An accurate technique for evaluating stress at boundary points in boundary element method

In plane elasticity, the displacements (u,v) and the stresses (sigma(n), sigma(t), sigma(nt)) at the boundary points are the most interested quantities in analysis. The displacements (u,v) and the stresses (sigma(n), sigma(nt)) at the boundary points are the values given before and or obtained after solving the boundary integral equation (BIE). It is more difficult to evaluate the stress sigma(t). In this paper, the following equation is suggested to evaluate the stress sigma(t) sigma(t) = 3 - kappa/kappa + 1 sigma(n) + 8 mu/kappa + 1Re(d{u + iv}/dz) where mu denotes the shear modulus of elasticity, kappa = 3 - 4v in plane strain condition, v is Poisson's ratio, z = x + iy is the complex variable, d{u + iv}/dz is a derivative in a specified direction. Particular advantage of the suggested equation is that all the quantities used in the right-hand side of equation can be obtained from the numerical solution of BIE. Numerical examples are given to demonstrate the efficiency of the suggested method. (C) 2000 Elsevier Science Ltd. All rights reserved.