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Influences of porosity and tangential edge constraint on thermo-torsional postbuckling of FGM toroidal shell segments surrounded by an elastic medium

Nhu Trang L. T., Van Tung H.

Archives of Mechanics

2023

Vol. 75, nr 4

401--429

For the first time, simultaneous influences of porosities, tangential constraints of boundary edges, surrounding elastic media and elevated temperature on the buckling and postbuckling behaviors of a functionally graded toroidal shell segment are investigated in this paper. Porosities exist in the functionally graded material (FGM) according to even and uneven distributions. Properties of constituent materials are assumed to be temperature dependent and effective properties of the porous FGM are determined using a modified rule of mixture. Governing equations are based on the classical shell theory taking into account geometrical nonlinearity and interactive pressure from surrounding elastic medium. Multi-term analytical solutions are assumed to satisfy simply supported boundary conditions and the Galerkin method is adopted to derive nonlinear load – deflection relations and buckling loads. Parametric studies are carried out to analyze the effects of porosity, shell geometry, degree of tangential edge constraint, elevated temperature and elastic media on the buckling resistance and postbuckling strength of toroidal shell segments under a torsional load. The study reveals that tangential edge restraints have considerably beneficial and detrimental influences on the nonlinear stability of torsion-loaded FGM shells at room and elevated temperatures, respectively. The results also find out that the shear layer and the elastic layer of surrounding medium significantly enhances and alleviates the buckling resistance capacity and severity of the snap-through response of the torsion-loaded porous FGM toroidal shell segment, respectively.

Nonlinear postbuckling behavior of auxetic-core toroidal shell segments with Graphene reinforced face sheets under axial loads

Nam V. H., Duc V. M., Doan C. V., Thanh Xuan N. T., Phuong N. T.

Archives of Mechanics

2022

Vol. 74, nr 2-3

89--108

The main aim of this paper is to provide an analytical approach for the nonlinear buckling behaviors of toroidal shell segments made by three layers included honeycomb auxetic-core and two Graphene reinforced face sheets under axial compressive or tensile loads. The auxetic core is designed in a honeycomb form and three distribution laws of Graphene are considered for two symmetric face sheets. The homogenization technique for honeycomb auxetic plates and shells is applied to establish the stiffness formulations of the core. By approximating the doubly curved coordinate to the simpler coordinate with the Stein and McElman assumption, the nonlinear basic equations are formulated using the nonlinear Donnell shell theory and the model of the two-parameter foundation. The Galerkin method can be performed three times for three states of buckling responses and the expressions of the load-deflection postbuckling curves can be determined. The numerical examinations present that the bifurcation buckling occurs with both axial tensile and compressive loads for convex and concave shells and the significantly beneficial effects of auxetic core and functionally graded Graphene reinforced face sheets on nonlinear buckling responses of shell segments.