In this paper, a weighted residual method for the elastic-plastic analysis near a crack tip is systematically given by taking the model of power-law hardening under plane strain condition as a sample. The elastic-plas...In this paper, a weighted residual method for the elastic-plastic analysis near a crack tip is systematically given by taking the model of power-law hardening under plane strain condition as a sample. The elastic-plastic solutions of the crack lip field and an approach based on the superposition of the nonlinear finite element method on the complete solution in the whole crack body field, to calculate the plastic stress intensity factors, are also developed. Therefore, a complete analvsis based on the calculation both for the crack tip field and for the whole crack body field is provided.展开更多
The meshless weighted least-square (MWLS) method was developed based on the weighted least-square method. The method possesses several advantages, such as high accuracy, high stability and high e?ciency. Moreover, t...The meshless weighted least-square (MWLS) method was developed based on the weighted least-square method. The method possesses several advantages, such as high accuracy, high stability and high e?ciency. Moreover, the coe?cient matrix obtained is symmetric and semi- positive de?nite. In this paper, the method is further examined critically. The e?ects of several parameters on the results of MWLS are investigated systematically by using a cantilever beam and an in?nite plate with a central circular hole. The numerical results are compared with those obtained by using the collocation-based meshless method (CBMM) and Galerkin-based meshless method (GBMM). The investigated parameters include the type of approximations, the type of weight functions, the number of neighbors of an evaluation point, as well as the manner in which the neighbors of an evaluation point are determined. This study shows that the displacement accuracy and convergence rate obtained by MWLS is comparable to that of the GBMM while the stress accuracy and convergence rate yielded by MWLS is even higher than that of GBMM. Furthermore, MWLS is much more e?cient than GBMM. This study also shows that the instability of CBMM is mainly due to the neglect of the equi- librium residuals at boundary nodes. In MWLS, the residuals of all the governing equations are minimized in a weighted least-square sense.展开更多
The vibroimpact systems with bilateral barriers are often encountered in practice.However,the dynamics of the vibroimpact system with bilateral barriers is full of challenges.Few closed-form solutions were obtained.In...The vibroimpact systems with bilateral barriers are often encountered in practice.However,the dynamics of the vibroimpact system with bilateral barriers is full of challenges.Few closed-form solutions were obtained.In this paper,we propose a novel method for random vibration analysis of single-degree-of-freedom(SDOF)vibroim-pact systems with bilateral barriers under Gaussian white noise excitations.A periodic approximate transformation is employed to convert the equations of the motion to a con-tinuous form.The probabilistic description of the system is subsequently defined through the corresponding Fokker-Planck-Kolmogorov(FPK)equation.The closed-form station-ary probability density function(PDF)of the response is obtained by solving the reduced FPK equation and using the proposed iterative method of weighted residue together with the concepts of the circulatory probability flow and the potential probability flow.Finally,the versatility of the proposed approach is demonstrated by its application to two typical examples.Note that the solution obtained by using the proposed method can be used as the benchmark to examine the accuracy of approximate solutions obtained by other methods.展开更多
The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and nea...The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and near the canyon surfaces using weighted-residuals(moment method).The wave displacement fields are computed by the residual method for the cases of elliptic,circular,rounded-rectangular and flat-elliptic canyons,The analysis demonstrates that the resulting surface displacement depends,as in similar previous analyses,on several factors including,but not limited,to the angle of the wedge,the geometry of the vertex,the frequencies of the incident waves,the angles of incidence,and the material properties of the media.The analysis provides intriguing results that help to explain geophysical observations regarding the amplification of seismic energy as a function of site conditions.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
Generally the incompressible viscous flow problem is described by the Navier-Stokes equation. Based on the weighted residual method the discrete formulation of element-free Galerkin is inferred in this paper. By the s...Generally the incompressible viscous flow problem is described by the Navier-Stokes equation. Based on the weighted residual method the discrete formulation of element-free Galerkin is inferred in this paper. By the step-bystep computation in the field of time, and adopting the least-square estimation of the-same-order shift, this paper has calculated both velocity and pressure from the decoupling independent equations. Each time fraction Newton-Raphson iterative method is applied for the velocity and pressure. Finally, this paper puts the method into practice of the shear-drive cavity flow, verifying the validity, high accuracy and stability.展开更多
In this paper, a parallel algorithm with iterative form for solving finite element equation is presented. Based on the iterative solution of linear algebra equations, the parallel computational steps are introduced in...In this paper, a parallel algorithm with iterative form for solving finite element equation is presented. Based on the iterative solution of linear algebra equations, the parallel computational steps are introduced in this method. Also by using the weighted residual method and choosing the appropriate weighting functions, the finite element basic form of parallel algorithm is deduced. The program of this algorithm has been realized on the ELXSI-6400 parallel computer of Xi'an Jiaotong University. The computational results show the operational speed will be raised and the CPU time will be cut down effectively. So this method is one kind of effective parallel algorithm for solving the finite element equations of large-scale structures.展开更多
In this paper, using the integration method, it is sought to solve the problem for the laminar boundary_layer on a flat plate. At first, a trial function of the velocity profile which satisfies the basical boundary co...In this paper, using the integration method, it is sought to solve the problem for the laminar boundary_layer on a flat plate. At first, a trial function of the velocity profile which satisfies the basical boundary conditions is selected. The coefficients in the trial function awaiting decision are decided by using some numerical results of the boundary_layer differential equations. It is similar to the method proposed by Peng Yichuan, but the former is simpler. According to the method proposed by Peng, when the awaiting decision coefficients of the trial function are decided, it is sought to solve a third power algebraic equation. On the other hand, in this paper, there is only need for solving a linear algebraic equation. Moreover, the accuracy of the results of this paper is higher than that of Peng.展开更多
In this paper, the solution to the structure consisting of a bead and a board is given as a result of the application of the subregion function method which was suggested in ref. [1]. The same problem is also computed...In this paper, the solution to the structure consisting of a bead and a board is given as a result of the application of the subregion function method which was suggested in ref. [1]. The same problem is also computed with finite element method. The comparison between the two results shows that the application of the subregion function in the method of weighted residuals is practical and effective, especially for solving compound structures.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
In this Paper, we have proposed a new weighted residual method known as orthogonal collocation-based on mixed interpolation (OCMI). Mixed interpolation uses the classical polynomial approximation with two correction t...In this Paper, we have proposed a new weighted residual method known as orthogonal collocation-based on mixed interpolation (OCMI). Mixed interpolation uses the classical polynomial approximation with two correction terms given in the form of sine and cosine function. By these correction terms, we can control the error in the solution. We have applied this approach to a non-linear boundary value problem (BVP) in ODE which governs the electrohydrodynamic flow in a cylindrical conduit. The solution profiles shown in the figures are in good agreement with the work of Paullet (1999) and Ghasemi et al. (2014). Our solution is monotonic decreasing and satisfies , where, α governs the strength of non-linearity and for large values of α solutions are . The residual errors are given in Table 1 and Table 2 which are significantly small. Comparison of residual errors between our proposed method, Least square method and Homotopy analysis method is also given and shown via the Table 3 where as the profiles of the residual error are depicted in Figures 4-8. Table and graphs show that efficiency of the proposed method. The error bound and its L2-norm with relevant theorems for mixed interpolation are also given.展开更多
文摘In this paper, a weighted residual method for the elastic-plastic analysis near a crack tip is systematically given by taking the model of power-law hardening under plane strain condition as a sample. The elastic-plastic solutions of the crack lip field and an approach based on the superposition of the nonlinear finite element method on the complete solution in the whole crack body field, to calculate the plastic stress intensity factors, are also developed. Therefore, a complete analvsis based on the calculation both for the crack tip field and for the whole crack body field is provided.
基金Project supported by the National Natural Science Foundation of China (No.10172052).
文摘The meshless weighted least-square (MWLS) method was developed based on the weighted least-square method. The method possesses several advantages, such as high accuracy, high stability and high e?ciency. Moreover, the coe?cient matrix obtained is symmetric and semi- positive de?nite. In this paper, the method is further examined critically. The e?ects of several parameters on the results of MWLS are investigated systematically by using a cantilever beam and an in?nite plate with a central circular hole. The numerical results are compared with those obtained by using the collocation-based meshless method (CBMM) and Galerkin-based meshless method (GBMM). The investigated parameters include the type of approximations, the type of weight functions, the number of neighbors of an evaluation point, as well as the manner in which the neighbors of an evaluation point are determined. This study shows that the displacement accuracy and convergence rate obtained by MWLS is comparable to that of the GBMM while the stress accuracy and convergence rate yielded by MWLS is even higher than that of GBMM. Furthermore, MWLS is much more e?cient than GBMM. This study also shows that the instability of CBMM is mainly due to the neglect of the equi- librium residuals at boundary nodes. In MWLS, the residuals of all the governing equations are minimized in a weighted least-square sense.
基金Project supported by the National Natural Science Foundation of China(Nos.11672111,11332008,11572215,and 11602089)the Program for New Century Excellent Talents in Fujian Province University+1 种基金the Natural Science Foundation of Fujian Province of China(No.2019J01049)the Promotion Program for Young and Middle-Aged Teacher in Science and Technology Research of Huaqiao University(Nos.ZQNYX307 and ZQNYX505)
文摘The vibroimpact systems with bilateral barriers are often encountered in practice.However,the dynamics of the vibroimpact system with bilateral barriers is full of challenges.Few closed-form solutions were obtained.In this paper,we propose a novel method for random vibration analysis of single-degree-of-freedom(SDOF)vibroim-pact systems with bilateral barriers under Gaussian white noise excitations.A periodic approximate transformation is employed to convert the equations of the motion to a con-tinuous form.The probabilistic description of the system is subsequently defined through the corresponding Fokker-Planck-Kolmogorov(FPK)equation.The closed-form station-ary probability density function(PDF)of the response is obtained by solving the reduced FPK equation and using the proposed iterative method of weighted residue together with the concepts of the circulatory probability flow and the potential probability flow.Finally,the versatility of the proposed approach is demonstrated by its application to two typical examples.Note that the solution obtained by using the proposed method can be used as the benchmark to examine the accuracy of approximate solutions obtained by other methods.
文摘The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and near the canyon surfaces using weighted-residuals(moment method).The wave displacement fields are computed by the residual method for the cases of elliptic,circular,rounded-rectangular and flat-elliptic canyons,The analysis demonstrates that the resulting surface displacement depends,as in similar previous analyses,on several factors including,but not limited,to the angle of the wedge,the geometry of the vertex,the frequencies of the incident waves,the angles of incidence,and the material properties of the media.The analysis provides intriguing results that help to explain geophysical observations regarding the amplification of seismic energy as a function of site conditions.
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.
文摘Generally the incompressible viscous flow problem is described by the Navier-Stokes equation. Based on the weighted residual method the discrete formulation of element-free Galerkin is inferred in this paper. By the step-bystep computation in the field of time, and adopting the least-square estimation of the-same-order shift, this paper has calculated both velocity and pressure from the decoupling independent equations. Each time fraction Newton-Raphson iterative method is applied for the velocity and pressure. Finally, this paper puts the method into practice of the shear-drive cavity flow, verifying the validity, high accuracy and stability.
基金This work has been carried out as of a research project which has been supported by the National Structural Strength & Vibration Laboratory of Xi'an Jiaotong University with National Fund
文摘In this paper, a parallel algorithm with iterative form for solving finite element equation is presented. Based on the iterative solution of linear algebra equations, the parallel computational steps are introduced in this method. Also by using the weighted residual method and choosing the appropriate weighting functions, the finite element basic form of parallel algorithm is deduced. The program of this algorithm has been realized on the ELXSI-6400 parallel computer of Xi'an Jiaotong University. The computational results show the operational speed will be raised and the CPU time will be cut down effectively. So this method is one kind of effective parallel algorithm for solving the finite element equations of large-scale structures.
文摘In this paper, using the integration method, it is sought to solve the problem for the laminar boundary_layer on a flat plate. At first, a trial function of the velocity profile which satisfies the basical boundary conditions is selected. The coefficients in the trial function awaiting decision are decided by using some numerical results of the boundary_layer differential equations. It is similar to the method proposed by Peng Yichuan, but the former is simpler. According to the method proposed by Peng, when the awaiting decision coefficients of the trial function are decided, it is sought to solve a third power algebraic equation. On the other hand, in this paper, there is only need for solving a linear algebraic equation. Moreover, the accuracy of the results of this paper is higher than that of Peng.
文摘In this paper, the solution to the structure consisting of a bead and a board is given as a result of the application of the subregion function method which was suggested in ref. [1]. The same problem is also computed with finite element method. The comparison between the two results shows that the application of the subregion function in the method of weighted residuals is practical and effective, especially for solving compound structures.
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.
文摘In this Paper, we have proposed a new weighted residual method known as orthogonal collocation-based on mixed interpolation (OCMI). Mixed interpolation uses the classical polynomial approximation with two correction terms given in the form of sine and cosine function. By these correction terms, we can control the error in the solution. We have applied this approach to a non-linear boundary value problem (BVP) in ODE which governs the electrohydrodynamic flow in a cylindrical conduit. The solution profiles shown in the figures are in good agreement with the work of Paullet (1999) and Ghasemi et al. (2014). Our solution is monotonic decreasing and satisfies , where, α governs the strength of non-linearity and for large values of α solutions are . The residual errors are given in Table 1 and Table 2 which are significantly small. Comparison of residual errors between our proposed method, Least square method and Homotopy analysis method is also given and shown via the Table 3 where as the profiles of the residual error are depicted in Figures 4-8. Table and graphs show that efficiency of the proposed method. The error bound and its L2-norm with relevant theorems for mixed interpolation are also given.