Some New Results on the Bending of a Circular Plate Subject to a bansverse Point Force

Abstract

Two influence functions of a unit transverse point force are obtained for a thin circular Poisson Kirchhoff plate. One of these functions is constructed for a plate whose edge is elastically clamped in such a way that the edge's slope is zero, while the shear force on the edge is directly proportional to the deflection function. The other influence function is obtained for a plate that is elastically supported, with the deflection being zero and the radial bending moment being directly proportional to the slope on the plate's edge. The plates of a uniform thickness are built of an elastic isotropic homogeneous material. The extended version of the classical method of eigenfunction expansion is used. The singular components of the influence functions are explicitly split off, while their regular components are obtained in the form containing uniformly convergent trigonometric series.