerged breakwaters, and the reflection coeffcient and transmission coefficient are given for the case of wave passing by a rectangular submerged breakwater, a rigid submerged barrier breakwater and a trapezium submerged breakwater in a constant water depth. The results are compared with the analytical solution and experimental results. Good agreement is obtained. Through comparison with the results using the dual boundary element method (DBEM), it is found that the SBFEM can obtain higher accuracy with fewer elements. Many submerged breakwaters with different dimensions are computed by the SBFEM, and the changing character of the reflection coeffcient and the transmission coefficient are given in the current study. 展开更多
关键词 scaled boundary finite element method (SBFEM) potential flow wave action submerged breakwater reflection coeffwien transmission coeffwient
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Flow simulation considering adsorption boundary layer based on digital rock and finite element method 被引量:1
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作者 Yong-Fei Yang Ke Wang +7 位作者 Qian-Fei Lv Roohollah Askari Qing-Yan Mei Jun Yao Jie-Xin Hou Kai Zhang Ai-Fen Li Chen-Chen Wang 《Petroleum Science》 SCIE CAS CSCD 2021年第1期183-194,共12页
Due to the low permeability of tight reservoirs,throats play a significant role in controlling fluid flow.Although many studies have been conducted to investigate fluid flow in throats in the microscale domain,compara... Due to the low permeability of tight reservoirs,throats play a significant role in controlling fluid flow.Although many studies have been conducted to investigate fluid flow in throats in the microscale domain,comparatively fewer works have been devoted to study the effect of adsorption boundary layer(ABL)in throats based on the digital rock method.By considering an ABL,we investigate its effects on fluid flow.We build digital rock model based on computed tomography technology.Then,microscopic pore structures are extracted with watershed segmentation and pore geometries are meshed through Delaunay triangulation approach.Finally,using the meshed digital simulation model and finite element method,we investigate the effects of viscosity and thickness of ABL on microscale flow.Our results demonstrate that viscosity and thickness of ABL are major factors that significantly hinder fluid flow in throats. 展开更多
关键词 Digital rock Low-permeability rocks CT technology Adsorption boundary layer Numerical simulation finite element method
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Three-Dimensional Thermo-Elastic-Plastic Finite Element Method Modeling for Predicting Weld-Induced Residual Stresses and Distortions in Steel Stiffened-Plate Structures 被引量:1
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作者 Myung Su Yi Chung Min Hyun Jeom Kee Paik 《World Journal of Engineering and Technology》 2018年第1期176-200,共25页
The objective of the present paper is to develop nonlinear finite element method models for predicting the weld-induced initial deflection and residual stress of plating in steel stiffened-plate structures. For this p... The objective of the present paper is to develop nonlinear finite element method models for predicting the weld-induced initial deflection and residual stress of plating in steel stiffened-plate structures. For this purpose, three-dimensional thermo-elastic-plastic finite element method computations are performed with varying plate thickness and weld bead length (leg length) in welded plate panels, the latter being associated with weld heat input. The finite element models are verified by a comparison with experimental database which was obtained by the authors in separate studies with full scale measurements. It is concluded that the nonlinear finite element method models developed in the present paper are very accurate in terms of predicting the weld-induced initial imperfections of steel stiffened plate structures. Details of the numerical computations together with test database are documented. 展开更多
关键词 STEEL Stiffened-Plate Structures Weld-Induced Initial Distortion Weld-Induced Residual Stress Nonlinear finite element method THREE-DIMENSIONAL ther-mo-Elastic-Plastic finite element Analysis Full Scale Measurements
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FINITE ELEMENT METHOD FOR SOLVING TWO-DIMENSIONAL DIFFUSION-REACTION EQUATIONS OF BOUNDARY LAYER TYPE IN POROUS CATALYST PELLET
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作者 潘天舒 孙启文 +1 位作者 房鼎业 朱炳辰 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 1995年第2期29-41,共13页
In this paper,finite element method(FEM)is used to solve two-dimensional diffu-sion-reaction equations of boundary layer type.This kind of equations are usually too complicatedand diffcult to be solved by applying the... In this paper,finite element method(FEM)is used to solve two-dimensional diffu-sion-reaction equations of boundary layer type.This kind of equations are usually too complicatedand diffcult to be solved by applying the traditional methods used in chemical engineering becauseof the steep gradients of concentration and temperature.But,these difficulties are easy to be over-comed when the FEM is used.The integraded steps of solving this kind of problems by the FEMare presented in this paper.By applying the FEM to the two actual examples,the conclusion can bereached that the FEM has the advantages of simplicity and good accuracy. 展开更多
关键词 finite element method diffusion-reaction equation boundary layer type
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Mathematical analysis of EEP method for one-dimensional finite element postprocessing
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作者 赵庆华 周叔子 朱起定 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第4期441-445,共5页
For a class of two-point boundary value problems, by virtue of onedimensional projection interpolation, it is proved that the nodal recovery derivative obtained by Yuan's element energy projection (EEP) method has ... For a class of two-point boundary value problems, by virtue of onedimensional projection interpolation, it is proved that the nodal recovery derivative obtained by Yuan's element energy projection (EEP) method has the accuracy O(h^min{2k,k+4}) The theoretical analysis coincides the reported numerical results. 展开更多
关键词 superconvergence stress element energy projection method finite element two-point boundary value problems projection interpolation
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ANALYSIS OF ROLLING BY ELASTO-PLASTIC FINITE DEFORMATION CONTACT BOUNDARY ELEMENT METHOD 被引量:7
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作者 Huang Qingxue Shen Guangxian Xiao Hong Taiyuan Heavy Mahcinery Institute Yanshan University 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 1997年第4期50-55,共0页
A multinonlinear boundary element method is established dealing with elasto plastic finite deformation contact problem, and it is employed to analysis rolling process. With rollers as elastic bodies, workpieces as el... A multinonlinear boundary element method is established dealing with elasto plastic finite deformation contact problem, and it is employed to analysis rolling process. With rollers as elastic bodies, workpieces as elastio plastic bodies, rolling problem can be viewed as a frictional elasto plastic contact problem. With fewer assumptions in the simulation of the rolling process, a novel and accurate method is proposed for analysis of rolling problems. 展开更多
关键词 boundary element method Elasto plastic finite deformation ROLLING
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The Calculation of Stress-Strain State of Anisotropic Composite Finite-Element Area with Different Boundary Conditions on the Surface
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作者 Bergulyov Anton 《World Journal of Mechanics》 2014年第1期31-36,共6页
The numerical analytic research approach of stress-strain state of anisotropic composite finite element area with different boundary conditions on the surface, is represented below. The problem is solved by using a sp... The numerical analytic research approach of stress-strain state of anisotropic composite finite element area with different boundary conditions on the surface, is represented below. The problem is solved by using a spatial model of the elasticity theory. Differential equation system in partial derivatives reduces to one-dimensional problem using spline collocation method in two coordinate directions. Boundary problem for the system of ordinary higher-order differential equation is solved by using the stable numerical technique of discrete orthogonalization. 展开更多
关键词 COMPOSITE finite-element Areas boundary Conditions ELASTICITY theory SPLINE Approximation COLLOCATION methods
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Prediction of grain scale plasticity of NiTi shape memory alloy based on crystal plasticity finite element method 被引量:5
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作者 Li HU Shu-yong JIANG +1 位作者 Lai-xin SHI Yan-qiu ZHANG 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2019年第4期775-784,共10页
Grain scale plasticity of NiTi shape memory alloy(SMA)during uniaxial compression deformation at 400℃was investigated through two-dimensional crystal plasticity finite element simulation and corresponding analysis ba... Grain scale plasticity of NiTi shape memory alloy(SMA)during uniaxial compression deformation at 400℃was investigated through two-dimensional crystal plasticity finite element simulation and corresponding analysis based on the obtained orientation data.Stress and strain distributions of the deformed NiTi SMA samples confirm that there exhibits a heterogeneous plastic deformation at grain scale.Statistically stored dislocation(SSD)density and geometrically necessary dislocation(GND)density were further used in order to illuminate the microstructure evolution during uniaxial compression.SSD is responsible for sustaining plastic deformation and it increases along with the increase of plastic strain.GND plays an important role in accommodating compatible deformation between individual grains and thus it is correlated with the misorientation between neighboring grains,namely,a high GND density corresponds to large misorientation between grains and a low GND density corresponds to small misorientation between grains. 展开更多
关键词 grain scale plasticity NiTi shape memory alloy crystal plasticity finite element method plastic deformation microstructure evolution
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A Computational Study with Finite Element Method and Finite Difference Method for 2D Elliptic Partial Differential Equations 被引量:2
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作者 George Papanikos Maria Ch. Gousidou-Koutita 《Applied Mathematics》 2015年第12期2104-2124,共21页
In this paper, we consider two methods, the Second order Central Difference Method (SCDM) and the Finite Element Method (FEM) with P1 triangular elements, for solving two dimensional general linear Elliptic Partial Di... In this paper, we consider two methods, the Second order Central Difference Method (SCDM) and the Finite Element Method (FEM) with P1 triangular elements, for solving two dimensional general linear Elliptic Partial Differential Equations (PDE) with mixed derivatives along with Dirichlet and Neumann boundary conditions. These two methods have almost the same accuracy from theoretical aspect with regular boundaries, but generally Finite Element Method produces better approximations when the boundaries are irregular. In order to investigate which method produces better results from numerical aspect, we apply these methods into specific examples with regular boundaries with constant step-size for both of them. The results which obtained confirm, in most of the cases, the theoretical results. 展开更多
关键词 finite element method finite Difference method Gauss Numerical Quadrature DIRICHLET boundary CONDITIONS NEUMANN boundary CONDITIONS
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Two-scale finite element method for piezoelectric problem in periodic structure 被引量:2
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作者 邓明香 冯永平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第12期1525-1540,共16页
The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-sc... The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented. 展开更多
关键词 two-scale method PIEZOELECTRICITY periodic structure finite element method homogenization constant
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Modeling the Interaction between Vacancies and Grain Boundaries during Ductile Fracture
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作者 Mingjian Li Ping Yang Pengyang Zhao 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第8期2019-2034,共16页
The experimental results in previous studies have indicated that during the ductile fracture of pure metals,vacancies aggregate and form voids at grain boundaries.However,the physical mechanism underlying this phenome... The experimental results in previous studies have indicated that during the ductile fracture of pure metals,vacancies aggregate and form voids at grain boundaries.However,the physical mechanism underlying this phenomenon remains not fully understood.This study derives the equilibrium distribution of vacancies analytically by following thermodynamics and the micromechanics of crystal defects.This derivation suggests that vacancies cluster in regions under hydrostatic compression to minimize the elastic strain energy.Subsequently,a finite element model is developed for examining more general scenarios of interaction between vacancies and grain boundaries.This model is first verified and validated through comparison with some available analytical solutions,demonstrating consistency between finite element simulation results and analytical solutions within a specified numerical accuracy.A systematic numerical study is then conducted to investigate the mechanism that might govern the micromechanical interaction between grain boundaries and the profuse vacancies typically generated during plastic deformation.The simulation results indicate that the reduction in total elastic strain energy can indeed drive vacancies toward grain boundaries,potentially facilitating void nucleation in ductile fracture. 展开更多
关键词 Ductile fracture VACANCY grain boundary MICROMECHANICAL finite element method
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