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- W1572881036 abstract "An initial stability of Kirchhoff plates is presented in the paper. Using proposed approach, there is no need to introduce Kirchhoff forces at the plate corner and equivalent shear forces at a plate boundary. Two unknown and independent variables are considered at the boundary element node. The Bettie theorem is used to derive the boundary integral equation. The collocation version of boundary element method with ”constant” type of elements is presented. The source points are located slightly outside a plate boundary, hence the quasi-diagonal integrals of fundamental functions are non-singular. To describe a plate curvature, the set of internal collocation points is introduced. Introduction Initial stability of thin plates considering internal continuous supports is solved using the Boundary Element Method (BEM). Modelling of a plate bending problem with internal plate supports requires modification of governing boundary integral equation. The most popular approach was proposed by Bezine [1] in which, the forces at the internal supports are treated as unknown variables. This techniques is also used by de Paiva and Venturini [2, 3], Hartmann and Zotemantel [4], Abdel-Akher and Hartley [5] and Litewka [6]. The second approach was proposed by Rashed [7] in application of a coupled BEM-flexibility force method in bending analysis of plates with internal supports. Shi [8] applied Bezine technique to solve free vibration and buckling problem of orthotropic thin plates. This paper presents a modified formulation for bending analysis of plates supported on a boundary with additional internal linear supports. This formulation can be applied in static, dynamic and buckling problems [9-11]. The physical boundary conditions are applied which leads to reduce of number of independent variables by one. In this formulation there is no need to introduce the equivalent shear forces at the boundary and concentrated forces at the plate corners. Similar to Hartley [12], the source points of boundary elements were located slightly outside a plate boundary, hence all of quasi-diagonal integrals are non-singular. Internal support was introduced using Bezine techniques. Please cite this article as: Michal Guminiak, Initial stability analysis of plates considering continuous internal supports by the BEM, Scientific Research of the Institute of Mathematics and Computer Science, 2009, Volume 8, Issue 1, pages 47-62. The website: http://www.amcm.pcz.pl/ M. Guminiak 48 1. Integral formulation of thin plate bending in modified approach On the plate boundary there are considered amplitudes of variables: the shear force , n T bending moment , n M torsional moment ns M and deflection , w angle of rotation in normal direction n φ and angle of rotation in tangent direction s φ . Only two of them are independent. The boundary integral equation are derived using Bettie theorem. Two plates are considered: infinite plate, subjected unit concentrated loading and the real one (Fig. 1)." @default.
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- W1572881036 date "2009-01-01" @default.
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- W1572881036 title "Initial stability analysis of plates considering continuous internal supports by the BEM" @default.
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