A triangular finite element for plane elasticity with in-plane rotation

الملخص EN

Journal of the Islamic University of Gaza,(Natural Sciences Series) Vol.12, No.l, PP.

83-95, 2004 A TRIANGULAR FINITE ELEMENT FOR PLANE ELASTICITY WITH IN-PLANE ROTATION Attia I.

Mousa Faulty of Engineering, Islamic University of Gaza, Salah M.

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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.

KEYWORDS: strain based approach, triangular element, plane elasticity, in-plane rotation 1.

INTRODUCTION The development of displacement fields by the use of strain-based approach was first applied to curved elements.

It was revealed that to obtain satisfactory converged results, the finite elements based on independent polynomial displacement functions require the curved structures to be divided into a large number of elements, [1], [2].

This work has shown that there are two essential components to any displacement field.

The first of which relates to rigid body modes of displacements while the second component is due to the straining of the element and these are