Jordan Journal of Civil Engineering

Static Analysis of Functionally Graded Beams under Bending Using a New Polynomial Shear Function


Aissa Boussouar; Bachir Taallah; Ali Zaidi;


This paper presents a static analysis to establish a mathematical model using high order bending theories to predict the shear strain in the displacement fields for functionally graded beams under bending. The new polynomial shear function developed which represents the originality of this research work satisfies the boundary conditions and stress nullities on the lower and upper faces of the section through the thickness. This new model considering a hyperbolic shape function does not need a shear correction factor. It is noted that the material properties are considered to vary in the thickness direction. Furthermore, a simple power-law distribution in terms of constituent volume fractions is assumed. The analytical model is developed by differential equations obtained from the virtual work principle and also equilibrium equations and boundary conditions considered. The solution model is based on a variation approach to evaluate the displacement field component and the basic constitutive laws. The solution of the analytical model is explored using illustrative case. The obtained results in terms of displacement field including shear strain and shear stresses predicted from the proposed model are compared to those obtained from the literature.


Higher-order theories, Beams, Displacement, Static analysis, New polynomial shear function, Shear stress.