The penalty and hybrid methods are being much used in dealing with the general incompatible element, With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower, and the...The penalty and hybrid methods are being much used in dealing with the general incompatible element, With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower, and the condition number and sparsity are not so good. With the hybrid method, convergence can be assured only when the rank condition is satisfied. So the construction of the element is extremely limited. This paper presents the mixed hybrid penalty element method, which combines the two methods together. And it is proved theoretically that this new method is convergent, and it has the same accuracy, condition number and sparsity as the compatible element. That is to say, they are optimal to each other.Finally, a new triangle element for plate bending with nine freedom degrees is constructed with this method (three degreesof freedom are given on each corner -- one displacement and tworotations), the calculating formula of the element stiffness matrix is almost the same as that of the old triangle element for plate bending with nine degrees of freedom But it is converged to true solution with arbitrary irregrlar triangle subdivision. If the true solution u?H3 with this method the linear and quadratic rates of convergence are obtianed for three bending moments and for the displacement and two rotations respectively.展开更多
In this paper, the boundary element method is applied to investigate the internal state of stress of autofretted tube with notch and the calculated results are important in the practical design.
Objective The aim of this study is to evaluate the applicable value of finite element analysis(FEA)for presurgical planning in the treatment of temporomandibular joint(TMJ)ankylosis.Methods CT image data of one patien...Objective The aim of this study is to evaluate the applicable value of finite element analysis(FEA)for presurgical planning in the treatment of temporomandibular joint(TMJ)ankylosis.Methods CT image data of one patient with unilateral展开更多
There is a common difficulty in elastic-plastic impact codes such as EPIC[2,3] NONSAP[4], etc.. Most of these codes use the simple linear functions usually taken from static problem to represent the displacement compo...There is a common difficulty in elastic-plastic impact codes such as EPIC[2,3] NONSAP[4], etc.. Most of these codes use the simple linear functions usually taken from static problem to represent the displacement components. In such finite element formulation, the stress components are constant in each element and they are discontinuous in any two neighboring elements. Therefore, the bases of using the virtual work principle in such elements are unreliable. In this paper, we introduce a new method, namely, the compatible stress iterative method, to eliminate the above-said difficulty. The calculated examples show that the calculation using the new method in dynamic finite element analysis of high velocity impact is valid and stable, and the element stiffness can be somewhat reduced.展开更多
The Finite Element Method of Lines （FEMOL） is a semi-analytic approach and takes a position between FEM and analytic methods. First, FEMOL in Fracture Mechanics is presented in detail. Then, the method is applied to...The Finite Element Method of Lines （FEMOL） is a semi-analytic approach and takes a position between FEM and analytic methods. First, FEMOL in Fracture Mechanics is presented in detail. Then, the method is applied to a set of examples such as edge-crack plate, the central-crack plate, the plate with cracks emanating from a hole under tensile or under combination loads of tensile and bending. Their dimensionless stress distribution, the stress intensify factor （SIF） and crack opening displacement （COD） are obtained, and comparison with known solutions by other methods are reported. It is found that a good accuracy is achieved by FEMOL. The method is successfully modified to remarkably increase the accuracy and reduce convergence difficulties. So it is a very useful and new tool in studying fracture mechanics problems.展开更多
The numerical quadrature methods for dealing with the problems of singular and near-singular integrals caused by Burton-Miller method are proposed, by which the conventional and fast multipole BEMs （boundary element ...The numerical quadrature methods for dealing with the problems of singular and near-singular integrals caused by Burton-Miller method are proposed, by which the conventional and fast multipole BEMs （boundary element methods） for 3D acoustic problems based on constant elements are improved. To solve the problem of singular integrals, a Hadamard finite-part integral method is presented, which is a simplified combination of the methods proposed by Kirkup and Wolf. The problem of near-singular integrals is overcome by the simple method of polar transformation and the more complex method of PART （Projection and Angular ＆ Radial Transformation）. The effectiveness of these methods for solving the singular and near-singular problems is validated through comparing with the results computed by the analytical method and/or the commercial software LMS Virtual.Lab. In addition, the influence of the near-singular integral problem on the computational precisions is analyzed by computing the errors relative to the exact solution. The computational complexities of the conventional and fast multipole BEM are analyzed and compared through numerical computations. A large-scale acoustic scattering problem, whose degree of freedoms is about 340,000, is implemented successfully. The results show that, the near singularity is primarily introduced by the hyper-singular kernel, and has great influences on the precision of the solution. The precision of fast multipole BEM is the same as conventional BEM, but the computational complexities are much lower.展开更多
There is a growing trend within energy and environmental simulation to consider tightly coupled solutions to multiphysics problems.This can be seen in nuclear reactor analysis where analysts are interested in coupled ...There is a growing trend within energy and environmental simulation to consider tightly coupled solutions to multiphysics problems.This can be seen in nuclear reactor analysis where analysts are interested in coupled flow,heat transfer and neutronics,and in nuclear fuel performance simulation where analysts are interested in thermomechanics with contact coupled to species transport and chemistry.In energy and environmental applications,energy extraction involves geomechanics,flow through porous media and fractured formations,adding heat transport for enhanced oil recovery and geothermal applications,and adding reactive transport in the case of applications modeling the underground flow of contaminants.These more ambitious simulations usually motivate some level of parallel computing.Many of the physics coupling efforts to date utilize simple code coupling or first-order operator splitting,often referred to as loose coupling.While these approaches can produce answers,they usually leave questions of accuracy and stability unanswered.Additionally,the different physics often reside on distinct meshes and data are coupled via simple interpolation,again leaving open questions of stability and accuracy.∗Corresponding author.Email addresses:Derek.Gaston@inl.gov(D.Gaston),This paper is the first part of a two part sequence on multiphysics algorithms and software.Part I examines the importance of accurate time and space integration and that the degree of coupling used for the solution should match the requirements of the simulation.It then discusses the preconditioned Jacobian-free Newton Krylov solution algorithm that is used for both multiphysics and multiscale solutions.Part II[1]presents the software framework;the Multiphysics Object Oriented Simulation Environment(MOOSE)and discusses applications based on it.展开更多
This paper is the second part of a two part sequence on multiphysics algorithms and software.The first[1]focused on the algorithms;this part treats the multiphysics software framework and applications based on it.Tigh...This paper is the second part of a two part sequence on multiphysics algorithms and software.The first[1]focused on the algorithms;this part treats the multiphysics software framework and applications based on it.Tight coupling is typically designed into the analysis application at inception,as such an application is strongly tied to a composite nonlinear solver that arrives at the final solution by treating all equations simultaneously.The applicationmust also take care tominimize both time and space error between the physics,particularly if more than one mesh representation is needed in the solution process.This paper presents an application framework that was specifically designed to support tightly coupled multiphysics analysis.The Multiphysics Object Oriented Simulation Environment(MOOSE)is based on the Jacobian-freeNewton-Krylov(JFNK)method combined with physics-based preconditioning to provide the underlying mathematical structure for applications.The report concludes with the presentation of a host of nuclear,energy,and environmental applications that demonstrate the efficacy of the approach and the utility of a well-designed multiphysics framework.展开更多
文摘The penalty and hybrid methods are being much used in dealing with the general incompatible element, With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower, and the condition number and sparsity are not so good. With the hybrid method, convergence can be assured only when the rank condition is satisfied. So the construction of the element is extremely limited. This paper presents the mixed hybrid penalty element method, which combines the two methods together. And it is proved theoretically that this new method is convergent, and it has the same accuracy, condition number and sparsity as the compatible element. That is to say, they are optimal to each other.Finally, a new triangle element for plate bending with nine freedom degrees is constructed with this method (three degreesof freedom are given on each corner -- one displacement and tworotations), the calculating formula of the element stiffness matrix is almost the same as that of the old triangle element for plate bending with nine degrees of freedom But it is converged to true solution with arbitrary irregrlar triangle subdivision. If the true solution u?H3 with this method the linear and quadratic rates of convergence are obtianed for three bending moments and for the displacement and two rotations respectively.
文摘In this paper, the boundary element method is applied to investigate the internal state of stress of autofretted tube with notch and the calculated results are important in the practical design.
文摘Objective The aim of this study is to evaluate the applicable value of finite element analysis(FEA)for presurgical planning in the treatment of temporomandibular joint(TMJ)ankylosis.Methods CT image data of one patient with unilateral
文摘There is a common difficulty in elastic-plastic impact codes such as EPIC[2,3] NONSAP[4], etc.. Most of these codes use the simple linear functions usually taken from static problem to represent the displacement components. In such finite element formulation, the stress components are constant in each element and they are discontinuous in any two neighboring elements. Therefore, the bases of using the virtual work principle in such elements are unreliable. In this paper, we introduce a new method, namely, the compatible stress iterative method, to eliminate the above-said difficulty. The calculated examples show that the calculation using the new method in dynamic finite element analysis of high velocity impact is valid and stable, and the element stiffness can be somewhat reduced.
文摘The Finite Element Method of Lines （FEMOL） is a semi-analytic approach and takes a position between FEM and analytic methods. First, FEMOL in Fracture Mechanics is presented in detail. Then, the method is applied to a set of examples such as edge-crack plate, the central-crack plate, the plate with cracks emanating from a hole under tensile or under combination loads of tensile and bending. Their dimensionless stress distribution, the stress intensify factor （SIF） and crack opening displacement （COD） are obtained, and comparison with known solutions by other methods are reported. It is found that a good accuracy is achieved by FEMOL. The method is successfully modified to remarkably increase the accuracy and reduce convergence difficulties. So it is a very useful and new tool in studying fracture mechanics problems.
基金supported by the National Natural Science Foundation of China(11304344,11404364)the Project of Hubei Provincial Department of Education(D20141803)+1 种基金the Natural Science Foundation of Hubei Province(2014CFB378)the Doctoral Scientific Research Foundation of Hubei University of Automotive Technology(BK201604)
文摘The numerical quadrature methods for dealing with the problems of singular and near-singular integrals caused by Burton-Miller method are proposed, by which the conventional and fast multipole BEMs （boundary element methods） for 3D acoustic problems based on constant elements are improved. To solve the problem of singular integrals, a Hadamard finite-part integral method is presented, which is a simplified combination of the methods proposed by Kirkup and Wolf. The problem of near-singular integrals is overcome by the simple method of polar transformation and the more complex method of PART （Projection and Angular ＆ Radial Transformation）. The effectiveness of these methods for solving the singular and near-singular problems is validated through comparing with the results computed by the analytical method and/or the commercial software LMS Virtual.Lab. In addition, the influence of the near-singular integral problem on the computational precisions is analyzed by computing the errors relative to the exact solution. The computational complexities of the conventional and fast multipole BEM are analyzed and compared through numerical computations. A large-scale acoustic scattering problem, whose degree of freedoms is about 340,000, is implemented successfully. The results show that, the near singularity is primarily introduced by the hyper-singular kernel, and has great influences on the precision of the solution. The precision of fast multipole BEM is the same as conventional BEM, but the computational complexities are much lower.
文摘There is a growing trend within energy and environmental simulation to consider tightly coupled solutions to multiphysics problems.This can be seen in nuclear reactor analysis where analysts are interested in coupled flow,heat transfer and neutronics,and in nuclear fuel performance simulation where analysts are interested in thermomechanics with contact coupled to species transport and chemistry.In energy and environmental applications,energy extraction involves geomechanics,flow through porous media and fractured formations,adding heat transport for enhanced oil recovery and geothermal applications,and adding reactive transport in the case of applications modeling the underground flow of contaminants.These more ambitious simulations usually motivate some level of parallel computing.Many of the physics coupling efforts to date utilize simple code coupling or first-order operator splitting,often referred to as loose coupling.While these approaches can produce answers,they usually leave questions of accuracy and stability unanswered.Additionally,the different physics often reside on distinct meshes and data are coupled via simple interpolation,again leaving open questions of stability and accuracy.∗Corresponding author.Email addresses:Derek.Gaston@inl.gov(D.Gaston),This paper is the first part of a two part sequence on multiphysics algorithms and software.Part I examines the importance of accurate time and space integration and that the degree of coupling used for the solution should match the requirements of the simulation.It then discusses the preconditioned Jacobian-free Newton Krylov solution algorithm that is used for both multiphysics and multiscale solutions.Part II[1]presents the software framework;the Multiphysics Object Oriented Simulation Environment(MOOSE)and discusses applications based on it.
文摘This paper is the second part of a two part sequence on multiphysics algorithms and software.The first[1]focused on the algorithms;this part treats the multiphysics software framework and applications based on it.Tight coupling is typically designed into the analysis application at inception,as such an application is strongly tied to a composite nonlinear solver that arrives at the final solution by treating all equations simultaneously.The applicationmust also take care tominimize both time and space error between the physics,particularly if more than one mesh representation is needed in the solution process.This paper presents an application framework that was specifically designed to support tightly coupled multiphysics analysis.The Multiphysics Object Oriented Simulation Environment(MOOSE)is based on the Jacobian-freeNewton-Krylov(JFNK)method combined with physics-based preconditioning to provide the underlying mathematical structure for applications.The report concludes with the presentation of a host of nuclear,energy,and environmental applications that demonstrate the efficacy of the approach and the utility of a well-designed multiphysics framework.
