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|Title||New Strain-Based Triangular and Rectangular Finite Elements for Plane Elasticity Problems|
In this thesis, the Finite Element Method of structural analysis is used to investigate and compare the performance of several strain-based elements. Two new strain-based triangular and rectangular finite elements in Cartesian coordinates system, for two dimensional elasticity problems are developed. Each of these elements has three degrees of freedom per node. The “Strain Based Approach” is used to develop and formulate these two dimensional finite elements. In this approach, finite elements are formulated based on assumed polynomial strains rather than displacements. Two main computer programs are developed to analyze the new finite elements. To test the performance of these elements, they are used to solve two common plane elasticity problems. The problems considered included are: the problem of a plane deep cantilever beam fixed at one end and loaded by a point load at the free end; and the problem of a simply supported beam loaded at the mid-span by a point load. The finite element solutions obtained for these problems are compared with the analytical values given by the elasticity solutions. Results obtained using the new triangular and rectangular elements are also compared to those of the well-known constant strain triangular element (CST) and the bilinear rectangular element (BRE) respectively. In all cases, convergence curves for deflection at specific points within each problem are plotted to show that acceptable levels of accuracy. Furthermore, convergence curves for bending stress at points on the upper surface and shear stress at points on the neutral axis are plotted; again convergence is ensured.
|Publisher||the islamic university|
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