Turan, MuhittinHacioğlu, Mahmut İlter2026-02-282026-02-282023https://doi.org/10.17714/gumusfenbil.1185301https://search.trdizin.gov.tr/tr/yayin/detay/1187345https://hdl.handle.net/20.500.12403/5808In this study, free vibration and static analysis of functionally graded (FG) beams with the finite element method based on high-order shear deformation beam theory are investigated. A finite element with 5 nodes and 16 degrees of freedom is proposed for the finite element method. The material property of the FG beam changes depending on a specific power-law function along the beam thickness. Equilibrium equations are derived from the Lagrange's equation. Dimensionless natural frequencies, dimensionless displacements, and dimensionless normal and shear stresses of FG beam were obtained according to different power-law indexes (p), various boundary conditions, and various slenderness (L/h). The results obtained from the study were compared with the literature and it was seen that the proposed finite element gave very good results for FG beams. It is concluded that the proposed high-order shear deformation beam element can be used to solve such problems. With the power-law index value increase, the dimensionless natural frequencies decrease while the dimensionless maximum displacements increase. © 2023, Gumushane University. All rights reserved.trinfo:eu-repo/semantics/openAccessFinite element methodFree vibration analysisFunctionally graded beamHigher-order shear deformation beam theoryStatic analysisArticle13241443110.17714/gumusfenbil.11853012-s2.0-1050040181231187345