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Plate bending analysis with isosceles trapezoidal bar cells Ha, Huy Kinh

Abstract

A bar cell in the shape of an isosceles trapezoid is devised for use in flexure problems of circular plates. The cell members are endowed with elastic properties such that it deforms in the same manner as a piece of plate in condition of arbitrary uniform bending about any axis in the plane of a plate. The stiffness matrix of the cell is derived explicitly. Two methods of computation of stresses are described, one by the nodal forces and the other by the nodal displacements. The validity of the cell is tested on two examples whose exact solutions are known. One involves a semicircular clamped plate under uniform load, and the other a simply-supported circular plate under an eccentric concentrated load. The results compared favourably with the theory of elasticity solutions and the no-bar finite element solutions. Good trend of convergence of solutions is indicated on reduction of the element size.

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