Nonlinear mechanics of a slender beam composited by three-directional functionally graded materials

Abstract In view of some advanced facilities such as aerospace and marine structures are often suffered by multi-directional loads in engineering, especially for slender structures undergoing large deformation and catastrophic failure, we use the three-directional (3D) functionally graded materials (FGMs) to fabricate the slender beams to resist 3D loads and study the nonlinear mechanics to provide an insight reference for possible applications. Assume the materials properties as continuously varying with an arbitrary function in three directions, the governing equation is derived based on Hamilton’s principle and geometric nonlinearity. The generalized differential quadrature method (GDQM) combined with an iterative technique is employed to calculate the nonlinear critical buckling load for predicting the dynamics. The Galerkin technique with the homotopy analysis method is utilized for determining the closed-form solutions to the nonlinear frequencies. Some numerical examples are presented to explore the effects of the physical parameters such as 3D FG indexes on the nonlinear mechanical behaviors in detail. It is found that the three directional FG indexes can tune the mechanical performance of the beam, such as improving on the load-bearing capacity and enhancing in the flexibility of dynamic design, which is tremendously different from nonlinear behaviors of 2D and 1D FGMs beams.