An Alternative Approach to Initial Stability Analysis of Kirchhoff Plates Resting on Internal Supports by the Boundary Element Method - GUMINIAK, Michał Jan (Engineering Transactions, 2015)
An initial stability of Kirchhoff plates supported on boundary and resting on internal supports is analysed in this paper. The internal supports are understood to be part of a plate surface or a line belonging to the plate. The proposed approach avoids Kirchhoff forces at the plate corner and equivalent shear forces at the plate boundary. Two unknown and independent variables are always considered at a boundary element node depending on the type of a plate edge such as the shear force and bending moment for a clamped edge, and the shear force and angle of rotation in normal direction for a simply-supported edge. For a free edge, the deflection and angle of rotation in normal direction are considered as two independent variables with additional angle of rotation in tangent direction which depends on boundary deflections. The two governing integral equations are derived using Betti’s theorem. These equations have the form of boundary-domain integral equations. The constant type of boundary element is used. The singular and non-singular formulations of the boundary-domain integral equations with one and two collocation points associated with a single boundary element located slightly outside of a plate edge are presented. To establish a plate curvature by double differentiation of the basic boundary-domain integral equation, the plate domain is divided into rectangular subdomains associated with suitable collocation points. According to the alternative approach, a plate curvature is also established by considering three collocation points located in close proximity to each other along a line parallel to one of the two axes of global coordinate system and establishment of appropriate difference operators.