Analytical and fe modeling of a bi-directional functionally graded timoshenko beam under thermomechanical loading

Functionally graded materials (FGMs) have variable volume fractions in different directions, making structural analysis challenging due to shear deformation. This study investigates the behaviour of a two-directional functionally graded material (TDFGM) Timoshenko beam by considering the thermal load. Varied material properties in both axial and transverse directions are analysed using a mathematical approach and a finite element model. The mathematical approach involves transforming the system of two ordinary differential equations to a single fourth-order differential equation to determine deflection and rotation. Additionally, a bilinear quadrilateral element is used to validate the mathematical solution. The results show that increasing grading parameters reduced transverse deflection when applying mechanical load. Under combined mechanical and thermal loading, higher temperatures on the beam's hot side lead to increased deflection. Also, it has been noticed that when TDFGM Timoshenko beams were heated for thermal loading, the beam deflected in the opposite direction of the applied mechanical load. The results agree with previous research and indicate alignment between mathematical and finite element solutions. The impact of end conditions on the deflection of Timoshenko beams made of TDFGM is discussed. The introduced methodology enhances TDFGM beam bending analysis, allowing control over behaviour through grading parameters and end conditions selection.