Impact response of inclined self-weighted functionally graded porous beams reinforced by graphene platelets

This study presents a theoretical analysis on the low-velocity impact response of inclined porous nanocomposite beams under various impulsive loads. The laminated beam model consists of multiple layers modelled as closed-cell cellular solids with identical thickness, where each layer contains uniformly distributed internal pores and is reinforced by dispersing graphene platelets into the matrix. The layer-wise continuous variations in both internal pore size/density and graphene fraction result in functionally graded lightweight beams with controllable density distributions and varying elastic moduli across the thickness direction. The material properties of each layer are determined according to Halpin-Tsai micromechanics model and the extended rule of mixture. The governing equations of the inclined beam are derived based on Timoshenko beam theory then solved by employing Ritz method for space domain and Newmark method for time domain. The static bending due to the self-weight of the beam is examined first, and then imported into the dynamic analysis as the initial stress state for the beam under impulsive impacts with six different pulse shapes. A comprehensive parametric study is conducted with a special focus on the combined effects of graded material distributions and inclined angle on the beam behaviour. Results show that a larger inclined angle reduces the beam deflection, and the rectangular impulsive load can lead to the largest mid-span deflection of fully clamped graded beams that may reach over 70% more than those under some of other impact load types. This study should provide insights into the design of lighter and stiffer inclined structural components subjected to various impulsive loading conditions.