Evaluating the Effect of Asymmetric Cross-section in Free Vibration and Bending Analysis Results of FG Sandwich Beam by Proposing Simple Efficient Element

Abstract

In this paper, the asymmetric effect of the cross-section on the free vibration and bending analysis of FG sandwich beams are evaluated. For this purpose, a simple, efficient element is formulated. The new element is created based on the Timoshenko beam theory. The third- and second-order polynomials will be used for vertical displacement and rotation fields, respectively. The proposed formulation will be written based on satisfying the equilibrium equation. Satisfying the equilibrium equation of the Timoshenko beam, in addition to increasing element efficiency, will reduce the number of nodal unknowns. Several benchmark tests with different boundary conditions are used for thin and thick beams to prove the efficiency of the proposed element. The responses of the good elements of other researchers have been used for comparison. Numerical tests prove the rapid convergence rate and high accuracy of the proposed element in free vibration and bending analysis of the beams with various cross-section types and different boundary conditions. The pinned-sliding support conditions for the beam are used to evaluate the asymmetric effect of the cross-section. The use of asymmetric cross-sections creates additional axial displacements and intensifies the deflection of the beam under the lateral load. By increasing the asymmetry, the additional axial displacement and vertical displacement increase. These additional deflections for thin beams are more than thick ones. Also, asymmetry results in increasing the natural frequencies of beams. In the free vibration analysis, the effect of asymmetry on thick beams is more than thin ones.