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Contribution to the design of polygonally shaped thin plates

The differential equation of thin plates can be solved using the finite element method and the finite difference method. By finite difference method the equation of this plates and the specified boundary conditions are reduced to the system of linear algebraic equations. If the plate area is discretized by the rectangular network the linear equation system can be obtained by varation procedure.This procedure is based on the princiole of the minimum total potential energy of the plate. Based on this procedure, a computer program was written in Fortran language and it constitutes the basis for calculations made in this paper. The theoretical and experimental analysis of displacement in thin plate of polygonal shape, with various boundary conditions, was performed on models made of transparent plexiglas plates. Based on results obtained by thereoretical and experimental research it can be concluded that the presented finite difference method gives good results in the design of thin polygonal plates.

poligonaly shaped thin plate; finite element method; finite difference method; boundary condition; variation procedure; minimum thotal potential energy; differential equation; system of linear algebraic equations

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