Elastic Analysis of Zoned Orthotropic Continua

A method is presented for determining the stresses and displacements, under plane strain or plane stress conditions, in a linear elastic multizoned continuum having an irregular boundary geometry. Each zone is homogeneous and consists in general of a different orthotropic material, with one plane of elastic symmetry parallel to the problem plane, and the other two planes orientated arbitrarily. The singular solution used is that for a point load acting within a homogeneous orthotropic infinite lamina. The derivation of this new solution is given. Since the principle of superposition applies, the numerical integration of multiples of such singular solutions around zone boundaries produces a result satisfying both the governing equations and the zone boundary conditions on discrete boundary elements. The main advantage of the method is that, since only the boundary is discretized, the system of equations is small compared with other numerical methods.