The Calculation Methods for Solving a Kind of Boundary Value Problems in Elasticity

This paper will study the numerical solutions for equations with a kind of boundary value conditions. The equations will be converted into nonlinear boundary integral equations by the potential theory, in which logarithmic singularity and Cauchy singularity are calculated simultaneously. Mechanical quadrature methods(MQMs) are presented to solve the nonlinear equations that the accuracy of the solutions are three order. According to the asymptotical compact convergence theory, the errors with an odd powers asymptotic expansion is obtained. Some results are shown regarding these approximations for problems by the numerical example.