Formulating a new efficient simple element for statics, buckling and free vibration analysis of Timoshenko's beam

The beams are really useful for the large number of engineering structures. In this article, a simple robust beam element will be formulated. Other researchers utilized several theories such as Euler-Bernoulli, Timoshenko and higher order shear for analyzing of the beams. The proposed formulation will be written based on satisfying the equilibrium equation. Using the equilibrium equation reduces number of unknowns in addition to improving the efficiency of new element. the suggested element has only two nod and tow degrees of freedom per node. The third and second order polynomials will be used for vertical displacement and rotation fields, respectively. After calculating the matrix of shape functions, the governing equations of statics, free vibration and buckling analysis could be written. Finally, using the suggested element, static analysis, free vibration and buckling were performed on the several problems. To prove the efficiency of the new element, the large number of benchmark tests will be utilized. These numerical tests have various support conditions and different aspect ratios. By the help of these tests, rapid convergence and high accuracy of proposed element will be shown. The new element has high efficiency in all of the static, free vibration and buckling analysis for both of thin and thick beams beside of its simplicity. Good element answers of other researchers are be available to have better comparison.