EXTENDED SEPARATION OF VARIABLES FOR NAVIERS EQUATION OF EQUILIBRIUM

Separation of variable techniques can be applied to elliptic equations , such as Navier's equation of equilibrium for a homogeneous medium, i n plane regions provided that each boundary segment defines an eigenva lue problem. More specifically, the region can be triangulated into '' convex'' elements and separation of variable methods used to generate families of solutions for each element. The precise combination of sol utions can be found by matching the appropriate field quantities acros s the internal boundaries created by the triangulation. In this paper the application of separation of variable techniques to ''convex'' ele ments is presented. The necessity of interpolating corner states to en hance the convergence of the Fourier series involved in matching presc ribed boundary conditions is demonstrated. The necessity of including singular functions to remedy incompleteness in the set of eigenfunctio ns is also demonstrated.