On the Discretization of a Shape by the Boundary Element Method in 2-D Elastostatics

抄録

The error included in solutions obtained by the boundary element method is caused by discretizing the boundary of analyzed shapes into many elements. In the present paper, the error tendencies are discussed in order to obtain reasonable usage of the boundary element method in 2-D elastostatics. The main results are the following: (1) Solution error rates obtained by the BEM depend on the boundary condition. However, the absolute values of the displacement error rates under traction conditions are equal to those of the traction error rates under the given displacement condition with different signs at some conditions. (2) In-plane bending cannot be solved in practice by the constant or linear element discretization. Quadratic element discretization can give us a satisfactory solution for almost all shapes. (3) The solution errors depend on Poisson's ratio according to the kind of a problem when the solution does not converge in small number of elements.