NONLINEAR BENDING ANALYSIS OF FGM BEAMS UNDER VARIOUS BOUNDARY CONDITIONS BY RITZ METHOD

Abstract

This paper deals with the nonlinear bending response of functionally graded beams (FG beams) with various boundary conditions using the Ritz method. The displacement components are developed in a series of increasing-order polynomials (Pb-Ritz) that satisfy the geometric boundary conditions. The bending beam model is built based on a high-order shear deformation beam theory, considering the von Kárman type of geometrical nonlinearity strains. First, the potential energies of internal and external forces are determined. The system of nonlinear governing equations is then derived using the minimum total potential energy principle. The Newton-Raphson iterative algorithm is used to solve this system of nonlinear equations. The convergence test and the validated example are conducted by comparing them with the available published results to show the accuracy of the obtained results. Parametric studies are also performed to clarify the effect of the material properties, geometric parameters, boundary conditions, and nonlinearity on the displacement and stress fields of the beam.