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 equat ions of the direct formulation at an internal point. The unknowns of t hese 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 det ermine the variables of interest in a small preselected region of the solution domain, without the need to solve the problem over the rest o f the boundary. In the numerical implementation of the integral equati ons, three possible approaches, namely, Airy's stress function (biharm onic), Neuber-Papkovich (harmonic), and direct expansion of integral e quations (biharmonic) are considered Numerical results from three test cases, including a stress concentration problem, are used to illustra te the applicability of the method to elastic stress analysis problems .