Geometrically nonlinear static analysis of functionally graded beams subjected to axial centric forces

Abstract

Since the neutral axis of a functionally graded (FG) beam does not coincide with the mid-plane, centrically applied forces P make the beam bend; on the other hand, the curvature deformation of the beam interacts with P causing additional moment, also known as the geometric nonlinear effect (P- effect). This paper investigates the geometric nonlinear effect of functionally graded beams subjected to axial static force. The material properties of the beam vary continuously in the thickness direction according to the power-law distributions. The governing equilibrium equations are established by using the principle of virtual work. The finite element method is employed to discretize the model and obtain a numerical approximation of the equilibrium equations. Numerical examples are carried out in Matlab programming language. The influences of geometric nonlinearity, boundary conditions, as well as different material property distributions on the behaviors of the beams are also analyzed and evaluated.