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Transverse Bending of Multilayer Equilateral Triangular Plates


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DOI: https://doi.org/10.15866/ireme.v17i12.23848

Abstract


This article explores the transverse bending of multilayer plates in the shape of an equilateral triangle using the finite difference method and triangular grids. The paper describes the adaptation of a numerical method for calculating the stiffness characteristics of multilayer plates of arbitrary shapes, provides formulas for determining the stiffness properties of the multilayer stack, and derives typical finite difference equations. The original three differential bending equations of multilayer plates of the 4th and 2nd order are replaced by finite-difference analogues taking into account the bending, torsional and shear stiffness of the multilayer package of plate thicknesses. The resulting three systems of linear algebraic equations are solved with the number of divisions of the sides of the plate into eight parts. As a result, the systems have the 21st order. The results of deflections in the nodes of a triangular grid are presented. The study is conducted on a three-layer stack, and the bending of an equilateral triangular plate is analysed using an applied program. Boundary conditions are considered at three edges of the plate, assuming either hinged or rigid supports. The technical issue of boundary conditions for the edges of triangular plates has been resolved by the idea of paired exclusion of deflections at contour nodes, which arises when using a mesh of different-sided triangles; no such problem arises when using a known rectangular mesh.
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Keywords


Multilayer Plate; Finite Difference Method; Bending of Triangular Plates

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