geometrically nonlinear analysis of axially functionally graded beams by using finite element method

The aim of this paper is to investigate geometrically nonlinear static analysis of an axially functionally graded cantilever beam subjected to transversal load. the considered problem is solved by finite element method with total lagrangian kinematic approach. the material properties of the beam vary along the longitudinal direction according to the power law function. the finite element model of the beam is considered in the three dimensional continuum approximation for an eight-node quadratic element. the geometrically nonlinear problem is solved by newton-raphson iteration method. in the numerical results, the effects of the material distribution on the geometrically nonlinear static displacements of the axially functionally graded beam are investigated. also, the differences among of material distributions are investigated in geometrically analysis.