An improved two-node finite element for stability and natural frequencies of axial-loaded Timoshenko beams

The linear flexural stiffness, incremental stiffness, mass, and consistent force matrices for a simple two-node Timoshenko beam element are developed based upon Hamilton's principle, where interdependent cubic and quadratic polynomials are used for the transverse and rotational displacements, respectively. The resulting linear flexural stiffness matrix is in agreement with the exact 2-node Timoshenko beam stiffness matrix. Numerical results are presented to show that the current element can accurately predict the buckling load and natural frequencies of axially-loaded isotropic and composite beams for a wide variety of beam-lengths and boundary conditions. The current element consistently outperforms the existing finite element approaches in studies involving the buckling or vibration behavior of axially-loaded short beams.