We propose the variational description of generating function approach of first kind for Hamil-tonian ODEs, and extend the approach to the semi-linear wave equations. In this way, we can construct any finite order acc...We propose the variational description of generating function approach of first kind for Hamil-tonian ODEs, and extend the approach to the semi-linear wave equations. In this way, we can construct any finite order accuracy scheme, and show that the resulting numerical scheme is multisymplectic. At last, we present some numerical experiments by using derived new scheme.展开更多
Semi-inverse method, which is an integration and an extension of Hu's try-and-error method, Chien's veighted residual method and Liu's systematic method, is proposed to establish generalized variational pr...Semi-inverse method, which is an integration and an extension of Hu's try-and-error method, Chien's veighted residual method and Liu's systematic method, is proposed to establish generalized variational principles with multi-variables without arty variational crisis phenomenon. The method is to construct an energy trial-functional with an unknown function F, which can be readily identified by making the trial-functional stationary and using known constraint equations. As a result generalized variational principles with two kinds of independent variables (such as well-known Hellinger-Reissner variational principle and Hu-Washizu principle) and generalized variational principles with three kinds of independent variables (such as Chien's generalized variational principles) in elasticity have been deduced without using Lagrange multiplier method. By semi-inverse method, the author has also proved that Hu-Washizu principle is actually a variational principle with only two kinds of independent variables, stress-strain relations are still its constraints.展开更多
The stress field in granular soils heap(including piled coal) will have a non-negligible impact on the settlement of the underlying soils. It is usually obtained by measurements and numerical simulations.Because the f...The stress field in granular soils heap(including piled coal) will have a non-negligible impact on the settlement of the underlying soils. It is usually obtained by measurements and numerical simulations.Because the former method is not reliable as pressure cells instrumented on the interface between piled coal and the underlying soft soil do not work well, results from numerical methods alone are necessary to be doubly checked with one more method before they are extended to more complex cases. The generalized stress field in granular soils heap is analyzed with Rayleighe Ritz method. The problem is divided into two cases: case A without horizontal constraint on the base and case B with horizontal constraint on the base. In both cases, the displacement functions u(x, y) and v(x, y) are assumed to be cubic polynomials with 12 undetermined parameters, which will satisfy the Cauchy’s partial differential equations, generalized Hooke’s law and boundary equations. A function is built with the Rayleighe Ritz method according to the principle of minimum potential energy, and the problem is converted into solving two undetermined parameters through the variation of the function, while the other parameters are expressed in terms of these two parameters. By comparison of results from the Rayleighe Ritz method and numerical simulations, it is demonstrated that the Rayleighe Ritz method is feasible to study the generalized stress field in granular soils heap. Solutions from numerical methods are verified before being extended to more complicated cases.展开更多
In the present paper, a generalization of the method of partial summation of the expansion of the thermodynamical potential is proposed. This generalization allows one to obtain the corresponding equations for higher-...In the present paper, a generalization of the method of partial summation of the expansion of the thermodynamical potential is proposed. This generalization allows one to obtain the corresponding equations for higher-order correlation matrices, as well as to formulate the variational method for their solution. We show that correlation matrices of equilibrium quantum system satisfy a variational principle for thermodynamic potential which is functional of these matrices that provides a thermodynamic consistency of the theory. This result is similar to a variational principle for correlation functions of classical systems.展开更多
各向异性非均匀介质中静态平面温度场问题与反平面应变、应力场问题近年来曾被许多作者研究过。在文献[1]中,David.L. Clements and C.Rogers在特殊情况下应用边界元方法得到了通解所满足的边界积分方程。本文将这二个问题化到广义解析...各向异性非均匀介质中静态平面温度场问题与反平面应变、应力场问题近年来曾被许多作者研究过。在文献[1]中,David.L. Clements and C.Rogers在特殊情况下应用边界元方法得到了通解所满足的边界积分方程。本文将这二个问题化到广义解析函数的边值问题,并且在文献[2]的基础上,提出了各向异性非均匀弹性介质中静态平面温度场问题与反平面应变、应力场问题的应力边值问题和位移边值问题的一种计算方法。采用这种方法,容易得到这二个边值问题的数值结果。最后,本文对具体例子进行讨论并且给出了该问题的数值结果。展开更多
基金the Special Funds for Major State Basic Reserch Project (G.1999,032800).
文摘We propose the variational description of generating function approach of first kind for Hamil-tonian ODEs, and extend the approach to the semi-linear wave equations. In this way, we can construct any finite order accuracy scheme, and show that the resulting numerical scheme is multisymplectic. At last, we present some numerical experiments by using derived new scheme.
文摘Semi-inverse method, which is an integration and an extension of Hu's try-and-error method, Chien's veighted residual method and Liu's systematic method, is proposed to establish generalized variational principles with multi-variables without arty variational crisis phenomenon. The method is to construct an energy trial-functional with an unknown function F, which can be readily identified by making the trial-functional stationary and using known constraint equations. As a result generalized variational principles with two kinds of independent variables (such as well-known Hellinger-Reissner variational principle and Hu-Washizu principle) and generalized variational principles with three kinds of independent variables (such as Chien's generalized variational principles) in elasticity have been deduced without using Lagrange multiplier method. By semi-inverse method, the author has also proved that Hu-Washizu principle is actually a variational principle with only two kinds of independent variables, stress-strain relations are still its constraints.
文摘The stress field in granular soils heap(including piled coal) will have a non-negligible impact on the settlement of the underlying soils. It is usually obtained by measurements and numerical simulations.Because the former method is not reliable as pressure cells instrumented on the interface between piled coal and the underlying soft soil do not work well, results from numerical methods alone are necessary to be doubly checked with one more method before they are extended to more complex cases. The generalized stress field in granular soils heap is analyzed with Rayleighe Ritz method. The problem is divided into two cases: case A without horizontal constraint on the base and case B with horizontal constraint on the base. In both cases, the displacement functions u(x, y) and v(x, y) are assumed to be cubic polynomials with 12 undetermined parameters, which will satisfy the Cauchy’s partial differential equations, generalized Hooke’s law and boundary equations. A function is built with the Rayleighe Ritz method according to the principle of minimum potential energy, and the problem is converted into solving two undetermined parameters through the variation of the function, while the other parameters are expressed in terms of these two parameters. By comparison of results from the Rayleighe Ritz method and numerical simulations, it is demonstrated that the Rayleighe Ritz method is feasible to study the generalized stress field in granular soils heap. Solutions from numerical methods are verified before being extended to more complicated cases.
文摘In the present paper, a generalization of the method of partial summation of the expansion of the thermodynamical potential is proposed. This generalization allows one to obtain the corresponding equations for higher-order correlation matrices, as well as to formulate the variational method for their solution. We show that correlation matrices of equilibrium quantum system satisfy a variational principle for thermodynamic potential which is functional of these matrices that provides a thermodynamic consistency of the theory. This result is similar to a variational principle for correlation functions of classical systems.
文摘各向异性非均匀介质中静态平面温度场问题与反平面应变、应力场问题近年来曾被许多作者研究过。在文献[1]中,David.L. Clements and C.Rogers在特殊情况下应用边界元方法得到了通解所满足的边界积分方程。本文将这二个问题化到广义解析函数的边值问题,并且在文献[2]的基础上,提出了各向异性非均匀弹性介质中静态平面温度场问题与反平面应变、应力场问题的应力边值问题和位移边值问题的一种计算方法。采用这种方法,容易得到这二个边值问题的数值结果。最后,本文对具体例子进行讨论并且给出了该问题的数值结果。
