Engineering Transactions, 64, 1, pp. 3–32, 2016
10.24423/engtrans.89.2016

### Static and free vibration analysis of thin plates of the curved edges by the Boundary Element Method considering an alternative formulation of boundary conditions

Michał Jan GUMINIAK
Poznan University of Technology, Institute of Structural Engineering
Poland

A static and dynamic analysis of Kirchhoff plates is presented in this paper. The proposed approach avoids Kirchhoff forces at the plate corners 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's theorem. The rectilinear and curved boundary element of the constant type are used. The non-singular formulation of the boundary (static analysis) and boundary-domain (free vibration analysis) integral equations with one and two collocation points associated with a single constant boundary element located at a plate edge are presented. Additionally, the classic three-node isoparametric curved boundary elements are introduced in static analysis according to the non-singular approach. Static fundamental solution and Bèzine technique are applied to the free vibration analysis. To establish the plate inertial forces, a plate domain is divided into triangular or annular sub-domains associated with one suitable collocation point.
Keywords: Boundary Element Method; Kirchhoff plates; fundamental solution
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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

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DOI: 10.24423/engtrans.89.2016