Influence Functions of a Point Force for Kirchhoff Plates with Rigid Inclusions

Abstract

AbstractA semi-analytic method is proposed for two problem settings for a Kirchhoff plate containing an absolutely rigid circular inclusion and undergoing a transverse point force. The settings differ by the location (within and out of inclusion) of the force application point. In both cases, the plate's stress-strain state is simulated with a boundary value problem for the biharmonic equation stated over a doubly connected region whose inner contour represents the edge of the inclusion. Boundary conditions imposed on the inner contour bring some parameters which are found via the equations of static equilibrium of the inclusion. A modification of the Kupradze'smethod of functional equationsis proposed for obtaining influence functions of a point force for such plates. Green's functions of the biharmonic equation for appropriately shaped simply connected regions are employed. Numerical differentiation is never required in the computing of stress components and the latter are subsequently found with accuracy level comparable with that attained for the deflection function.