Large deflection of functionally graded porous beams based on a geometrically exact theory with a fully intrinsic formulation

Abstract

• 3D large deflections of FG porous beams are studied using a geometrically exact beam theory. • Constitutive relation is obtained based on the concepts of continuum mechanics. • For solution, the Chebyshev collocation method is adopted for the numerical discretisation . • Two types of porosity distributions, namely cross-sectional and span-wise are considered. • To simulate different loading conditions, conservative and non-conservative (follower) loading scenarios are considered. Porous graded materials found in nature can be regarded as variable stiffness optimised load carrier elements that exhibit beneficial properties for real-life engineering designs. In order to investigate the nonlinear behaviour of variable stiffness bioinspired materials, the large deflection of functionally graded beams made from porous materials is considered in this work. Our purpose is to present an efficient and accurate methodology capable of capturing spatially large deflections of these structures with different types of loading conditions and porosity distributions. A geometrically exact beam model with fully intrinsic formulation is employed for the first time to study the large deflection behaviour of functionally graded beams under conservative and non-conservative (follower) loading scenarios. An orthogonal Chebyshev collocation method is used for the discretisation of the fully intrinsic formulation. Two types of porosity distributions, namely cross-sectional and span-wise, are considered and the effect of porosity distribution has been investigated for various benchmark classical test cases. For a given level of accuracy, it is shown that the span-wise functionally graded beam is computationally more demanding compared to the cross-sectional functionally graded beam. In addition to classical problems, two examples demonstrating 3D deflections of highly flexible structures made from porous material subject to combined loads are investigated. It is shown that the current paradigm, while being computationally efficient, can effectively capture the large deflections of functionally graded beams with excellent accuracy.