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BEHAVIOR OF BOUNDARY ELEMENT SOLUTIONS IN THE NEIGHBORHOOD OF THE BOUNDARY IN TWO DIMENSIONAL ELASTOSTATIC PROBLEMS

Kazuhisa ABE

Abstract

The author consider the accuracy of boundary element solutions in the neighborhood of a boundary in two dimensional elastic problems. A solution of boundary element method requires integrations on the boundary. It is known that a solution which is evaluated by numerical integration reduces the accuracy in the neighborhood of the boundary. This is by the reason that the integrand shows singurality on the boundary near the internal observation point. A method is presented for the estimation of the error on Gauss quatrature. By this method it is made sure that errors with displacements and stresses are to be expressed in simple forms. And it is possible to prognosticate the range in which the solution be incorrect. Application is made to evaluate stresses on the surface.

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Key concepts: Singular boundary method, Boundary knot method, Boundary (topology), Boundary element method, Method of fundamental solutions, Mathematical analysis, Mathematics, Range (aeronautics)