Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

In this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

Structural Dynamic Modification of Cylindrical Shells With Variable Thickness

In this paper, the effects of some geometrical parameters on dynamic behavior of cylindrical shells with constant and variable thickness are studied. The equation of motion for the shell with constant thickness is extracted based on classical shell theory using Hamilton’s principle. These equations which are a system of coupled partial differential equations are solved analytically and the natural frequency is determined for cylindrical shells with constant thickness. The natural frequency for cylindrical shells with variable thickness is determined using finite element method by employing ANSYS. The results are compared and the effect of different geometric parameters such as length, thickness, and radius on natural frequency is discussed. The specific ranges for geometric parameters have been determined in which there is no significant difference between shells with constant or variable thickness. Cylindrical shells with variable thickness have better stress and strain distribution and optimum weight, in compare with the shells with constant thickness and it is important to know in which ranges of dimensions and geometrical parameters, there are some significant differences between their mechanical properties such as natural frequency. The results are compared with some other references.

Derivation of a refined six-parameter shell model: descent from the three-dimensional Cosserat elasticity using a method of classical shell theory

Starting from the three-dimensional Cosserat elasticity, we derive a two-dimensional model for isotropic elastic shells. For the dimensional reduction, we employ a derivation method similar to that used in classical shell theory, as presented systematically by Steigmann (Koiter’s shell theory from the perspective of three-dimensional nonlinear elasticity. J Elast 2013; 111: 91–107). As a result, we obtain a geometrically nonlinear Cosserat shell model with a specific form of the strain energy density, which has a simple expression, with coefficients depending on the initial curvature tensor and on three-dimensional material constants. The explicit forms of the stress–strain relations and the local equilibrium equations are also recorded. Finally, we compare our results with other six-parameter shell models and discuss the relation to the classical Koiter shell model.

Nonlinear Dynamic Response of Nano-composite Sandwich Annular Spherical Shells

In this research, the nonlinear dynamic response of functionally graded carbon nanotube reinforced composite (FG-CNTRC) sandwich annular spherical shells supported by Pasternak’ foundation is considered by using the analytical approach. Unlike existing works, the structure has three layers: FG-CNTRC layer – homogeneous core – FG-CNTRC layer. Several examples are considered to analyse the behaviour of this sandwich-structured composite. The classical shell theory (CST) is used to derive theoretical formulation delineating nonlinear dynamic response of FG-CNTRC sandwich annular spherical shells. The numerical results explain the effect of material, geometrical parameters, and elastic foundations on the nonlinear dynamic response of the annular spherical shell.

A Method to Estimate Deformation Strains in the Context of Coke Drum Life Assessments: Part 1

In this paper, an analytical method to estimate the deformation strains that can quantify the severity of bulges, as it applies to coke drums, is presented. The proposed method is based on classical shell theory and API 579-1/ASME FFS-1 (2016) procedures involving triaxiality limits. In this first part of the work, only the theoretical development is presented along with the comparison of the results from this theoretical approach with two case studies that emulate the bulging due to different loading scenarios. The developed approach is then applied to a deformed coke drum. In the next part of this paper, the application of this approach on selected in-service coke drums that are equipped with strain gages will be presented. The authors would like to emphasize the well-known fact that the coke drum is a complex pressure vessel for which any single simplified assessment technique may not be sufficient to quantify the life or fitness-for-service (FFS) of a coke drum due to the complexities associated with the various parameters that affect the mechanical integrity of the coke drum. This paper is an attempt to advance the assessment techniques that are currently utilized in the industry.

Nonlinear dynamic buckling of full-filled fluid sandwich FGM circular cylinder shells

This paper is presented to solve the nonlinear dynamic buckling of sandwich functionally graded circular cylinder shells filled with fluid. Governing equations are derived using the classical shell theory and the geometrical nonlinearity in von Karman-Donnell sense is taken into account. Solutions of the problem are established by using Galerkin’s method and Rung-Kutta method. Effects of thermal environment, parameters of geometric, volume fraction index k and fluid on dynamic responses of shells are investigated.

Nonlinear thermal vibration and dynamic buckling of eccentrically stiffened sandwich-FGM cylindrical shells containing fluid

The governing equations for analysing thermal vibration and dynamic buckling of eccentrically stiffened sandwich functionally graded cylindrical shells full filled with fluid and surrounded by elastic foundations in thermal environment are derived by using the classical shell theory, the geometrical nonlinearity in von Karman-Donnell sense, the smeared stiffener technique and Pasternak’s foundation model. Solutions of the problem are established according to the Galerkin’s method and Runge–Kutta method. The effects of fluid pressure, stiffeners, geometrical ratios, temperature and elastic foundation on the dynamic responses of shells are investigated.

Buckling and postbuckling of axially-loaded CNT-reinforced composite cylindrical shell surrounded by an elastic medium in thermal environment

Buckling and postbuckling behaviors of nanocomposite cylindrical shells reinforced by single walled carbon nanotubes (SWCNTs), surrounded by an elastic medium, exposed to a thermal environment and subjected to uniform axial compression are investigated in this paper. Material properties of carbon nanotubes (CNTs) and isotropic matrix are assumed to be temperature dependent, and effective properties of nanocomposite are estimated by extended rule of mixture. The CNTs are embedded into matrix via uniform distribution (UD) or functionally graded (FG) distribution along the thickness direction. Governing equations are based on Donnell’s classical shell theory taking into account von Karman-Donnell nonlinear terms and interaction between the shell and surrounding elastic medium. Three-term form of deflection and stress function are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain load-deflection relation from which buckling and postbuckling behaviors are analyzed. Numerical examples are carried out to analyze the effects of CNT volume fraction and distribution types, geometrical ratios, environment temperature and surrounding elastic foundation on the buckling loads and postbuckling strength of CNTRC cylindrical shells.

Nonlinear buckling and post-buckling analysis of imperfect porous plates under mechanical loads

The nonlinear buckling and post-buckling response of imperfect porous plates is investigated analytically in this paper. The porous materials with elastic moduli are assumed to vary through the thickness of the plate according to two different distribution types. Governing equations are derived based on the classical shell theory taking into account Von Karman nonlinearity and initial geometrical imperfection. Explicit relations of load–deflection curves for rectangular porous plates are determined by applying stress function and Galerkin’s method. The accuracy of present theoretical formulation is verified by comparing it with available results in the literature. The effects of varying porosity distribution, porosity coefficient, boundary condition and imperfection on post-buckling behavior of the porous plate are studied in detail. A parametric study is carried out to investigate the effects of varying porosity distribution, porosity coefficient, boundary condition and imperfection on post-buckling behavior of the porous plate. The results show that the critical buckling loads decrease with increasing porosity coefficient and the post-buckling curves for nonlinear symmetric porosity distribution are always higher than those for nonlinear non-symmetric porosity.