LOCAL BOUNDARY INTEGRAL-EQUATION ANALYSIS OF ELASTOSTATICS PROBLEMS USING SERIES EXPANSIONS

Local boundary integral equations of two-dimensional elastostatics are derived by differentiating the conventional zero-order integral equations of the direct formulation at an internal point. The unknowns of these higher-order integral equations, together with those of the zero-order ones, are approximated by series (Taylor or Fourier), which use either harmonic or biharmonic functions. This makes it possible to determine the variables of interest in a small preselected region of the solution domain, without the need to solve the problem over the rest of the boundary. In the numerical implementation of the integral equations, three possible approaches, namely, Airy's stress function (biharmonic), Neuber-Papkovich (harmonic), and direct expansion of integral equations (biharmonic) are considered Numerical results from three test cases, including a stress concentration problem, are used to illustrate the applicability of the method to elastic stress analysis problems.