The problem is solved by use of the boundary integral equation method and the high order finite element discretization on the assumption that the flow of water is inviscid, incompressible and irrotational, and the bub...The problem is solved by use of the boundary integral equation method and the high order finite element discretization on the assumption that the flow of water is inviscid, incompressible and irrotational, and the bubble gas obeys the isoentropic rule. The evolution of bubble is simulated by means of mixed Euler-Lagrangian method. The comparison of the numerical results with the 'exact solution' of a spheric bub ble and experimental data shows that the mathematical model is reasonable and the 3-D numerical method has high accuracy. Important behaviour of bubble, such as immigration and jetting, and dynamic load on an ellipsoid near explosion are derived.展开更多
The purpose of this paper is to study the solution of the celebrated Whittaker equations by using analytical mechanics methods, including the Lagrange-Noether method, Hamilton-Poisson method and potential integral met...The purpose of this paper is to study the solution of the celebrated Whittaker equations by using analytical mechanics methods, including the Lagrange-Noether method, Hamilton-Poisson method and potential integral method.展开更多
From the Boltzmann's constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given....From the Boltzmann's constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given. By using the variational integral method, the convolution-type functional was given and the corresponding generalized variational principles and potential energy principle of viscoelastic solids with voids were presented. It can be shown that the variational principles correspond to the differential equations and the initial and boundary conditions of viscoelastic body with voids. As an application, a generalized variational principle of viscoelastic Timoshenko beams with damage was obtained which corresponds to the differential equations of generalized motion and the initial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids.展开更多
This paper is intended to apply the potential integration method to the differential equations of the Birkhoffian system. The method is that, for a given Birkhoffian system, its differential equations are first rewrit...This paper is intended to apply the potential integration method to the differential equations of the Birkhoffian system. The method is that, for a given Birkhoffian system, its differential equations are first rewritten as 2n first-order differential equations. Secondly, the corresponding partial differential equations are obtained by potential integration method and the solution is expressed as a complete integral. Finally, the integral of the system is obtained.展开更多
The motion of free surfaces in incompressible, irrotational, inviscid flows isstudied by evolution equations for the position of the free surfaces and appropriatedirect boundary integral equation for the velocity pote...The motion of free surfaces in incompressible, irrotational, inviscid flows isstudied by evolution equations for the position of the free surfaces and appropriatedirect boundary integral equation for the velocity potential. In order to maintainthe stability of computation, some compatible relationship must be satisfied. Thenumerical result for the standing wave identified the stability of method.展开更多
文摘The problem is solved by use of the boundary integral equation method and the high order finite element discretization on the assumption that the flow of water is inviscid, incompressible and irrotational, and the bubble gas obeys the isoentropic rule. The evolution of bubble is simulated by means of mixed Euler-Lagrangian method. The comparison of the numerical results with the 'exact solution' of a spheric bub ble and experimental data shows that the mathematical model is reasonable and the 3-D numerical method has high accuracy. Important behaviour of bubble, such as immigration and jetting, and dynamic load on an ellipsoid near explosion are derived.
基金Project supported by the National Natural Science Foundation （Grant No 10572021） and the Doctoral Program Foundation of Institution of Higher Education of China （Grant No 20040007022）.
文摘The purpose of this paper is to study the solution of the celebrated Whittaker equations by using analytical mechanics methods, including the Lagrange-Noether method, Hamilton-Poisson method and potential integral method.
文摘From the Boltzmann's constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given. By using the variational integral method, the convolution-type functional was given and the corresponding generalized variational principles and potential energy principle of viscoelastic solids with voids were presented. It can be shown that the variational principles correspond to the differential equations and the initial and boundary conditions of viscoelastic body with voids. As an application, a generalized variational principle of viscoelastic Timoshenko beams with damage was obtained which corresponds to the differential equations of generalized motion and the initial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)
文摘This paper is intended to apply the potential integration method to the differential equations of the Birkhoffian system. The method is that, for a given Birkhoffian system, its differential equations are first rewritten as 2n first-order differential equations. Secondly, the corresponding partial differential equations are obtained by potential integration method and the solution is expressed as a complete integral. Finally, the integral of the system is obtained.
文摘The motion of free surfaces in incompressible, irrotational, inviscid flows isstudied by evolution equations for the position of the free surfaces and appropriatedirect boundary integral equation for the velocity potential. In order to maintainthe stability of computation, some compatible relationship must be satisfied. Thenumerical result for the standing wave identified the stability of method.
