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

Abstract

Porous graded materials found in nature can be regarded as variable stiffness optimized 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. It is shown that to obtain a given level of accuracy, 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 a 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.

Large displacements of FGSW beams in thermal environment using a finite element formulation

“…Newton-Raphson based method is used in combination with the spherical arc-length control technique herein to solve Eq. (20). Detail implementation of the spherical arclength control method is given in [31].…”

“…The effect of plastic deformation on buckling and nonlinear bending of FGM beams is considered using the finite element method [18,19]. A geometrically exact beam model with fully intrinsic formulation is employed by Masjedi et al [20] to study the large deflection behaviour of functionally graded beams under conservative and nonconservative loading.…”

Dynamic Analysis of Functionally Graded Porous (FGP) Elliptic Cylindrical Shell Based on Jacobi Polynomials Ritz Method

“…Furthermore, the FGP material gives another way for the optimal design of structures on dynamic behavior [3]. In recent years, a significant number of articles have focused on the free vibrations, buckling, and bending behaviors of porous functionally graded structures [4][5][6].…”

Vibration analysis of rotating porous functionally graded material beams using exact formulation

“…The FGMs are normally made from isotropic materials (metals and ceramics) and have remarkable properties such as high strength, low weight, long fatigue life and wear resistance. Therefore, these materials have extensively been used in different applications, and hence, various analyses (static, dynamics…) on the behaviour of structures made of FGMs have been carried out (Cong et al, 2018; Jin et al, 2019; Khaneh Masjedi et al, 2019; Lee and Lee, 2017; Pradhan and Chakraverty, 2013; Sarkar and Ganguli, 2014; Zahedinejad et al, 2020). The dynamic behaviour of FGM structures is an active research area and has attracted the interest of many researchers (Amoozgar et al, 2017; Giunta et al, 2011; Lü et al, 2008; Şimşek and Kocatürk, 2009; Sina et al, 2009; Vo et al, 2014).…”