A higher-order finite element for static, free vibration, and buckling analyses of functionally graded beams

This study proposes a high-order 16-degree-of-freedom finite element for the static, free vibration, and buckling analysis of functionally graded (FG) beams, considering the shear deformation effects. In addition to the finite element solution, the accuracy of the proposed finite element is validated using the Ansys Mechanical Apdl program. The first section presents information on FG materials and a comprehensive literature review. The second section provides explicit formulations for FG beams' static, free vibration, and buckling analyses using the high-order finite element. The third section gives the numerical results of the natural frequencies, critical buckling loads, displacements, and stresses of the FG beams obtained with the proposed finite element and Ansys program. In addition, these methods were compared among themselves and with the literature. The fourth section discusses the obtained results within the scope of the study and proposes future research directions.