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 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
In this paper, the minimal residual （MRES） method for solving nonsymmetric equation systems was improved, the recurrence relation was deduced between the approximate solutions of the linear equation system Ax = b, a...In this paper, the minimal residual （MRES） method for solving nonsymmetric equation systems was improved, the recurrence relation was deduced between the approximate solutions of the linear equation system Ax = b, and a more effective method was presented, which can reduce the operational count and the storage.展开更多
In the aerospace field, residual stress directly affects the strength, fatigue life and dimensional stability of thin-walled structural components, and is a key factor to ensure flight safety and reliability. At prese...In the aerospace field, residual stress directly affects the strength, fatigue life and dimensional stability of thin-walled structural components, and is a key factor to ensure flight safety and reliability. At present, research on residual stress at home and abroad mainly focuses on the optimization of traditional detection technology, stress control of manufacturing process and service performance evaluation, among which research on residual stress detection methods mainly focuses on the improvement of the accuracy, sensitivity, reliability and other performance of existing detection methods, but it still faces many challenges such as extremely small detection range, low efficiency, large error and limited application range.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
The downward continuation of potential fields is a process of calculating their values in a lower plane based on those of a certain plane.This technology is not only a data processing method for resource exploration b...The downward continuation of potential fields is a process of calculating their values in a lower plane based on those of a certain plane.This technology is not only a data processing method for resource exploration but also plays an extremely important role in military applications.However,the downward continuation of potential fields is a typical linear inverse problem that is ill-posed.Generalized minimal residuals(GMRES)is an eff ective solution to ill-posed inverse problems,but it is unstable under the condition wherein the GMRES is directly applied in the calculation process.Moreover,the long-term behavior of its iterative computation is a disordered,divergent result.Therefore,to obtain stable solutions,GMRES is applied to solve the normal equations of the downward continuation of potential fields;it is also used to prequalify for occasional interruptions in the operation process by adding the damping coefficient,thus strengthening the stability conditions of the equations of residual minimization.Finally,the stable downward continuation of the potential fields method is proposed.As indicated by the theoretical data and the measured testing data,the method proposed in this paper has the advantages of high-precision and excellent stability.Furthermore,compared with the Tikhonov iteration method,the proposed method avoids the need to choose regularization parameters.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
Lagrangian-Eulerian formulations based on a generalized variational principle of fluid-solid coupling dynamics are established to describe flow-induced vibration of a structure under small deformation in an incompress...Lagrangian-Eulerian formulations based on a generalized variational principle of fluid-solid coupling dynamics are established to describe flow-induced vibration of a structure under small deformation in an incompressible viscous fluid flow. The spatial discretization of the formulations is based on the multi-linear interpolating functions by using the finite element method for both the fluid and solid structures. The generalized trapezoidal rule is used to obtain apparently non-symmetric linear equations in an incremental form for the variables of the flow and vibration. The nonlinear convective term and time factors are contained in the non-symmetric coefficient matrix of the equations. The generalized minimum residual （GMRES） method is used to solve the incremental equations. A new stable algorithm of GMRES-Hughes-Newmark is developed to deal with the flow-induced vibration with dynamical fluid-structure interaction in complex geometries. Good agreement between the simulations and laboratory measurements of the pressure and blade vibration accelerations in a hydro turbine passage was obtained, indicating that the GiViRES-Hughes-Newmark algorithm presented in this paper is suitable for dealing with the flow-induced vibration of structures under small deformation.展开更多
Residual stress measurement is of critical significance to in-service security and the reliability of engineering components, and has been an active area of scientific interest. This paper offers a review o[ several p...Residual stress measurement is of critical significance to in-service security and the reliability of engineering components, and has been an active area of scientific interest. This paper offers a review o[ several prominent mechanical release methods for residual stress measurement and recent developments, focusing on the hole-drilling method combined with advanced optical sensing. Some promising trends for mechanical release methods are also analyzed.展开更多
The effect of vibratory stress relief （VSR） is usually evaluated with the indirect method of observing the change of amplitude frequency response characteristics of structures. A new kind of evaluating method of VSR...The effect of vibratory stress relief （VSR） is usually evaluated with the indirect method of observing the change of amplitude frequency response characteristics of structures. A new kind of evaluating method of VSR based on the ultrasonic time-of-arrival method （UTM）, which can obtain the residual stress directly through measuring the propagation time of ultrasonic wave in the material, is presented. At first, the principle of the measuring method of residual stress based on UTM is analyzed. Then the measuring system of the method is described, which is in virtue of ultrasonic flaw detector and high-sampling-rate digital oscillograph. And a set of calibration system that contains a piece of standard specimen is also introduced. Experimental results prove the relation between the residual stress and the propagation time of ultrasonic in workpieces. Finally, the measuring and calibration systems are applied in evaluating the effect of VSR. The final test results show that the method is effective.展开更多
The bi-conjugate gradients(Bi-CG)and bi-conjugate residual(Bi-CR)methods are powerful tools for solving nonsymmetric linear systems Ax=b.By using Kronecker product and vectorization operator,this paper develops the Bi...The bi-conjugate gradients(Bi-CG)and bi-conjugate residual(Bi-CR)methods are powerful tools for solving nonsymmetric linear systems Ax=b.By using Kronecker product and vectorization operator,this paper develops the Bi-CG and Bi-CR methods for the solution of the generalized Sylvester-transpose matrix equationp i=1(Ai X Bi+Ci XTDi)=E(including Lyapunov,Sylvester and Sylvester-transpose matrix equations as special cases).Numerical results validate that the proposed algorithms are much more efcient than some existing algorithms.展开更多
We show how to combine in a natural way(i.e.,without any test nor switch)the conservative and non-conservative formulations of an hyperbolic system that has a conservative form.This is inspired from two different clas...We show how to combine in a natural way(i.e.,without any test nor switch)the conservative and non-conservative formulations of an hyperbolic system that has a conservative form.This is inspired from two different classes of schemes:the residual distribution one(Abgrall in Commun Appl Math Comput 2(3):341–368,2020),and the active flux formulations(Eyman and Roe in 49th AIAA Aerospace Science Meeting,2011;Eyman in active flux.PhD thesis,University of Michigan,2013;Helzel et al.in J Sci Comput 80(3):35–61,2019;Barsukow in J Sci Comput 86(1):paper No.3,34,2021;Roe in J Sci Comput 73:1094–1114,2017).The solution is globally continuous,and as in the active flux method,described by a combination of point values and average values.Unlike the“classical”active flux methods,the meaning of the point-wise and cell average degrees of freedom is different,and hence follow different forms of PDEs;it is a conservative version of the cell average,and a possibly non-conservative one for the points.This new class of scheme is proved to satisfy a Lax-Wendroff-like theorem.We also develop a method to perform nonlinear stability.We illustrate the behaviour on several benchmarks,some quite challenging.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
Computer programs have definitely become indispensable for designing power transformer. Among several applications, computer programs are mostly used for electric field calculation and thus electrical insulation conce...Computer programs have definitely become indispensable for designing power transformer. Among several applications, computer programs are mostly used for electric field calculation and thus electrical insulation concerns. In consequence, studies based on analytical approach to basic studies of correlated problems have become even more important because they form the very basis of knowledge that is necessary to every transformer designer in view of taking all the advantages of computational analyses. On the other hand, one of the most important basic studies consists in the evaluation of voltage surge distribution along transformer windings for which the method of separation of variables has been extensively used thanks to some simplifying assumptions. With this aim, authors have developed and previously published works that show the applicability of an alternative and useful analytical method that is the method of the residues, which requires no simplification to be assumed. In this work, another important step is taken towards proofing the total applicability of this promising method that is through a practical problem. A comparison to the numerical method TLM （transmission line method） is also performed and concordance with TLM and experimental data confirms the proposal of the method of residues can be also applicable to several others problems of electromagnetism.展开更多
Based on the orthotropic elastic theory of rock masses, the X-ray method was used to measure the distribution of macro-residual strain energy density along a depth profile,using core samples taken from 47 large-apertu...Based on the orthotropic elastic theory of rock masses, the X-ray method was used to measure the distribution of macro-residual strain energy density along a depth profile,using core samples taken from 47 large-aperture deep boreholes in four regions of Southwest China： the Longmenshan, Anninghe, Honghe, and Xianshuihe fault zones.Then, the vertical gradients of the macro-residual strain energy density and the macroresidual strain energy contained in high-energy cuboid block segments along each fault zone were determined. The results demonstrate that the macro-residual strain energy stored at shallow levels in the rock mass in these fault zones may be partly responsible for generating many large earthquakes and may explain why the large earthquakes in this region are typically shallow.展开更多
Analysis and design of linear periodic control systems are closely related to the periodic matrix equations.The biconjugate residual method(BCR for short)have been introduced by Vespucci and Broyden for efficiently so...Analysis and design of linear periodic control systems are closely related to the periodic matrix equations.The biconjugate residual method(BCR for short)have been introduced by Vespucci and Broyden for efficiently solving linear systems Aα=b.The objective of this paper is to provide one new iterative algorithm based on BCR method to find the symmetric periodic solutions of linear periodic matrix equations.This kind of periodic matrix equations has not been dealt with yet.This iterative method is guaranteed to converge in a finite number of steps in the absence of round-off errors.Some numerical results are performed to illustrate the efficiency and feasibility of new method.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
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In this paper, the minimal residual （MRES） method for solving nonsymmetric equation systems was improved, the recurrence relation was deduced between the approximate solutions of the linear equation system Ax = b, and a more effective method was presented, which can reduce the operational count and the storage.
文摘In the aerospace field, residual stress directly affects the strength, fatigue life and dimensional stability of thin-walled structural components, and is a key factor to ensure flight safety and reliability. At present, research on residual stress at home and abroad mainly focuses on the optimization of traditional detection technology, stress control of manufacturing process and service performance evaluation, among which research on residual stress detection methods mainly focuses on the improvement of the accuracy, sensitivity, reliability and other performance of existing detection methods, but it still faces many challenges such as extremely small detection range, low efficiency, large error and limited application range.
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.
基金This research is supported by the National Key Research and Development Program of China under Grant No.2018YFC1505401the Key Research and Development Projects of the Sichuan Science and Technology Department under Grant Nos.2019YFG0460,2020YFG0303,and 2021YJ0031+1 种基金the Technology Research and Development Program of China Railway Group Limited under Grant No.CZ01-Key Point-05the Fundamental Research Funds for the Central Universities under Grant No.2682021GF019.
文摘The downward continuation of potential fields is a process of calculating their values in a lower plane based on those of a certain plane.This technology is not only a data processing method for resource exploration but also plays an extremely important role in military applications.However,the downward continuation of potential fields is a typical linear inverse problem that is ill-posed.Generalized minimal residuals(GMRES)is an eff ective solution to ill-posed inverse problems,but it is unstable under the condition wherein the GMRES is directly applied in the calculation process.Moreover,the long-term behavior of its iterative computation is a disordered,divergent result.Therefore,to obtain stable solutions,GMRES is applied to solve the normal equations of the downward continuation of potential fields;it is also used to prequalify for occasional interruptions in the operation process by adding the damping coefficient,thus strengthening the stability conditions of the equations of residual minimization.Finally,the stable downward continuation of the potential fields method is proposed.As indicated by the theoretical data and the measured testing data,the method proposed in this paper has the advantages of high-precision and excellent stability.Furthermore,compared with the Tikhonov iteration method,the proposed method avoids the need to choose regularization parameters.
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.
基金supported by the National Natural Science Foundation of China (No. 50839003)the Natural Science Foundation of Yunnan Province (No. 2008GA027)
文摘Lagrangian-Eulerian formulations based on a generalized variational principle of fluid-solid coupling dynamics are established to describe flow-induced vibration of a structure under small deformation in an incompressible viscous fluid flow. The spatial discretization of the formulations is based on the multi-linear interpolating functions by using the finite element method for both the fluid and solid structures. The generalized trapezoidal rule is used to obtain apparently non-symmetric linear equations in an incremental form for the variables of the flow and vibration. The nonlinear convective term and time factors are contained in the non-symmetric coefficient matrix of the equations. The generalized minimum residual （GMRES） method is used to solve the incremental equations. A new stable algorithm of GMRES-Hughes-Newmark is developed to deal with the flow-induced vibration with dynamical fluid-structure interaction in complex geometries. Good agreement between the simulations and laboratory measurements of the pressure and blade vibration accelerations in a hydro turbine passage was obtained, indicating that the GiViRES-Hughes-Newmark algorithm presented in this paper is suitable for dealing with the flow-induced vibration of structures under small deformation.
基金the financial support from the National Basic Research Program of China(Project‘973’)(Nos.2010CB631005 and 2011CB606105)the National Natural Science Foundation of China(Nos.91216301,11172151,11232008,11072033 and 11372037)+1 种基金Tsinghua University Initiative Scientific Research Program,Program for New Century Excellent Talents in University(grant No.NCET-12-0036)Natural Science Foundation of Beijing,China(grant No.3122027)
文摘Residual stress measurement is of critical significance to in-service security and the reliability of engineering components, and has been an active area of scientific interest. This paper offers a review o[ several prominent mechanical release methods for residual stress measurement and recent developments, focusing on the hole-drilling method combined with advanced optical sensing. Some promising trends for mechanical release methods are also analyzed.
基金This project is supported by National Natural Science Foundation of China(No.50305036).
文摘The effect of vibratory stress relief （VSR） is usually evaluated with the indirect method of observing the change of amplitude frequency response characteristics of structures. A new kind of evaluating method of VSR based on the ultrasonic time-of-arrival method （UTM）, which can obtain the residual stress directly through measuring the propagation time of ultrasonic wave in the material, is presented. At first, the principle of the measuring method of residual stress based on UTM is analyzed. Then the measuring system of the method is described, which is in virtue of ultrasonic flaw detector and high-sampling-rate digital oscillograph. And a set of calibration system that contains a piece of standard specimen is also introduced. Experimental results prove the relation between the residual stress and the propagation time of ultrasonic in workpieces. Finally, the measuring and calibration systems are applied in evaluating the effect of VSR. The final test results show that the method is effective.
文摘The bi-conjugate gradients(Bi-CG)and bi-conjugate residual(Bi-CR)methods are powerful tools for solving nonsymmetric linear systems Ax=b.By using Kronecker product and vectorization operator,this paper develops the Bi-CG and Bi-CR methods for the solution of the generalized Sylvester-transpose matrix equationp i=1(Ai X Bi+Ci XTDi)=E(including Lyapunov,Sylvester and Sylvester-transpose matrix equations as special cases).Numerical results validate that the proposed algorithms are much more efcient than some existing algorithms.
基金the author was partially funded by the SNF project 200020_175784.
文摘We show how to combine in a natural way(i.e.,without any test nor switch)the conservative and non-conservative formulations of an hyperbolic system that has a conservative form.This is inspired from two different classes of schemes:the residual distribution one(Abgrall in Commun Appl Math Comput 2(3):341–368,2020),and the active flux formulations(Eyman and Roe in 49th AIAA Aerospace Science Meeting,2011;Eyman in active flux.PhD thesis,University of Michigan,2013;Helzel et al.in J Sci Comput 80(3):35–61,2019;Barsukow in J Sci Comput 86(1):paper No.3,34,2021;Roe in J Sci Comput 73:1094–1114,2017).The solution is globally continuous,and as in the active flux method,described by a combination of point values and average values.Unlike the“classical”active flux methods,the meaning of the point-wise and cell average degrees of freedom is different,and hence follow different forms of PDEs;it is a conservative version of the cell average,and a possibly non-conservative one for the points.This new class of scheme is proved to satisfy a Lax-Wendroff-like theorem.We also develop a method to perform nonlinear stability.We illustrate the behaviour on several benchmarks,some quite challenging.
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.
文摘Computer programs have definitely become indispensable for designing power transformer. Among several applications, computer programs are mostly used for electric field calculation and thus electrical insulation concerns. In consequence, studies based on analytical approach to basic studies of correlated problems have become even more important because they form the very basis of knowledge that is necessary to every transformer designer in view of taking all the advantages of computational analyses. On the other hand, one of the most important basic studies consists in the evaluation of voltage surge distribution along transformer windings for which the method of separation of variables has been extensively used thanks to some simplifying assumptions. With this aim, authors have developed and previously published works that show the applicability of an alternative and useful analytical method that is the method of the residues, which requires no simplification to be assumed. In this work, another important step is taken towards proofing the total applicability of this promising method that is through a practical problem. A comparison to the numerical method TLM （transmission line method） is also performed and concordance with TLM and experimental data confirms the proposal of the method of residues can be also applicable to several others problems of electromagnetism.
基金supported by the Joint Seismology Science Foundation(85012,850708,863017,88138,91046)Old Professor Science Foundation(201041)
文摘Based on the orthotropic elastic theory of rock masses, the X-ray method was used to measure the distribution of macro-residual strain energy density along a depth profile,using core samples taken from 47 large-aperture deep boreholes in four regions of Southwest China： the Longmenshan, Anninghe, Honghe, and Xianshuihe fault zones.Then, the vertical gradients of the macro-residual strain energy density and the macroresidual strain energy contained in high-energy cuboid block segments along each fault zone were determined. The results demonstrate that the macro-residual strain energy stored at shallow levels in the rock mass in these fault zones may be partly responsible for generating many large earthquakes and may explain why the large earthquakes in this region are typically shallow.
基金Supported by NSFC (No.12371378)NSF of Fujian Province (Nos.2024J01980,2023J01955)。
文摘Analysis and design of linear periodic control systems are closely related to the periodic matrix equations.The biconjugate residual method(BCR for short)have been introduced by Vespucci and Broyden for efficiently solving linear systems Aα=b.The objective of this paper is to provide one new iterative algorithm based on BCR method to find the symmetric periodic solutions of linear periodic matrix equations.This kind of periodic matrix equations has not been dealt with yet.This iterative method is guaranteed to converge in a finite number of steps in the absence of round-off errors.Some numerical results are performed to illustrate the efficiency and feasibility of new method.
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...
