UNIFIED FINITE ELEMENT MODEL FOR THE ANALYSIS OF BEAMS ON ELASTIC FOUNDATION

This paper presents a unified beam finite element for the analysis of shear deformable beam on elastic foundation. The beam stiffness and foundation matrices are obtained by introducing an analytical bending-shear rotation interaction factor which enables the decoupling of the bending and shear curvatures. Cubic and quadratic polynomials are used as shape functions for bending and shear deformation respectively. The resulting element is free from shear locking, a major drawback of previous finite element models, The results obtained using this element are seen to be in very good agreement with classical beam theories for combined bending and shear deformation. It is concluded that the effect of shear deformation on deflection of beams on elastic foundation is significant for span-to-depth ratios of 5 or less, and should therefore be accounted for in the design of such beams.