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Effect of Friction on Buckling Behavior in Shallow Spherical to Hemispherical Shells in Contact with Rigid Boundaries under Uniform External Pressure

Nguyen Xuan Cuong, Arai Yoshio, Araki Wakako

Advances in Science and Technology. Research Journal

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2024

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Vol. 18, no 1

10--25

EN

This study investigates the influence of friction on the buckling behavior of thin, elastic, spherical shells under uniform external pressure. The study spans a range of geometric parameters, from shallow shells to hemispheres. Three different end-edge boundary conditions—clamped, hinged, and frictional ends—are considered across a wide range of friction coefficients using an axisymmetric model and nonlinear buckling analysis. The spherical shell becomes increasingly susceptible to buckling when the friction coefficient falls below the converged friction coefficient. A formula is developed to estimate this converged friction coefficient for each geometric parameter. Furthermore, a boundary separating the effects of friction on critical pressure into distinct regions is established, and equations predicting critical pressure within each region are provided. The study also finds that friction influences the buckling mode transition in the shells. Due to significant changes in the theta angle of the no-bending point with increasing geometric parameter and friction coefficient, buckling mode transitions occur at lower friction coefficients in wider spherical shells. These findings provide valuable insights into the intricate interplay between geometric parameter, friction, and buckling behavior in shells. In practical applications, this study can be used to assess and enhance the safety and reliability of spherical shells.

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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

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2023

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Vol. 75, nr 4

401--429

EN

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.

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Nonlinear buckling analysis of network arch bridges

Błonka Adrian, Skrętkowicz Łukasz

Studia Geotechnica et Mechanica

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2022

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Vol. 44, nr 2

123--137

EN

The paper presents designing due to the instability in-plane problem of the net-arch bridge. Firstly, three essential nonlinear examples are benchmarked in a finite element software. Secondly, linear and nonlinear buckling analyses are conducted, with the purpose of investigating the impact of nonlinear behavior of cables on steel arch instability, involving a comparison of the critical load factor and form from both the linear buckling and the post-critical third-order theory analyses. The impact of prestress and tension, elevation, and hanger failure on instability is discussed. Moreover, a new method for determining nonlinear buckling form for the net-arch structure is proposed in order to allow implementation of Unique Global and Local Imperfection method in cable structures. Calculations are conducted in the finite element software. The model of the network arch bridge is based on the bridge over Vistula River in Cracow.

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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

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2022

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Vol. 74, nr 2-3

89--108

EN

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.