The numerical approach for finding the solution of fractional order systems of boundary value problems (BPVs) is derived in this paper. The implementation of the weighted residuals such as Galerkin, Least Square, and ...The numerical approach for finding the solution of fractional order systems of boundary value problems (BPVs) is derived in this paper. The implementation of the weighted residuals such as Galerkin, Least Square, and Collocation methods are included for solving fractional order differential equations, which is broadened to acquire the approximate solutions of fractional order systems with differentiable polynomials, namely Legendre polynomials, as basis functions. The algorithm of the residual formulations of matrix form can be coded efficiently. The interpretation of Caputo fractional derivatives is employed here. We have demonstrated these methods numerically through a few examples of linear and nonlinear BVPs. The results in absolute errors show that the present method efficiently finds the numerical solutions of fractional order systems of differential equations.展开更多
The semi? analytic perturbation weighted residuals method was used to solve the nonlinear bending problem of shallow shells, and the fifth order B spline was taken as trial function to seek an efficient method for n...The semi? analytic perturbation weighted residuals method was used to solve the nonlinear bending problem of shallow shells, and the fifth order B spline was taken as trial function to seek an efficient method for nonlinear bending problem of shallow shells. The results from the present method are in good agreement with those derived from other methods. The present method is of higher accuracy, lower computing time and wider adaptability. In addition, the design of computer program is simple and it is easy to be programmed.展开更多
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
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, 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
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
The weighted residuals method was used for obtaining the boundary integral representation of the velocity of the three-dimensional inviscid irrotational flow. It is shown that velocity in an arbitrary point of domain ...The weighted residuals method was used for obtaining the boundary integral representation of the velocity of the three-dimensional inviscid irrotational flow. It is shown that velocity in an arbitrary point of domain can be expressed through its values on the boundary. Boundary integral equations of the second kind for solving boundary-valued problems of the first and second kinds are developed. The result has been also generalised to the case of solenoidal vector fields with potential vorticity. It is shown that the resulting integral equations are Fredholm integral equations of the second kind and allow effective numerical solving of corresponding boundary-valued problems. Examples of numerical solutions for a sphere and an ellipsoid are given for demonstration of efficiency of the offered method.展开更多
The model of predicting distribution of strip thickness at the exit and tension stress is established by using weighted residual method and variational method with consideration of rolled metal lateral flow.A New meth...The model of predicting distribution of strip thickness at the exit and tension stress is established by using weighted residual method and variational method with consideration of rolled metal lateral flow.A New method of calculating loaded roll gap in relation to target tension stress is proposed.The minimum square summation of loaded roll gap deviation is used as an objective function for the first time to optimize initial work roll profile.展开更多
In this paper, the axisymmetric problems of arbitrary thick spherical shell and solid sphere are studied directly from equilibrium equations of three-dimensional problem, and the general solutions informs of Legendre ...In this paper, the axisymmetric problems of arbitrary thick spherical shell and solid sphere are studied directly from equilibrium equations of three-dimensional problem, and the general solutions informs of Legendre serifs for thick spherical shell and solid sphere are given by using the method of weighted residuals.展开更多
The fabrication of high-precision panels for the compact antenna test range (CATR) with a sandwich construction of two aluminum skin-plates and one aluminum middle plate,which are bonded to two aluminum honeycomb core...The fabrication of high-precision panels for the compact antenna test range (CATR) with a sandwich construction of two aluminum skin-plates and one aluminum middle plate,which are bonded to two aluminum honeycomb core-layers poses a lot of tricky problems. Of them,the force analysis of individual skin-layers and the springback calculation of sandwich are of utmost importance. Under reasonable assumptions,by using Fourier expansion of stress function and power series expansion of deflection function,two boun...展开更多
Conventional attractive magnetic force models (proportional to the coil current squared and inversely proportional to the gap squared) cannot simulate the nonlinear responses of magnetic bearings in the presence of el...Conventional attractive magnetic force models (proportional to the coil current squared and inversely proportional to the gap squared) cannot simulate the nonlinear responses of magnetic bearings in the presence of electromagnetic losses,flux leakage or saturation of iron.In this paper,based on results from an experimental set-up designed to study magnetic force,a novel parametric model is presented in the form of a nonlinear polynomial with unknown coefficients.The parameters of the proposed model are identified using the weighted residual method.Validations of the model identified were performed by comparing the results in time and frequency domains.The results show a good correlation between experiments and numerical simulations.展开更多
文摘The numerical approach for finding the solution of fractional order systems of boundary value problems (BPVs) is derived in this paper. The implementation of the weighted residuals such as Galerkin, Least Square, and Collocation methods are included for solving fractional order differential equations, which is broadened to acquire the approximate solutions of fractional order systems with differentiable polynomials, namely Legendre polynomials, as basis functions. The algorithm of the residual formulations of matrix form can be coded efficiently. The interpretation of Caputo fractional derivatives is employed here. We have demonstrated these methods numerically through a few examples of linear and nonlinear BVPs. The results in absolute errors show that the present method efficiently finds the numerical solutions of fractional order systems of differential equations.
文摘The semi? analytic perturbation weighted residuals method was used to solve the nonlinear bending problem of shallow shells, and the fifth order B spline was taken as trial function to seek an efficient method for nonlinear bending problem of shallow shells. The results from the present method are in good agreement with those derived from other methods. The present method is of higher accuracy, lower computing time and wider adaptability. In addition, the design of computer program is simple and it is easy to be programmed.
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.
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, 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The weighted residuals method was used for obtaining the boundary integral representation of the velocity of the three-dimensional inviscid irrotational flow. It is shown that velocity in an arbitrary point of domain can be expressed through its values on the boundary. Boundary integral equations of the second kind for solving boundary-valued problems of the first and second kinds are developed. The result has been also generalised to the case of solenoidal vector fields with potential vorticity. It is shown that the resulting integral equations are Fredholm integral equations of the second kind and allow effective numerical solving of corresponding boundary-valued problems. Examples of numerical solutions for a sphere and an ellipsoid are given for demonstration of efficiency of the offered method.
基金Sponsored by Doctoral Foundation of National Education Committee of ChinaNatural Science Foundation of Hebei Province of China
文摘The model of predicting distribution of strip thickness at the exit and tension stress is established by using weighted residual method and variational method with consideration of rolled metal lateral flow.A New method of calculating loaded roll gap in relation to target tension stress is proposed.The minimum square summation of loaded roll gap deviation is used as an objective function for the first time to optimize initial work roll profile.
文摘In this paper, the axisymmetric problems of arbitrary thick spherical shell and solid sphere are studied directly from equilibrium equations of three-dimensional problem, and the general solutions informs of Legendre serifs for thick spherical shell and solid sphere are given by using the method of weighted residuals.
基金National Natural Science Foundation of China (10477001, 60673056)
文摘The fabrication of high-precision panels for the compact antenna test range (CATR) with a sandwich construction of two aluminum skin-plates and one aluminum middle plate,which are bonded to two aluminum honeycomb core-layers poses a lot of tricky problems. Of them,the force analysis of individual skin-layers and the springback calculation of sandwich are of utmost importance. Under reasonable assumptions,by using Fourier expansion of stress function and power series expansion of deflection function,two boun...
文摘Conventional attractive magnetic force models (proportional to the coil current squared and inversely proportional to the gap squared) cannot simulate the nonlinear responses of magnetic bearings in the presence of electromagnetic losses,flux leakage or saturation of iron.In this paper,based on results from an experimental set-up designed to study magnetic force,a novel parametric model is presented in the form of a nonlinear polynomial with unknown coefficients.The parameters of the proposed model are identified using the weighted residual method.Validations of the model identified were performed by comparing the results in time and frequency domains.The results show a good correlation between experiments and numerical simulations.
