Non linear analysis of a functionally graded beam with variable thickness

摘要

The nonlinear analysis of a functionally graded beam under combined loads is investigated analytically in this paper. The point loads and moment is applied at the end of the beam. The area section is considered to vary continuously along the longitudinal axis of the beam. The most important idea for presentation of this paper is the application of the present method for a vast class of functionally graded and variable thickness beams. The gradation along the longitudinal axis of the beam is studied as a novel subject. Euler-Bernoulli theory is employed to derive the governing differential equation of a FG beam. The Adomian's Decomposition Method (ADM) is used for solution of the governing nonlinear differential equation. The analytical results are compared with those results obtained using the numerical simulation (FEM). This comparison indicates that the difference between them is not significant. The effect of non-homogenous coefficient on the rotation and deflection of the beam is studied for different values of non homogenous index. This study presents the general formulation to evaluate the deflection and rotation of the beams with variable properties.