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A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics 被引量:1
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作者 Liang Wang Xue Zhang +1 位作者 Jingjing Meng Qinghua Lei 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2024年第6期2172-2183,共12页
In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a gene... In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics. 展开更多
关键词 Particle finite element method Nodal integration Dynamic saturated media Second-order cone programming(SOCP)
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THE SUPERCLOSENESS OF THE FINITE ELEMENT METHOD FOR A SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEM ON A BAKHVALOV-TYPE MESH IN 2D
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作者 Chunxiao ZHANG Jin ZHANG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1572-1593,共22页
For singularly perturbed convection-diffusion problems,supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes,especially in the case of 2D.The difficulties arise from the width of ... For singularly perturbed convection-diffusion problems,supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes,especially in the case of 2D.The difficulties arise from the width of the mesh in the layer adjacent to the transition point,resulting in a suboptimal estimate for convergence.Existing analysis techniques cannot handle these difficulties well.To fill this gap,here a novel interpolation is designed delicately for the smooth part of the solution,bringing about the optimal supercloseness result of almost order 2 under an energy norm for the finite element method.Our theoretical result is uniform in the singular perturbation parameterεand is supported by the numerical experiments. 展开更多
关键词 singularly perturbed CONVECTION-DIFFUSION finite element method SUPERCLOSENESS Bakhvalov-type mesh
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A Deep Learning Approach to Shape Optimization Problems for Flexoelectric Materials Using the Isogeometric Finite Element Method
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作者 Yu Cheng Yajun Huang +3 位作者 Shuai Li Zhongbin Zhou Xiaohui Yuan Yanming Xu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第5期1935-1960,共26页
A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization... A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization problems.To improve the fitting ability of the neural network,we use the idea of pre-training to determine the structure of the neural network and combine different optimizers for training.The isogeometric analysis-finite element method(IGA-FEM)is used to discretize the flexural theoretical formulas and obtain samples,which helps ANN to build a proxy model from the model shape to the target value.The effectiveness of the proposed method is verified through two numerical examples of parameter optimization and one numerical example of shape optimization. 展开更多
关键词 Shape optimization deep learning flexoelectric structure finite element method isogeometric
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A New Isogeometric Finite Element Method for Analyzing Structures
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作者 Pan Su Jiaxing Chen +1 位作者 Ronggang Yang Jiawei Xiang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第11期1883-1905,共23页
High-performance finite element research has always been a major focus of finite element method studies.This article introduces isogeometric analysis into the finite element method and proposes a new isogeometric fini... High-performance finite element research has always been a major focus of finite element method studies.This article introduces isogeometric analysis into the finite element method and proposes a new isogeometric finite element method.Firstly,the physical field is approximated by uniform B-spline interpolation,while geometry is represented by non-uniform rational B-spline interpolation.By introducing a transformation matrix,elements of types C^(0)and C^(1)are constructed in the isogeometric finite element method.Subsequently,the corresponding calculation formats for one-dimensional bars,beams,and two-dimensional linear elasticity in the isogeometric finite element method are derived through variational principles and parameter mapping.The proposed method combines element construction techniques of the finite element method with geometric construction techniques of isogeometric analysis,eliminating the need for mesh generation and maintaining flexibility in element construction.Two elements with interpolation characteristics are constructed in the method so that boundary conditions and connections between elements can be processed like the finite element method.Finally,the test results of several examples show that:(1)Under the same degree and element node numbers,the constructed elements are almost consistent with the results obtained by traditional finite element method;(2)For bar problems with large local field variations and beam problems with variable cross-sections,high-degree and multi-nodes elements constructed can achieve high computational accuracy with fewer degrees of freedom than finite element method;(3)The computational efficiency of isogeometric finite element method is higher than finite element method under similar degrees of freedom,while as degrees of freedom increase,the computational efficiency between the two is similar. 展开更多
关键词 finite element method isogeometric analysis uniform B-spline non-uniform rational B-spline beam and bar
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Extended finite element-based cohesive zone method for modeling simultaneous hydraulic fracture height growth in layered reservoirs
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作者 Lei Yang Baixi Chen 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2024年第8期2960-2981,共22页
In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hy... In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hydraulic fractures in layered porous reservoirs with modulus contrast.The coupled hydromechanical model is first verified against an analytical solution and a laboratory experiment.Then,the fracture geometry(e.g.height,aperture,and area)and fluid pressure evolutions of multiple hydraulic fractures placed in a porous reservoir interbedded with alternating stiff and soft layers are investigated using the model.The stress and pore pressure distributions within the layered reservoir during fluid injection are also presented.The simulation results reveal that stress umbrellas are easily to form among multiple hydraulic fractures’tips when propagating in soft layers,which impedes the simultaneous height growth.It is also observed that the impediment effect of soft layer is much more significant in the fractures suppressed by the preferential growth of adjoining fractures.After that,the combined effect of in situ stress ratio and fracturing spacing on the multi-fracture height growth is presented,and the results elucidate the influence of in situ stress ratio on the height growth behavior depending on the fracture spacing.Finally,it is found that the inclusion of soft layers changes the aperture distribution of outmost and interior hydraulic fractures.The results obtained from this study may provide some insights on the understanding of hydraulic fracture height containment observed in filed. 展开更多
关键词 Hydraulic fracturing Layered reservoir Simultaneous height growth In situ stress Fracture spacing Extended finite element method(XFEM) Cohesive zone method(CZM)
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A Full Predictor-Corrector Finite Element Method for the One-Dimensional Heat Equation with Time-Dependent Singularities
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作者 Jake L. Nkeck 《Journal of Applied Mathematics and Physics》 2024年第4期1364-1382,共19页
The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent ... The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method. 展开更多
关键词 SINGULARITIES finite element methods Heat Equation Predictor-Corrector Algorithm
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Multiscale Finite Element Method for Coupling Analysis of Heterogeneous Magneto-Electro-Elastic Structures in Thermal Environment
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作者 Xinyue Li Xiaolin Li Hangran Yang 《Journal of Applied Mathematics and Physics》 2024年第9期3099-3113,共15页
Magneto-electro-elastic (MEE) materials, a new type of composite intelligent materials, exhibit excellent multifield coupling effects. Due to the heterogeneity of the materials, it is challenging to use the traditiona... Magneto-electro-elastic (MEE) materials, a new type of composite intelligent materials, exhibit excellent multifield coupling effects. Due to the heterogeneity of the materials, it is challenging to use the traditional finite element method (FEM) for mechanical analysis. Additionally, the MEE materials are often in a complex service environment, especially under the influence of the thermal field with thermoelectric and thermomagnetic effects, which affect its mechanical properties. Therefore, this paper proposes the efficient multiscale computational method for the multifield coupling problem of heterogeneous MEE structures under the thermal environment. The method constructs a multi-physics field with numerical base functions (the displacement, electric potential, and magnetic potential multiscale base functions). It equates a single cell of heterogeneous MEE materials to a macroscopic unit and supplements the macroscopic model with a microscopic model. This allows the problem to be solved directly on a macroscopic scale. Finally, the numerical simulation results demonstrate that compared with the traditional FEM, the multiscale finite element method (MsFEM) can achieve the purpose of ensuring accuracy and reducing the degree of freedom, and significantly improving the calculation efficiency. 展开更多
关键词 Multiscale finite element method MAGNETO-ELECTRO-ELASTIC Multifield Coupling Numerical Base Functions
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Hermite Finite Element Method for Vibration Problem of Euler-Bernoulli Beam on Viscoelastic Pasternak Foundation
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作者 Pengfei Ji Zhe Yin 《Engineering(科研)》 2024年第10期337-352,共16页
Viscoelastic foundation plays a very important role in civil engineering. It can effectively disperse the structural load into the foundation soil and avoid the damage caused by the concentrated load. The model of Eul... Viscoelastic foundation plays a very important role in civil engineering. It can effectively disperse the structural load into the foundation soil and avoid the damage caused by the concentrated load. The model of Euler-Bernoulli beam on viscoelastic Pasternak foundation can be used to analyze the deformation and response of buildings under complex geological conditions. In this paper, we use Hermite finite element method to get the numerical approximation scheme for the vibration equation of viscoelastic Pasternak foundation beam. Convergence and error estimation are rigourously established. We prove that the fully discrete scheme has convergence order O(τ2+h4), where τis time step size and his space step size. Finally, we give four numerical examples to verify the validity of theoretical analysis. 展开更多
关键词 Viscoelastic Pasternak Foundation Beam Vibration Equation Hermite finite element method Error Estimation Numerical Simulation
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Gradient Recovery Based Two-Grid Finite Element Method for Parabolic Integro-Differential Optimal Control Problems
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作者 Miao Yang 《Journal of Applied Mathematics and Physics》 2024年第8期2849-2865,共17页
In this paper, the optimal control problem of parabolic integro-differential equations is solved by gradient recovery based two-grid finite element method. Piecewise linear functions are used to approximate state and ... In this paper, the optimal control problem of parabolic integro-differential equations is solved by gradient recovery based two-grid finite element method. Piecewise linear functions are used to approximate state and co-state variables, and piecewise constant function is used to approximate control variables. Generally, the optimal conditions for the problem are solved iteratively until the control variable reaches error tolerance. In order to calculate all the variables individually and parallelly, we introduce a gradient recovery based two-grid method. First, we solve the small scaled optimal control problem on coarse grids. Next, we use the gradient recovery technique to recover the gradients of state and co-state variables. Finally, using the recovered variables, we solve the large scaled optimal control problem for all variables independently. Moreover, we estimate priori error for the proposed scheme, and use an example to validate the theoretical results. 展开更多
关键词 Optimal Control Problem Gradient Recovery Two-Grid finite element method
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TWO-DIMENSIONAL FINITE ELEMENT METHOD FOR DETERMINING NONLINEAR WAVE FORCES ON LARGE SUBMERGED BODIES
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作者 Huang He-ning, Institute of Marine Environmental Protection, State Oceanic Administration, Dalian 116023, P.R. Ch inaLi Jian-cu WangXue-geng, Department of Civil Engineering, Dalian Institute of Technology, Dalian 116024, P.R.China 《Journal of Hydrodynamics》 SCIE EI CSCD 1990年第2期17-26,共10页
In this paper, we first develop the far field asymptotic solutions of the second-order scattering waves for the vertical plane problem taking the second-order Stokes waves as the incident waves. The asymptotic solutio... In this paper, we first develop the far field asymptotic solutions of the second-order scattering waves for the vertical plane problem taking the second-order Stokes waves as the incident waves. The asymptotic solutions satisfy the Laplace equation, the sea bed and free surface boundary conditions and are the out-going waves. Then the radiation conditions of the second-order mattering waves are derived by using the asymptotic solutions. By using the two-dimensinal finite clement method with the radiation conditions imposed on the ar- tificial boundaries, the computer program, known as 'NWF2', for determining nonlinear wave forces on large submerged bodies has been written. As a numerical example, nonlinear wave forces on a semi-circu- lar cylinder lying on the sea bed arc presented. 展开更多
关键词 der two-dimensional finite element method FOR DETERMINING NONLINEAR WAVE FORCES ON LARGE SUBMERGED BODIES
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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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Modularized and Parametric Modeling Technology for Finite Element Simulations of Underground Engineering under Complicated Geological Conditions
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作者 Jiaqi Wu Li Zhuo +4 位作者 Jianliang Pei Yao Li Hongqiang Xie Jiaming Wu Huaizhong Liu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第7期621-645,共25页
The surrounding geological conditions and supporting structures of underground engineering are often updated during construction,and these updates require repeated numerical modeling.To improve the numerical modeling ... The surrounding geological conditions and supporting structures of underground engineering are often updated during construction,and these updates require repeated numerical modeling.To improve the numerical modeling efficiency of underground engineering,a modularized and parametric modeling cloud server is developed by using Python codes.The basic framework of the cloud server is as follows:input the modeling parameters into the web platform,implement Rhino software and FLAC3D software to model and run simulations in the cloud server,and return the simulation results to the web platform.The modeling program can automatically generate instructions that can run the modeling process in Rhino based on the input modeling parameters.The main modules of the modeling program include modeling the 3D geological structures,the underground engineering structures,and the supporting structures as well as meshing the geometric models.In particular,various cross-sections of underground caverns are crafted as parametricmodules in themodeling program.Themodularized and parametric modeling program is used for a finite element simulation of the underground powerhouse of the Shuangjiangkou Hydropower Station.This complicatedmodel is rapidly generated for the simulation,and the simulation results are reasonable.Thus,this modularized and parametric modeling program is applicable for three-dimensional finite element simulations and analyses. 展开更多
关键词 Underground engineering modularized and parametric modeling finite element method complex geological structure cloud modeling
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Probabilistic Analysis of Slope Using Finite Element Approach and Limit Equilibrium Approach around Amalpata Landslide of West Central, Nepal
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作者 Mahendra Acharya Khomendra Bhandari +2 位作者 Sandesh Dhakal Aasish Giri Prabin Kafle 《International Journal of Geosciences》 CAS 2024年第5期416-432,共17页
The stability study of the ongoing and recurring Amalpata landslide in Baglung in Nepal’s Gandaki Province is presented in this research. The impacted slope is around 200 meters high, with two terraces that have diff... The stability study of the ongoing and recurring Amalpata landslide in Baglung in Nepal’s Gandaki Province is presented in this research. The impacted slope is around 200 meters high, with two terraces that have different slope inclinations. The lower bench, located above the basement, consistently fails and sets others up for failure. The fluctuating water level of the slope, which travels down the slope masses, exacerbates the slide problem. The majority of these rocks are Amalpata landslide area experiences several structural disruptions. The area’s stability must be evaluated in order to prevent and control more harm from occurring to the nearby agricultural land and people living along the slope. The slopes’ failures increase the damages of house existing in nearby area and the erosion of the slope. Two modeling techniques the finite element approach and the limit equilibrium method were used to simulate the slope. The findings show that, in every case, the terrace above the basement is where the majority of the stress is concentrated, with a safety factor of near unity. Using probabilistic slope stability analysis, the failure probability was predicted to be between 98.90% and 100%. 展开更多
关键词 finite element Approach Limit Equilibrium method SLOPE Factor of Safety
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Finite Element Method for a Kind of Two-Dimensional Space-Fractional Diffusion Equation with Its Implementation 被引量:1
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作者 Beiping Duan Zhoushun Zheng Wen Cao 《American Journal of Computational Mathematics》 2015年第2期135-157,共23页
In this article, we consider a two-dimensional symmetric space-fractional diffusion equation in which the space fractional derivatives are defined in Riesz potential sense. The well-posed feature is guaranteed by ener... In this article, we consider a two-dimensional symmetric space-fractional diffusion equation in which the space fractional derivatives are defined in Riesz potential sense. The well-posed feature is guaranteed by energy inequality. To solve the diffusion equation, a fully discrete form is established by employing Crank-Nicolson technique in time and Galerkin finite element method in space. The stability and convergence are proved and the stiffness matrix is given analytically. Three numerical examples are given to confirm our theoretical analysis in which we find that even with the same initial condition, the classical and fractional diffusion equations perform differently but tend to be uniform diffusion at last. 展开更多
关键词 GALERKIN finite element method SYMMETRIC Space-Fractional Diffusion Equation Stability Convergence IMPLEMENTATION
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GENERALIZED WAVE EQUATION FINITE ELEMENT METHOD FOR SOLVING TWO-DIMENSIONAL TIDAL WAVES 被引量:1
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作者 吴伣康 赵汉中 《Chinese Journal of Oceanology and Limnology》 SCIE CAS CSCD 1992年第4期301-312,共12页
The study of tidal circulation has a long history . The numerical simulation of tidal flow has been developed greatly with the development of computer techniques in the past two decades. The generalized wave equation ... The study of tidal circulation has a long history . The numerical simulation of tidal flow has been developed greatly with the development of computer techniques in the past two decades. The generalized wave equation finite-element method is a relatively new numerical model for studying shallow water flow . This method was used to simulate tidal waves of the Gulf of St. Lawrence in Canada . The very good agreement of the numerical results with the field data indicated that the model is an effective and promising numerical method for solving two-dimensional tidal wave problems . 展开更多
关键词 TIDAL CIRCULATION finite-element method SHALLOW water equations . GENERALIZED wave equation
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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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Topology Optimization of Sound-Absorbing Materials for Two-Dimensional Acoustic Problems Using Isogeometric Boundary Element Method
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作者 Jintao Liu Juan Zhao Xiaowei Shen 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第2期981-1003,共23页
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.T... 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. 展开更多
关键词 Boundary element method isogeometric analysis two-dimensional acoustic analysis sound-absorbing materials topology optimization adjoint variable method
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A symplectic finite element method based on Galerkin discretization for solving linear systems
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作者 Zhiping QIU Zhao WANG Bo ZHU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第8期1305-1316,共12页
We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems.For the dynamic responses of continuous medium structures,the traditional numerical algorithm is ... We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems.For the dynamic responses of continuous medium structures,the traditional numerical algorithm is the dissipative algorithm and cannot maintain long-term energy conservation.Thus,a symplectic finite element method with energy conservation is constructed in this paper.A linear elastic system can be discretized into multiple elements,and a Hamiltonian system of each element can be constructed.The single element is discretized by the Galerkin method,and then the Hamiltonian system is constructed into the Birkhoffian system.Finally,all the elements are combined to obtain the vibration equation of the continuous system and solved by the symplectic difference scheme.Through the numerical experiments of the vibration response of the Bernoulli-Euler beam and composite plate,it is found that the vibration response solution and energy obtained with the algorithm are superior to those of the Runge-Kutta algorithm.The results show that the symplectic finite element method can keep energy conservation for a long time and has higher stability in solving the dynamic responses of linear elastic systems. 展开更多
关键词 Galerkin finite element method linear system structural dynamic response symplectic difference scheme
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ASYMPTOTICAL STABILITY OF NEUTRAL REACTION-DIFFUSION EQUATIONS WITH PCAS AND THEIR FINITE ELEMENT METHODS
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作者 韩豪 张诚坚 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1865-1880,共16页
This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their... This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results. 展开更多
关键词 neutral reaction-diffusion equations piecewise continuous arguments asymptotical stability finite element methods numerical experiment
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A dynamic large-deformation particle finite element method for geotechnical applications based on Abaqus
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作者 Weihai Yuan Jinxin Zhu +4 位作者 Neng Wang Wei Zhang Beibing Dai Yuanjun Jiang Yuan Wang 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2023年第7期1859-1871,共13页
In this paper,the application of Abaqus-based particle finite element method(PFEM)is extended from static to dynamic large deformation.The PFEM is based on periodic mesh regeneration with Delaunay triangulation to avo... In this paper,the application of Abaqus-based particle finite element method(PFEM)is extended from static to dynamic large deformation.The PFEM is based on periodic mesh regeneration with Delaunay triangulation to avoid mesh distortion.Additional mesh smoothing and boundary node smoothing techniques are incorporated to improve the mesh quality and solution accuracy.The field variables are mapped from the old to the new mesh using the closest point projection method to minimize the mapping error.The procedures of the proposed Abaqus-based dynamic PFEM(Abaqus-DPFEM)analysis and its implementation in Abaqus are detailed.The accuracy and robustness of the proposed approach are examined via four illustrative numerical examples.The numerical results show a satisfactory agreement with published results and further confirm the applicability of the Abaqus-DPFEM to solving dynamic large-deformation problems in geotechnical engineering. 展开更多
关键词 ABAQUS Collapse of granular materials DYNAMICS Large deformation Particle finite element method(PFEM) Rigid strip footing
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