The Boundary Element Method for Plate Analysis

2.3 Direct BEM for the plate equation

2.3.1 Rayleigh-Green identity

Consider the two-dimensional multiply connected domain $\mathrm{\Omega }$ of the $\mathit{xy}$ plane occupied by the plate. The domain is bounded by the $\mathit{K}+1$ non-intersecting curves ${\mathrm{\Gamma }}_0,{\mathrm{\Gamma }}_1,\dots ,{\mathrm{\Gamma }}_{\mathit{K}}$, forming the boundary $\mathrm{\Gamma }={\displaystyle {\cup }_{\mathit{k}=0}^{\mathit{K}}{\mathrm{\Gamma }}_{\mathit{k}}}$ of the plate, which may be piecewise smooth, i.e., it may have a finite number of corners ...