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Auxetic materials are usually designed as cores for structures subject to high impulse loads. Furthermore, the lightweight and high load capacity of the auxetic core construction is also an important advantage even for structures subjected to static loads. The combination of auxetic core and face sheets made by the advanced composite materials is a solution to dramatically increase the load-carrying capacity of the structure. In this paper, a new design of auxetic-core cylindrical shells with carbon nanotube-reinforced coatings is presented. Additionally, the nonlinear buckling behaviors of auxetic-core cylindrical shells with carbon nanotube-reinforced coatings under axially compressive loads are investigated. Three distributed types of functionally graded carbon nanotube-reinforced coatings and the honeycomb lattice form of the auxetic core are investigated. The homogenization model for auxetic lattice structures is considered to constitute the formulations of stiffnesses of the core layer. The nonlinear basic formulations are formulated by using the geometrically nonlinear Donnell shell theory considering Pasternak’s foundation. The Galerkin procedure can be applied three times for three states of buckling behaviors, and the expressions of the compressive load-maximal deflection and compressive load-average end shortening postbuckling curves are achieved. The numerically obtained investigations present the significant effects of auxetic core, volume fraction, direction arrangement and distributed law of carbon nanotube, foundation stiffnesses, geometrical parameters of auxetic core and shell on the critical buckling load and postbuckling behavior of structures.

In this paper, a new improved smeared stiffener technique for the higher-order shear deformable anisotropic stiffeners is presented. The thermo-electro-mechanical nonlinear buckling response of functionally graded graphene reinforcement composite (FG-GRC) laminated plates subjected to the combination of external and axial compression loads in the thermal environment with the inverse piezoelectric effect of a piezoelectric layer is analytically considered. It is proposed that the FG-GRC laminated plates are stiffened by the FG-GRC laminated stiffener system in the longitudinal or transverse directions at the bottom surface and the piezoelectric layer are attached at the top surface. The distribution law of graphene is suitably designed to ensure the piecewise continuity of material. The nonlinear higher-order shear deformation plate theory (HSDPT) is employed to formulate the stability equation system. The stress function is introduced and Galerkin’s method is employed to achieve the algebraically nonlinear stability equation system. Then, the simple calculation procedure can be applied to solve the acquired equation systems, and the expressions of critical buckling loads and postbuckling load-deflection curves are presented in explicit forms. The numerical investigations validate the significant influences of temperature, material, laminated stiffeners, and geometrical features on the nonlinear thermo-electro-mechanical buckling behavior of FG-GRC laminated plates.

Nonlinear buckling analysis for honeycomb auxetic-core sandwich toroidal shell segments with CNT-reinforced face sheets surrounded by elastic foundations under the radial pressure is presented in this study. The basic equation system of shells is established based on the von Kármán–Donnell nonlinear shell theory, combined with Stein and McElman approximation. Meanwhile, the foundation-shell elastic interaction is simulated by the foundation model based on the Pasternak assumption. The Galerkin procedure is utilized to achieve the pre-buckling and post-buckling responses for the shell, from which the radially critical buckling load is determined. Numerical analysis shows the various influences of auxetic-core layer, CNT-reinforced face sheets, and elastic foundation on the pre-buckling and postbuckling behavior of sandwich shells with CNT reinforced face sheets.

In this paper, an analytical approach for nonlinear buckling and post-buckling behavior of stiffened porous functionally graded plate rested on Pasternak's elastic foundation under mechanical load in thermal environment is presented. The orthogonal and/or oblique stiffeners are attached to the surface of plate and are included in the calculation by improving the Lekhnitskii's smeared stiffener technique in the framework of higher-order shear deformation plate theory. The complex equilibrium and stability equations are established based on the Reddy's higher-order shear deformation plate theory and taken into account the geometrical nonlinearity of von Kármán. The solution forms of displacements satisfying the different boundary conditions are chosen, the stress function method and the Galerkin procedure are used to solve the problem. The good agreements of the present analytical solution are validated by making the comparisons of the present results with other results. In addition, the effects of porosity distribution, stiffener, volume fraction index, thermal environment, elastic foundation… on the critical buckling load and post-buckling response of porous functionally graded material plates are numerically investigated.

This paper presents an analytical approach to investigate the nonlinear stability of multilayer-functionally graded plates stiffened by orthogonal and/or oblique functionally graded stiffeners subjected to axial compression and/or thermal load. The equilibrium equation system is established by using the first-order shear deformation plate theory taking into account the plate–foundation interaction, geometrical nonlinearity in von Kármán sense and initial geometrical imperfection. An improved Lekhnitskii’s smeared stiffener technique is applied for oblique stiffeners with thermal terms and shear deformation of stiffeners. The governing equations are solved by Galerkin procedure to obtain the explicit expressions of buckling loads and postbuckling load–deflection curves. Results show the effects of material and geometrical properties, boundary conditions, elastic foundation parameters and initial imperfection on the buckling and postbuckling load-carrying capacity of plates.

A semi-analytical approach to investigate the nonlinear vibration axisymmetric analysis of functionally graded sandwich shallow spherical caps under external pressure resting on elastic foundation in thermal environment is presented. The governing equations are derived by using the first-order shear deformation theory taking into account von Karman geometrical nonlinearity and Pasternak’s two-parameter elastic foundation. The motion equations are determined by Galerkin method and the obtained equation is numerically solved by using Runge–Kutta method. Results of nonlinear dynamic responses show the effects of foundation, material, geometric parameters, and temperature change on the nonlinear vibration of shells.

Based on the third order shear deformation shells theory (TSDT) with von Karman geometrical nonlinearity taking into account initial imperfection and smeared stiffener technique, this paper presents post-buckling analyses for imperfect functionally graded stiffened doubly curved shallow shells resting on elastic foundations under mechanical load, thermal load and thermo-mechanical load by an analytical method. Shells are reinforced by stiffeners system in which material properties of the stiffeners are assumed to be continuously graded in the thickness direction. The material properties are assumed to be temperature- dependent. Two cases of uniform rising temperature and nonlinearly changing of temperature across the thickness are considered. The expressions of thermal parameters are found in the analytical form. Applying Galerkin method, explicit expressions to determine the critical buckling load and the post-buckling mechanical and thermal load-deflection curves are obtained. In the case of temperature-dependent material properties, an iterative algorithm has been presented. The effects of thermal element, FGM stiffeners, geometrical and material parameters, initial imperfection, and foundation are investigated.