A static analysis of three-dimensional functionally graded beams by hierarchical modelling and a collocation meshless solution method

In this paper, a mesh-free strong-form solution is used to investigate the static response of beams made of functionally graded materials. Thanks to a compact notation, the a priori expansion order of the three-dimensional displacement field upon the cross-section can be assumed as a free parameter resulting in a hierarchical kinematic modelling. Several higher-order theories as well as Timoshenko's classical model can be formulated straightforwardly. The governing differential equations and boundary conditions are obtained as a fundamental nucleus, and an algebraic system is derived via collocation with multiquadric radial basis functions. Results are validated towards three-dimensional FEM models and also against an analytical Navier-type solution. The numerical investigations demonstrate that the presented approach yields accurate results.