A new analytical approach to the nonlinear buckling and postbuckling behavior of functionally graded graphene reinforced composite laminated cylindrical, parabolic, and half‐sinusoid shallow imperfect panels

Abstract

This paper presents and analyzes the nonlinear buckling responses of three types of shallow imperfect panels (cylindrical panel, parabolic panel, and half‐sinusoid panel) made from functionally graded graphene reinforced composite (FG‐GRC) on nonlinear elastic foundations subjected to axial compressive load in thermal environments. The nonlinear governing equations are formulated on Reddy's higher‐order shear deformation shell theory (HSDST) and take into account von Karman‐type nonlinearity. A new approximation technique to determine the stress function in average sense is developed and Galerkin's method is used to obtain the algebraically nonlinear equation system. Then, the simple calculation process can be used to solve the obtained equation systems, and the formulations to calculate the critical buckling loads and postbuckling load‐deflection curves are expressed in explicit form. The results can be flexibly applied to FG‐GRC panels with different curvatures in engineering designs. The effects of panel types, geometrical parameters, temperature increase, initial imperfection, and nonlinear elastic foundations on the critical buckling loads and postbuckling curves of cylindrical, parabolic, and half‐sinusoid FG‐GRC panels are discussed in numerical results. Numerical results also show a small disadvantage in the load‐carrying capacity of cylindrical panels compared to parabolic panels and half‐sinusoid shallow panels.Highlights Postbuckling of cylindrical, parabolic, and half‐sinusoid panels are studied. The panels are made of functionally graded graphene reinforced composite. Reddy's higher‐order shear deformation shell theory is applied. A new approximation technique to determine the stress function is developed. Critical buckling loads and postbuckling expressions are explicitly obtained.

Nonlinear vibration and dynamic buckling responses of stiffened functionally graded graphene‐reinforced cylindrical, parabolic, and sinusoid panels using the higher‐order shear deformation theory

“…Due to the complex curvature in the compatibility Equation ( 12), the stress function forms of PPs and SPs can not be determined exactly. In this paper, the stress function form of PPs and SPs is also chosen according to the exact form of CPs with linear and nonlinear terms, as [51] 𝜁 = 𝜁 1 cos 2𝛼𝑥 + 𝜁 2 cos 2𝛽𝑦 + 𝜁 3 sin 𝛼𝑥 sin 𝛽𝑦 + 1 2…”

“…An approximate technique to determine the stress function forms for PPs and SPs can be performed by substituting Equations ( 15) and ( 16) into Equation (12), then, the like-Galerkin method is applied, as [51] 𝑑𝑦.…”

“…where The strain energy of the panels, the work done by the external loads, and the kinetic energy considering the panelsviscoelastic foundation interaction are calculated as [51]…”

“…The design of FG-GRC plates and CPs with stiffeners was proposed and the smeared stiffener technique was improved for FG-GRC stiffeners to investigate the buckling and postbuckling analysis of the structures [47][48][49][50]. The nonlinear buckling and postbuckling analysis of FG-GRC laminated CPs, parabolic panels (PPs), and sinusoid panels (SPs) were studied using the Galerkin method [51]. The free vibration, nonlinear resonance, and nonlinear vibration problems of FG-GPLRC conical panels and cylindrical shells were investigated [52][53][54] using the HSDT.…”

Nonlinear buckling and postbuckling analysis of cylindrical and sinusoid FG-GPLRC panels under axial compressive load

“…Nonlinear buckling of FG-GRC higher-order shear deformable plates and cylindrical panels were investigated using the Galerkin method [19][20][21][22]. The buckling and postbuckling behavior of FG-GRC panels under external pressure and axial compression with complex curvatures such as parabola and sinusoid panels were also studied [23,24].…”