THE GENERALIZED GALERKIN’S EQUATION OF THE FINITE ELEMENT,THE BOUNDARY VARIATIONAL EQUATIONS AND THE BOUNDARY INTEGRAL EQUATIONS

Based on[1 ],we have further applied the variational princi-ple of the variable boundary to investigate the discretizationanalysis of the solid system and derived the generalized Ga-lerkin’s equations of the finite element.the boundary varia-tional equations and the boundary integral equations.These e-quations indicate that the unknown functions of the solid sys-tem must satisfy the conditions in the element S_a or on the boun-dariesГ_a.These equations are applied to establishing the discreti-zation equations in order to obtain the numerical solution ofthe unknown functions.At a time these equations can be usedas the basis for the simplified calculation in various corres-ponding cases.In this paper,the results of boundary integral equationsshow that the calculation of integration is not accurate alongthe surfaceГ_a of interior element S_a by J-integral suggestedby Rice[2].

The generalized Galerkin's equation of the finite element,the boundary variational equations and the boundary integral equations

Based on [1], we have further applied the variational principle of the variable boundary to investigate the discretization analysis of the solid system and derived the generalized Ga-lerkin’s equations of the finite element, the boundary variational equations and the boundary integral equations.These e-quations indicate that the unknown functions of the solid system must satisfy the conditions in the element S_a or on theboundaries Γ_a.These equations are applied to establishing the discretization equations in order to obtain the numerical solution of the unknown functions. At a time these equations can be used as the basis for the simplified calculation in various corresponding cases.In this paper, the results of boundary integral equations show that the calculation Γ_a of integration is not accurate along the surface of interior element S_a by J-integral suggested by Rice [2].