ATRIANGULAR FINITE ELEMENT FOR PLANE ELASTICITY WITH IN- PLANE ROTATION

Attia I. Mousa, Salah M. Tayeh

Abstract


In the present paper the strain-based approach is applied to develop a new triangular finite element for the general plane elasticity. This triangular finite element has three degrees of freedom (two general external degrees of freedom and the in-plane rotation) at each of the three corner nodes. This element is based on linear and quadratic variations of the three components of strain. This element is used to obtain solutions to two dimensional elasticity problems where the contribution of the shear stress on deformation can be significant. The performance of the element is investigated by applying it to two well-known plane elasticity problems; a cantilever beam loaded at the free end and a simply supported beam loaded by a point load at the mid-span. Convergence curves are plotted for vertical deflection at the points of application of load as well as for bending stress at points at the upper tension fibre and shearing stress at internal points in each problem. It is found that the solutions obtained using this element are satisfactory for results of deflection, bending stress and the shearing stress even when only a small number of elements is used in the finite element solution.

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