An investigation on the shear deformation under bending conditions of cantilever FGM beams using a new polynomial shear function

Abstract

In this paper, a static analysis to establish a mathematical model using high order bending theories considering shear strains in displacement fields which have not been taken into account by other theories for functionally graded material (FGM) cantilever beams under bending. A new polynomial shear function is used in this investigation, when satisfied the stress-free boundary conditions. These theories do not require a shear correction factor and consider a hyperbolic shape function. Material properties are assumed to vary in the thickness direction, a simple power-law distribution in terms of volume fractions of constituents is considered. Illustrative cases, a cantilever FGM beam subjected to a concentrated shear force at the free end, and also as a cantilever FGM beam with uniformly distributed load are presented the originality of this research work, in this investigation. The mathematical model is established by differential equations which are derived by the principle of virtual work. Equilibrium equations and boundary conditions are introduced. The solution model is based on a variation approach (integrals) to predict the field component of displacements and the basic constitutive laws. The solution of the analytical model is presented. The results in terms of displacement fields including rotation of the section, and shear stresses, predicted from the proposed model, are presented.