Analysis of the static and dynamic thermomechanical behavior of FGM and sandwich beams

Abstract

This work presents a new high-order shear deformation theory using the enhanced Timoshenko beam theory (ETBT) to analyze FGM beams' behaviors. The developed model exhibits a quadratic distribution of shear stress along the thickness and meets the zero-shear stress condition at both the top and bottom surfaces of the beam without using the shear correction factor. Based on the proposed model, a two-nodded finite element is formulated to analyze FG and sandwich beams' static, buckling, and free vibration behaviors. This element has only three unknowns, unlike other higher-order models, which use a great number of variables. The stiffness and geometrical matrices have been derived using the principle of total potential energy. The concept of a physical neutral axis is introduced to avoid the stretching-bending phenomenon. The accuracy and the performance of the proposed model have been confirmed through comparisons with the results of the existing literature. In addition, the effect of the power law index, length-to thickness ratio, and boundary conditions on displacement, stresses, critical temperature and buckling load, and natural frequencies is investigated. The obtained results indicate that the formulated finite element is reliable for predicting the static, buckling, and free vibration behaviors of FGM beams.