The Trefftz-type boundary solution methods([1]) are applied in analysing moderately thick plate bending problems. A new type of locking problem caused by the overflow of Trefftz functions has been found and a so-calle...The Trefftz-type boundary solution methods([1]) are applied in analysing moderately thick plate bending problems. A new type of locking problem caused by the overflow of Trefftz functions has been found and a so-called variable-reducing procedure for eliminating such a phenomenon is also proposed.展开更多
In this paper,the equal-norm multiple-scale Trefftz method combined with the implicit Lie-group scheme is applied to solve the two-dimensional nonlinear sloshing problem with baffles.When considering solving sloshing ...In this paper,the equal-norm multiple-scale Trefftz method combined with the implicit Lie-group scheme is applied to solve the two-dimensional nonlinear sloshing problem with baffles.When considering solving sloshing problems with baffles by using boundary integral methods,degenerate geometry and problems of numerical instability are inevitable.To avoid numerical instability,the multiple-scale characteristic lengths are introduced into T-complete basis functions to efficiently govern the high-order oscillation disturbance.Again,the numerical noise propagation at each time step is eliminated by the vector regularization method and the group-preserving scheme.A weighting factor of the group-preserving scheme is introduced into a linear system and then used in the initial and boundary value problems(IBVPs)at each time step.More importantly,the parameters of the algorithm,namely,the T-complete function,dissipation factor,and time step,can obtain a linear relationship.The boundary noise interference and energy conservation are successfully overcome,and the accuracy of the boundary value problem is also improved.Finally,benchmark cases are used to verify the correctness of the numerical algorithm.The numerical results show that this algorithm is efficient and stable for nonlinear two-dimensional sloshing problems with baffles.展开更多
In the solution domain, the inhomogeneous part of Poisson equation is approximated with the 5-order polynomial using Galerkin method, and the particular solution of the polynomial can be determined easily. Then, the s...In the solution domain, the inhomogeneous part of Poisson equation is approximated with the 5-order polynomial using Galerkin method, and the particular solution of the polynomial can be determined easily. Then, the solution of the Poisson equation is approximated by superposition of the particular solution and the Tcomplete functions related to the Laplace equation. Unknown parameters are determined by Galerkin method, so that the approximate solution is to satisfy the boundary conditions. Comparison with analogous results of others numerical method, the two calculating examples of the paper indicate that the accuracy of the method is very high, which also has a very fast convergence rate.展开更多
This paper presents a hybrid Trefftz （HT） boundary element method （BEM） by using two indirect techniques for mode III fracture problems. Two Trefftz complete functions of Laplace equation for normal elements and a...This paper presents a hybrid Trefftz （HT） boundary element method （BEM） by using two indirect techniques for mode III fracture problems. Two Trefftz complete functions of Laplace equation for normal elements and a special purpose Trefftz function for crack elements are proposed in deriving the Galerkin and the collocation techniques of HT BEM. Then two auxiliary functions are introduced to improve the accuracy of the displacement field near the crack tips, and stress intensity factor （SIF） is evaluated by local crack elements as well. Furthermore, numerical examples are given, including comparisons of the present results with the analytical solution and the other numerical methods, to demonstrate the efficiency for different boundary conditions and to illustrate the convergence influenced by several parameters. It shows that HT BEM by usingthe Galerkin and the collocation techniques is effective for mode III fracture problems.展开更多
This paper attempts to further extend the so-called Trefftz direct method(TDM), which has been developed and applied to a wide variety of boundary value problems in recent years. In this approach, the complete system ...This paper attempts to further extend the so-called Trefftz direct method(TDM), which has been developed and applied to a wide variety of boundary value problems in recent years. In this approach, the complete system of solutions of the partial differential equations is used as weighting functions and a non-singular boundary integral equation is used as the starting formulation. Several relative problems are discussed here. They are the problems of necessary and sufficient conditions for Trefftz-type boundary integral equations: the relationship between the Trefftz method and the variational principle and the infrequently encountered but possible singular problems in the Trefftz method and the treatment in practice. Numerical results are presented to illustrate the computational efficiency of the approach and to demonstrate its advantages.展开更多
Trefftz有限元法(Trefftz finite element method,TFEM)因其独特的优良品质而备受关注.针对正交各向异性轴对称位势问题,提出了一种4节点四边形环状单元.在该单元模型中,首先假设两套独立的位势插值模式:即单元域内场和网线场,然后代入...Trefftz有限元法(Trefftz finite element method,TFEM)因其独特的优良品质而备受关注.针对正交各向异性轴对称位势问题,提出了一种4节点四边形环状单元.在该单元模型中,首先假设两套独立的位势插值模式:即单元域内场和网线场,然后代入修正变分泛函并利用Gauss散度定理消除区域积分,最后根据驻值原理导得只含边界积分的单元刚度方程.数值算例表明了该单元的准确性、稳定性以及对网格畸变的不敏感性.展开更多
Based on the indirect Trefftz approach, a wave number method （WNM） is proposed to deal with three-dimensional steady-state acoustic problems. In the WNM, the dynamic pressure response variable is approximated by a s...Based on the indirect Trefftz approach, a wave number method （WNM） is proposed to deal with three-dimensional steady-state acoustic problems. In the WNM, the dynamic pressure response variable is approximated by a set of wave functions, which exactly satisfy the Helmholtz equation. The set of wave functions comprise the exact solutions of the homogeneous part of the governing equations and some particular solution functions. The unknown coefficients of the wave functions can be obtained by enforcing the pressure approximation to satisfy the boundary conditions. Compared with the boundary element method （BEM）, the WNM have a smaller system matrix, and is applicable to the radiation problems since the wave functions are independent of the domain size. A 3D acoustic cavity is exemplified to show the properties of the method. The results show that the wave number method is more efficient than the BEM, and it is fairly accurate.展开更多
A wave number method （WNM） is proposed to deal with the two-dimensional coupled structural-acoustic problem. Based on an indirect Trefftz approach, the displacement and the pressure response are approximated respect...A wave number method （WNM） is proposed to deal with the two-dimensional coupled structural-acoustic problem. Based on an indirect Trefftz approach, the displacement and the pressure response are approximated respectively by a set of wave functions, which exactly satisfy the governing equations and are independent of the size of the coupled system. The wave functions comprise the exact solutions of the homogeneous part of the governing equations and some particular solution functions, which arise from the external excitation. The weighting coefficients of the wave functions can be obtained by enforcing the pressure approximation to satisfy the boundary conditions and it is performed by applying the weighted residual formulation. The example is computed by the WNM and the BEM. The results show that, the WNM can attain the same accuracy and convergence as the BEM with less degrees of freedom.展开更多
Conventional element based methods for modeling acoustic problems are limited to low-frequency applications due to the huge computational efforts.For high-frequency applications,probabilistic techniques,such as statis...Conventional element based methods for modeling acoustic problems are limited to low-frequency applications due to the huge computational efforts.For high-frequency applications,probabilistic techniques,such as statistical energy analysis(SEA),are used.For mid-frequency range,currently no adequate and mature simulation methods exist.Recently,wave based method has been developed which is based on the indirect TREFFTZ approach and has shown to be able to tackle problems in the mid-frequency range.In contrast with the element based methods,no discretization is required.A sufficient,but not necessary,condition for convergence of this method is that the acoustic problem domain is convex.Non-convex domains have to be partitioned into a number of(convex)subdomains.At the interfaces between subdomains,specific coupling conditions have to be imposed.The considered two-dimensional coupled vibro-acoustic problem illustrates the beneficial convergence rate of the proposed wave based prediction technique with high accuracy.The results show the new technique can be applied up to much higher frequencies.展开更多
基金National Natural Science Foundation of China(No.19872019)Solid Mechanics Open Research laboratory of Tongji University
文摘The Trefftz-type boundary solution methods([1]) are applied in analysing moderately thick plate bending problems. A new type of locking problem caused by the overflow of Trefftz functions has been found and a so-called variable-reducing procedure for eliminating such a phenomenon is also proposed.
基金The second author greatly appreciates the financial support provided by the Ministry of Science and Technology,Taiwan,ROC,under Contract No.MOST 108-2221-E-019-015.
文摘In this paper,the equal-norm multiple-scale Trefftz method combined with the implicit Lie-group scheme is applied to solve the two-dimensional nonlinear sloshing problem with baffles.When considering solving sloshing problems with baffles by using boundary integral methods,degenerate geometry and problems of numerical instability are inevitable.To avoid numerical instability,the multiple-scale characteristic lengths are introduced into T-complete basis functions to efficiently govern the high-order oscillation disturbance.Again,the numerical noise propagation at each time step is eliminated by the vector regularization method and the group-preserving scheme.A weighting factor of the group-preserving scheme is introduced into a linear system and then used in the initial and boundary value problems(IBVPs)at each time step.More importantly,the parameters of the algorithm,namely,the T-complete function,dissipation factor,and time step,can obtain a linear relationship.The boundary noise interference and energy conservation are successfully overcome,and the accuracy of the boundary value problem is also improved.Finally,benchmark cases are used to verify the correctness of the numerical algorithm.The numerical results show that this algorithm is efficient and stable for nonlinear two-dimensional sloshing problems with baffles.
文摘In the solution domain, the inhomogeneous part of Poisson equation is approximated with the 5-order polynomial using Galerkin method, and the particular solution of the polynomial can be determined easily. Then, the solution of the Poisson equation is approximated by superposition of the particular solution and the Tcomplete functions related to the Laplace equation. Unknown parameters are determined by Galerkin method, so that the approximate solution is to satisfy the boundary conditions. Comparison with analogous results of others numerical method, the two calculating examples of the paper indicate that the accuracy of the method is very high, which also has a very fast convergence rate.
基金the National Natural Science Foundation of China(10472082).
文摘This paper presents a hybrid Trefftz （HT） boundary element method （BEM） by using two indirect techniques for mode III fracture problems. Two Trefftz complete functions of Laplace equation for normal elements and a special purpose Trefftz function for crack elements are proposed in deriving the Galerkin and the collocation techniques of HT BEM. Then two auxiliary functions are introduced to improve the accuracy of the displacement field near the crack tips, and stress intensity factor （SIF） is evaluated by local crack elements as well. Furthermore, numerical examples are given, including comparisons of the present results with the analytical solution and the other numerical methods, to demonstrate the efficiency for different boundary conditions and to illustrate the convergence influenced by several parameters. It shows that HT BEM by usingthe Galerkin and the collocation techniques is effective for mode III fracture problems.
基金Supported by National Natural Science Foundation of China(No.19872019).
文摘This paper attempts to further extend the so-called Trefftz direct method(TDM), which has been developed and applied to a wide variety of boundary value problems in recent years. In this approach, the complete system of solutions of the partial differential equations is used as weighting functions and a non-singular boundary integral equation is used as the starting formulation. Several relative problems are discussed here. They are the problems of necessary and sufficient conditions for Trefftz-type boundary integral equations: the relationship between the Trefftz method and the variational principle and the infrequently encountered but possible singular problems in the Trefftz method and the treatment in practice. Numerical results are presented to illustrate the computational efficiency of the approach and to demonstrate its advantages.
文摘Trefftz有限元法(Trefftz finite element method,TFEM)因其独特的优良品质而备受关注.针对正交各向异性轴对称位势问题,提出了一种4节点四边形环状单元.在该单元模型中,首先假设两套独立的位势插值模式:即单元域内场和网线场,然后代入修正变分泛函并利用Gauss散度定理消除区域积分,最后根据驻值原理导得只含边界积分的单元刚度方程.数值算例表明了该单元的准确性、稳定性以及对网格畸变的不敏感性.
文摘Based on the indirect Trefftz approach, a wave number method （WNM） is proposed to deal with three-dimensional steady-state acoustic problems. In the WNM, the dynamic pressure response variable is approximated by a set of wave functions, which exactly satisfy the Helmholtz equation. The set of wave functions comprise the exact solutions of the homogeneous part of the governing equations and some particular solution functions. The unknown coefficients of the wave functions can be obtained by enforcing the pressure approximation to satisfy the boundary conditions. Compared with the boundary element method （BEM）, the WNM have a smaller system matrix, and is applicable to the radiation problems since the wave functions are independent of the domain size. A 3D acoustic cavity is exemplified to show the properties of the method. The results show that the wave number method is more efficient than the BEM, and it is fairly accurate.
基金Project supported by the National Natural Science Foundation of China (No.10472035).
文摘A wave number method （WNM） is proposed to deal with the two-dimensional coupled structural-acoustic problem. Based on an indirect Trefftz approach, the displacement and the pressure response are approximated respectively by a set of wave functions, which exactly satisfy the governing equations and are independent of the size of the coupled system. The wave functions comprise the exact solutions of the homogeneous part of the governing equations and some particular solution functions, which arise from the external excitation. The weighting coefficients of the wave functions can be obtained by enforcing the pressure approximation to satisfy the boundary conditions and it is performed by applying the weighted residual formulation. The example is computed by the WNM and the BEM. The results show that, the WNM can attain the same accuracy and convergence as the BEM with less degrees of freedom.
基金This project is supported by National Natural Science Foundation of China(No.10472035).
文摘Conventional element based methods for modeling acoustic problems are limited to low-frequency applications due to the huge computational efforts.For high-frequency applications,probabilistic techniques,such as statistical energy analysis(SEA),are used.For mid-frequency range,currently no adequate and mature simulation methods exist.Recently,wave based method has been developed which is based on the indirect TREFFTZ approach and has shown to be able to tackle problems in the mid-frequency range.In contrast with the element based methods,no discretization is required.A sufficient,but not necessary,condition for convergence of this method is that the acoustic problem domain is convex.Non-convex domains have to be partitioned into a number of(convex)subdomains.At the interfaces between subdomains,specific coupling conditions have to be imposed.The considered two-dimensional coupled vibro-acoustic problem illustrates the beneficial convergence rate of the proposed wave based prediction technique with high accuracy.The results show the new technique can be applied up to much higher frequencies.
