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

Abstract

A functionally graded material beam with generalized boundary conditions is contemplated in the present study in order to examine the deformation and stress behavior under thermal and thermo-mechanical load. Three discrete combinations of functionally graded materials have been deliberate in including a wide range of materials and material properties. The variation of material properties has been taken along the height of the beam cross-section as per power law formulation. The formulation has been derived, applying the principle of virtual work in order to acquire governing equations for FG Timoshenko beams. The development of governing equations is made through applying a unique method of unified formulation (Li [16]) in which the displacement variables are arranged in the form of aindependent variable that subsequently reduces the equations to a single fourth order differential equation similar to the equation given by classical beam theoryand 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 formulation employed in this research has been generalized for various loading conditions, and in the present work, thermal and thermo-mechanical load has been pondered where temperature has been varied in accordance with 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.