An Investigation of Stress and Deformation Behavior of Functionally Graded Timoshenko Beams subjected to Thermo-Mechanical Load

Document Type: Research Paper


1 Department of Mechanical Engineering, National Institute of Technology Raipur, CG, India

2 Department of Mechanical Engineering, NIT Raipur

3 Department of Mechanical Engineering NIT Raipur


A functionally graded material beam with generalized boundary conditions is considered in the present work to study the deformation and stress behavior under thermal and thermo-mechanical load. Three discrete combinations of functionally graded materials have been con-sidered to include a wide range of materials and material property. The variation of material properties has been taken along the height of the beam cross-section as per power law formula-tion. The formulation has been derived using the principle of virtual work to obtain governing equations for FG Timoshenko beams. The development of governing equations is made using a unique method of unified formulation (Li [16]) in which the displacement variables are arranged in the form of a independent variable that subsequently reduces the equations to a single fourth order differential equation similar to the equation given by classical beam theory and is been extended to thermo-mechanical loading in the present work. The transverse shear stress/ strain for Timoshenko beams have been taken care of within this unified formulation. The for-mulation reported in this work has been generalized for various loading conditions and in the present work thermal and thermo-mechanical load has been considered where temperature has been varied along the beam height. Exact solutions of the fourth order differential equation for the deformation and stress have been obtained for three types of boundary conditions viz.- Clamped-Free (C-F), Simply Supported (S-S) and Propped Cantilever (C-S). The study has been extended to cover wide range of temperature distribution so as to include uniform, linear and non-linear temperature profiles. Deformation and stresses; axial stresses and transverse (shear) stresses, have been reported for different power law index values.