Thermal post-buckling and vibration analysis of thermally buckled antisymmetrically laminated beams using a 20 DOF finite element

The purpose of this study is to use the finite element method to analyze thermal buckling, post-buckling, and vibrations of thermally buckled composite beams including shear deformation. The beam element used has ten degrees of freedom at each node: axial displacement, transverse displacement due to bending and shear, twisting angle, inplane shear rotation and their derivatives with respect to x. Hermitian polynomials and Lagrange's equation were used to derive the equations of motion. The equations of motion were divided into static and dynamic parts. For buckling analysis, the eigenvalue problem was solved for the critical temperature. The scaled first mode shape was used as the trial displacement vector for post-buckling deflection analysis, which employed a Newton-Raphson type iterative procedure. Once the final static deflection was achieved, the dynamic part of the equation of motion was used to solve the eigenvalue problem for the natural frequencies and mode shapes of the thermally buckled beams.