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UBC Theses and Dissertations

Plane stress analysis with isosceles trapizoidal bar cells Charania, Hajimohammed Gulamhussin


A bar cell in the form of an isosceles trapezoid suitable for solution of two dimensional problems is introduced involving two new concepts, one that of overlapping bars and the other of a variable angle parameter. Based on the Identity of corner displacements of the cell and a similarly shaped piece of plate in conditions of uniform stress, expressions for the bar areas are derived in terms of Poisson's ratio, the geometry of the cell and a variable angle parameter. The stiffness matrix of the cell is derived further by combining different displacement modes. Two methods of calculating stresses, one by the nodal displacements and the other by the nodal force concentrations, are described. Two examples involving a rectangular plate and a partial sector of a circular plate illustrate the application of the finite element method using trapezoidal bar as well as no-bar cells and their results are compared with the exact elasticity solution.

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