A new simple finite element method for free vibration and buckling analysis of symmetrically laminated beams

In this paper, a new 2-node element is proposed for free vibration and buckling analysis of symmetrically laminated beams. The element’s formulation is based on first order shear deformation theory (FSDT). For this aim, the deflection and rotation field of the element is selected from third and second order functions, respectively. Moreover, the shear strain is assumed to be constant along with the element. By establishing the total strain energy in the element and stationary with respect to shear strain, the explicit form of the shape functions of deflection and rotation fields of the proposed element, are obtained. It should be mentioned, by decreasing the element’s thickness, these shape functions are approach to the Euler-Bernoulli shape’s functions and the shear locking problem does not occurred in the element. By utilizing the obtained shape functions, the explicit form of the stiffness matrix are calculated for the element. On the other hand, by using the governing equation of the free vibration and buckling of the beam, the explicit form of the translation and rotary mass matrices, and geometric stiffness matrix of the element are obtained. Finally, several numerical tests fulfill to assess the robustness of the developed element. For this purpose, free vibration and buckling analysis of symmetrically laminated beams with different boundary conditions and aspect ratios, are performed. The results of the numerical tests demonstrate high accuracy and efficiency of the proposed element for free vibration and buckling analysis of laminated beams.