In this paper, the exact two-node Timoshenko beam finite element is formulated using a new model for representing beam rotation in a shear deformable beam. An exact relationship between bending rotation and shear rotation was achieved using an analytical bending and shear rotation interdependent shape functions obtained from a consideration of the asymmetrical beam flexural mode, which is shown to embody bending and shearing kinematics. These functions enable the total beam cross sectional rotation to be expressed in terms of bending and shear rotation, and subsequently lead to the use of the usual cubic interpolation and linear interpolation to model the bending rotation and shear rotation based beam curvatures respectively. The formulation ensures the circumvention of the shear-locking phenomenon, permitting complete interaction between bending and shear deformation fields and thus allows for a straightforward derivation of the exact Timoshenko beam stiffness matrix and consistent nodal load vector as obtained in classical structural analysis.

No abstract

No abstract