Analytical solutions for the thermo-mechanical bending of FG beams using a higher order shear deformation theory (HSDT)

Abstract

The aim of this paper is to analyze a thermo-mechanical behavior of functionally graded beam in thermal environment. Therefore, this research work investigates a thermal, mechanical and thermo-mechanical bending of functionally graded beam resting on simple supports and using a higher order shear deformation theory. the proposed kinematic uses only three variables, which is even less than the first order shear deformation theory (FSDT) and the conventional higher order shear deformation theories (HSDTs). The present model adopts a new displacement field, The material properties of the FG beam are varied along the thickness direction according to the power law distribution (P-FGM). The governing equations for the thermo-mechanical bending investigation are obtained through the principal of virtual work and solved via Navier-type solution method was used to obtain results. All the results are presented in non-dimensional form and validated it by developing the classical beam theory (CBT), and other higher order theories. Parametric studies are thus elaborated to see the influence of the characteristic’s geometries and mechanical in particular: thickness of the FG beam, material index and ratio (width, length).