Buckling Analysis of Thin Plates on Elastic Foundation by the Boundary/Domain Elements Method
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Abstract
The aim of this paper is to develop the boundary/domain elements method to analyze the buckling of thin plates on elastic foundation. The boundary/domain elements method is established by using the Analog Equation Method (AEM). According to the AEM, the original governing differential equations are replaced by three uncoupled equations with fictitious sources under the same boundary conditions: two Poisson’s equations for the membrane displacements and one plate equation for the transverse displacement. The solution of the actual problem is attained from the known integral representations of the solution of the potential and plate problems. Therefore, the kernels of the boundary and domain integral equations are conveniently established and readily calculated in such a way that the buckling of thin plates on elastic foundation can be easily analyzed. Subsequently, the reliability and accuracy of the boundary/domain elements method are evaluated by comparing the obtained results with the available exact solutions. The influences of the stiffness of elastic foundation, plate thickness, in-plane supports and Poisson’s ratio on the critical load buckling are thoroughly studied. Finally, the application of the boundary/domain elements method is demonstrated by analyzing the plates with complex shapes.
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