Limit load analysis and imperfection sensitivity of porous FG micro-tubes surrounded by a nonlinear softening elastic me
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O R I G I NA L PA P E R
Hadi Babaei
· M. Reza Eslami
Limit load analysis and imperfection sensitivity of porous FG micro-tubes surrounded by a nonlinear softening elastic medium
Received: 27 May 2020 / Revised: 8 July 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract An imperfection sensitivity analysis for the nonlinear post-buckling behavior of functionally graded (FG) porous micro-tubes is performed in this research. The case of geometrically imperfect micro-tubes surrounded by a nonlinear elastic medium under axial compressive load is analyzed. Properties of the microtube with uniform distributed porosity are FG across the radius of the cross-section. Two types of boundary conditions as simply-supported and clamped are considered. The high-order shear deformation theory of tubes is utilized to approximate the displacement field. Differential equations governing the equilibrium position of the micro-tube are extracted using the virtual displacement principle. These nonlinear equations are analytically solved by means of the two-step perturbation technique and Galerkin procedure. It is shown that when the imperfect micro-tube is in contact with a sufficiently soft foundation, the post-buckling path of the structure is unstable, and therefore the structure is imperfection sensitive. Since the imperfection sensitivity of micro-tubes is not reported in literature, results of this study are compared with buckling responses of perfect FGM tubes. The effects of porosity coefficient, power law index, length scale parameter, and geometrical parameters upon the limit buckling load of imperfect micro-tubes are investigated. 1 Introduction A nonlinear elastic foundation can be attached to thin-walled structures as either hardening or softening. The sufficiently soft type of nonlinear elastic foundation is associated with a limit point buckling behavior instead of bifurcation one. Imperfection sensitivity of the buckling behavior of homogeneous isotropic columns and spherical shells with initial deflections is studied by Keener [1]. In this investigation, the cases of imperfect thin structures resting on a nonlinear softening elastic foundation are analyzed by employing the analytical methods. Elishakoff [2] presented a study on the static/dynamic imperfection sensitivity of non-symmetric thin shells resting on a nonlinear elastic foundation. The approximate solutions are presented to obtain the static limit loads of the imperfect structures based on the Koiter model. Also, the dynamic limit loads are obtained using the Budiansky and Hutchinson model. Sheinman and Adan [3] proposed a solution method for imperfection sensitivity of an elastic beam resting on a nonlinear elastic foundation. The governing equilibrium equations of the compressive loaded beam are derived based on the higher-order shear deformation beam model and are solved using the special finite-difference scheme and Newton’s method. An imperfection sensitivity analysis for the postbuckling behavior of elastic beams under sudden ax
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