Engineering Transactions, 62, 1, pp. 33-59, 2014
10.24423/engtrans.42.2014

### An Alternative Approach of Initial Stability Analysis of Kirchhoff Plates by the Boundary Element Method

Michał GUMINIAK
Poznan University of Technology Piotrowo 5, 60-965 Poznań
Poland

An initial stability of Kirchhoff plates is analysed in the paper. Proposed approach avoids Kirchhoff forces at the plate corner and equivalent shear forces at a plate boundary. Two unknown variables are considered at the boundary element node. The governing integral equations are derived using Betti theorem. The integral equations have the form of boundary and domain integral equations. The constant type of boundary element are used. The singular and non-singular formulation of the boundary-domain integral equations with one and two collocation points associated with a single boundary element located at a plate edge are presented. To establish a plate curvature by double differentiation of basic boundary-domain integral equation, a plate domain is divided into rectangular sub-domains associated with suitable collocation points. A plate curvature can also be establish by considering three collocation points located in close proximity to each other along line parallel to one of the two axes of global coordinate system and establishment of appropriate differential operators.
Keywords: the boundary element method, Kirchhoff plates, initial stability, fundamental solution.
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DOI: 10.24423/engtrans.42.2014