DEDUCING A SHEAR FLEXIBLE BEAM ELEMENT USING THE CO-ROTATIONAL FORMULATION AND THE PRINCIPLE OF COMPLEMENTARY VIRTUAL WORK

Abstract

In this work is described a shear flexible beam element model without shear locking and integrating Euler-Bernoulli's and Timoshenko's beam theories. The unified stiffness matrix of this beam is obtained by using the co-rotational formulation that is based on the separation of displacement fields into rigid body modes and deformation modes. The principle of complementary virtual work is also used for finding the unified stiffness matrix. The stiffness matrix is then implemented in a finite element software for linear analysis of plane frames. Some examples are presented and numerical results demonstrate that a shear flexible beam element do not show shear locking effects. Keywords: Co-rotational approach, Complementary virtual work, Shear flexible beam element.