A new high order three-node Timoshenko beam element for static analysis of beam and plane frame structures

In this paper a new high order element is proposed for analysis of beams with shear deformation effect. In each node of this element exist translation and rotation degrees of freedom. The element’s formulation is based on the first-order shear deformation theory (FSDT). For this aim, displacement field of the element is selected from fifth order. Moreover, the shear strain is varied as quadratic function throughout the element. It is worth emphasizing that the quadratic function can be used for axial displacement field. By employing of curvature and shear strain relations of Timoshenko beam theory, the exact and explicit shape functions of the displacement fields is obtained. By utilizing these shape functions, beam elements’ stiffness matrix is also calculated. Finally, several numerical tests are performed to assess the robustness of the suggested element. The results of the numerical testes are proven the absence of the shear locking and high accuracy and efficiency of the proposed element for analysis of beam and frame structures. It should be mentioned, due to utilizing fifth order function for displacement field, the proposed element calculate exact solution for displacements and internal forces throughout the element for triangular distributed loads.