Abstract
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 Galerkin's equations of the finite element, the boundary variational equations and the boundary integral equations. These equations indicate that the unknown functions of the solid system must satisfy the conditions in the element Sa or on the boundaries Гa.
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 of integration is not accurate along the surface Гa of interior element Sa by J-integral suggested by Rice [2].
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References
Niu Xiang-jun,The Solid Variational Principles of the Discrete Form — The Variational Principles of the Discrete Analysis by the Finite Element Method, Applied Mathematics and Mechanics, Vol. 2, No. 5, (1982), 505–520.
Rice, J.R.,A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Crack, Journal of Applied Mechanics, Vol. 35, No. 2, June (1968).
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Xiang-jun, N. The generalized Galerkin's equation of the finite element, the boundary variational equations and the boundary integral equations. Appl Math Mech 4, 261–268 (1983). https://doi.org/10.1007/BF01895450
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DOI: https://doi.org/10.1007/BF01895450