Inhomogeneous Cylindrical Shells Research Articles

Free Vibrations of Thin-Walled Gas Pipelines Taking into Account the Influence of Longitudinal Force During Trench Laying

A numerical experiment was carried out to determine the frequencies of free oscillations of an inhomogeneous pipeline at various mechanical and geometric parameters.This made it possible to establish the influence of factors such as longitudinal force, thickness of the reinforced concrete shell, internal working pressure and the coefficient of the soil bed on the system’s own vibrations. For calculations, a model of an inhomogeneous cylindrical two-layer shell of finite length consisting of a steel pipe and a protective reinforced concrete layer was chosen.

Construction of homogeneous solutions of the torsion problem for a radially inhomogeneous transversely isotropic cylinder

The torsion problem for a radially inhomogeneous transversely isotropic cylinder of small thickness was investigated by the method of asymptotic integration of elasticity theory equations. It is assumed that the side part of the cylinder is stress-free, and boundary conditions are set at the ends of the cylinder, leaving the cylinder in equilibrium. The elastic moduli are thought to be arbitrary continuous functions of the variable along the cylinder radius. The formulated boundary value problem is reduced to a spectral problem containing a small parameter characterizing the thin-walledness of the cylinder. Homogeneous solutions are built, i.e. any solutions of the equilibrium equation satisfying the condition of no stresses on the side surfaces. It is shown that the solution of the torsion problem consists of a penetrating solution and a boundary layer character solution similar to Saint-Venant's edge effect in the theory of inhomogeneous plates. The penetrating solution determines the internal stress-strain state of a radially inhomogeneous cylinder. The stress state determined by the penetrating solution is equivalent to the torsional moments of stresses acting in the cross-section perpendicular to the cylinder axis. Solutions having the boundary layer character are localized at the ends of the cylinder and decrease exponentially with distance from the ends. These solutions are absent in applied shell theories. Asymptotic formulas for displacement and stresses are built, which make it possible to calculate the three-dimensional stress-strain state of a radially inhomogeneous transversely isotropic cylinder of small thickness. Based on the obtained asymptotic expansions, it is possible to assess the applicability of applied theories and build a refined applied theory for radially inhomogeneous cylindrical shells

Stability Analysis of Shear Deformable Inhomogeneous Nanocomposite Cylindrical Shells under Hydrostatic Pressure in Thermal Environment

In this study, the stability of inhomogeneous nanocomposite cylindrical shells (INCCSs) under hydrostatic pressure in a thermal environment is presented. The effective material properties of the inhomogeneous nanocomposite cylindrical shell are modeled on the basis of the extended mixture rule. Based on the effective material properties, the fundamental relations and stability equations are derived for thermal environments. In this process, the first-order shear deformation theory (FSDT) for the homogeneous orthotropic shell is generalized to the inhomogeneous shell theory. This is accomplished using the modified Donnell-type shell theory. The analytical expressions are obtained for hydrostatic buckling pressure of INCCSs in the framework of FSDT and classical shell theory (CST) by obtaining a solution based on Galerkin’s procedure. The numerical examples presented include both comparisons and original results. The last section shows the influences of carbon nanotube (CNT) models, volume fraction, and shell characteristics on the hydrostatic buckling pressure in the thermal environment.

Creep of an inhomogeneous polymeric cylindrical shell under heating

The article presents the calculation of a polymer thick-walled cylindrical shell, taking into account creep under the action of a uneven temperature field. The relevance of the work lies in the widespread intro-duction of polymer pipes in the repair and construction of pipelines for heating, sewerage, and water supply systems. The problem is solved in an axisymmetric formulation under plane deformation conditions. The calculation is based on the non-linear Maxwell-Gurevich equation, which is widely used in the calculations of polymer structures. In the problem under consideration, the cylindrical shell is in a flat de-formed state. It is also believed that temperature is a function of radius and time.

СВОБОДНЫЕ КОЛЕБАНИЯ ТОНКОСТЕННОГО ДВУХСЛОЙНОГО ТРУБОПРОВОДА С УЧЕТОМ ВЛИЯНИЯ ПРОДОЛЬНОЙ СЖИМАЮЩЕЙ СИЛЫ ПРИ ПОЛУПОДЗЕМНОЙ ПРОКЛАДКЕ

The article considers a cylindrical two-layer shell subjected to a longitudinal compressive force. An inhomogeneous cylindrical two-layer shell of finite length, consisting of a steel pipe and a protective reinforced concrete layer, was adopted as the calculation scheme. Based on the use of the assumptions of the theory of shells by Vasiliy Z. Vlasov, the equation of motion of the shell in efforts and displacements was obtained. A system of differential equations has been formed and solved taking into account the assumptions of this theory of cylindrical shells, the solution for determining the frequency of free vibrations taking into account the effect of internal working pressure, inhomogeneous ground pressure on the pipe wall and a longitudinal compressive force has been obtained.

Projection-Iterative Schemes for the Implementation of Variational-Grid Methods in the Problems of Elastoplastic Deformation of Inhomogeneous Thin-Walled Structures

We present projection-iterative schemes for the realization of the variational-grid (finite-element and local-variation) methods aimed at the solution of various variational problems of mechanics for elastic and elastoplastic solids with inclusions and holes. By using the solutions of the problems of elastoplastic deformation of inhomogeneous isotropic plates and cylindrical shells with holes of various kinds as examples, we analyze the mutual influence of the holes and inclusions. We investigate the problem of convergence of the proposed schemes and demonstrate their efficiency from the viewpoint of reduction of the computer time required for their practical applications.

Solution of the axisymmetric problem of thermoelasticity of a radially inhomogeneous cylindrical shell by numerical-analytical method and the finite element method

The aim of research is to compare two calculation methods using the example of solving the axisymmetric thermoelasticity problem. Methods. The calculation of a thick-walled cylindrical shell on the temperature effect was carried out by the numerical-analytical method and the finite element method, implemented in the LIRA-CAD software package. The shell consists of three layers: two layers of heat-resistant concrete and an outer steel layer. In the calculation, a piecewise linear inhomogeneity of the shell due to its three-layer structure and continuous inhomogeneity caused by the influence of a stationary temperature field is taken into account. The numerical-analytical method of calculation involves the derivation of a resolving differential equation, which is solved by the sweep method, it is possible to take into account the nonlinear nature of the deformation of the material using the method of successive approximations. To solve this problem by the finite element method, a similar computational model of the shell was constructed in the LIRA-CAD software package. The solution of the problem of thermoelasticity for an infinite cylinder (under conditions of a plane deformed state) and for a cylinder of finite length with free ends is given. Results . Comparison of the calculation results is carried out according to the obtained values of ring stresses σθ.

Calculation of Equal Strength Thick-Walled Concrete Cylinder with Free Ends

The article discusses radially inhomogeneous thick-walled cylindrical shells in which inhomogeneity may be due to various reasons (structure, the effect of the temperature field, etc.).Thick-walled shells are called equal-stressed, if the principle stress σ1 in all points of the body is constant. In inhomogeneous body, in addition to the elastic modulus of a material, its strength can also variable. In accordance with the first theory of strength, if the stress σ1 is variable and at each point the strength of the material is equal, then the thick-walled shell is called equal-strength. The article discusses the modelling of equal strength concrete thick-walled shell with free ends.

Analysis of the prediction of a bilayered cylindrical shell’s reduced cutoff frequency with data-driven approaches

Abstract The reduced cutoff frequency is one of the most important properties of elastic circumferential waves of cylindrical shells. For homogeneous thin cylindrical shells, this frequency can be calculated based on the eigen modes theory. In contrast, this theory is not practical for inhomogeneous cylindrical shells. This paper presented the methods of reduced cutoff frequency prediction using data-driven approaches. Three widely known data-driven methods, the Artificial Neural Network (ANN), the Adaptive-Network-based Fuzzy Inference System (ANFIS), the Support Vector Machine (SVM), are employed to develop the prediction models. The training and testing datasets for these models are determined from the plane of modal identification. In this study, the considered bilayered cylindrical shells are made of stainless steel/polymer. Three prediction scenarios are assessed. The difference between these scenarios is the physical and geometrical parameters which considered as relevant entries of data-driven approaches. In the first and second scenarios, a comparative analysis indicates that the ANN models performed better than other models with highest prediction accuracy value of 0.9761 and the lowest mean relative error (MRE) of 0.4017%. In the third scenario the SVM model was the best model with highest accuracy of 0.9895 and lowest root mean square error (RMSE) of 0.0227.

Axisymmetric Thermal Stress in an Inhomogeneous Circular Cylindrical Shell Due to Cyclic Temperature Change

Axisymmetric Thermal Stress in an Inhomogeneous Circular Cylindrical Shell Due to Cyclic Temperature Change

Application of the method of spline-collocations to the solution of dynamic and static problems for structurally inhomogeneous cylindrical shells

Application of the method of spline-collocations to the solution of dynamic and static problems for structurally inhomogeneous cylindrical shells

Stability of Inhomogeneous Cylindrical Shells Under Distributed External Pressure in a Three-Dimensional Statement

The problem of the stability of anisotropic cylindrical shells is numerically solved in a three-dimensional statement. The shells are made of a material with one plane of elastic symmetry. By using the Bubnov–Galerkin method to approximate unknown functions with respect to the longitudinal coordinate by trigonometric series, the problem is reduced to a one-dimensional one that is solved by the discrete-orthogonalization method. The results are tested.

Solitary waves in an inhomogeneous cylindrical shell interacting with an elastic medium

A new generalized sixth-order nonintegrable equation is derived to model axisymmetric longitudinal wave propagation in an inhomogeneous cylindrical shell interacting with a nonlinear elastic medium. Exact soliton-like solutions to this equation are constructed with allowance for geometric and physical nonlinearities, both individually and in combination.

ИДЕНТИФИКАЦИЯ МАТЕРИАЛЬНЫХ ПАРАМЕТРОВ МОДЕЛЕЙ ВЯЗКОУПРУГОГО И УПРУГОПЛАСТИЧЕСКОГО ДЕФОРМИРОВАНИЯ ДВУХСЛОЙНЫХ МЕТАЛЛОПЛАСТИКОВЫХ ЦИЛИНДРИЧЕСКИХ ОБОЛОЧЕК ПРИ ВЗРЫВНОМ НАГРУЖЕНИИ

A computational-experimental method of the identification of material parameters of defining relations of viscoelastic and (or) elastoplastic deformation of composite and isotropic materials is developed, based on minimizing the mismatch between experimental data results of numerical analysis of the dynamic behavior of two-layer metallic-plastic cylindrical shells under explosive loading. The computational-experimental identification method is tested; it is shown that it can be effectively used in determining material parameters of viscoelastic and (or) elastoplastic models of nonlinear deformation of metallic-plastic cylindrical shells under explosive loading. The present computational-experimental method of the identification of material parameters of defining relations makes it possible to determine with acceptable accuracy material parameters of viscoelastic and (or) elastoplastic defining relations of the dynamic behavior of inhomogeneous metallic-plastic cylindrical shells. Keywords: composite materials, cylindrical shells, identification, mathematical modeling, pulsed loading.

Nonstationary Deformation of Longitudinally and Transversely Reinforced Cylindrical Shells on an Elastic Foundation

The problem of the forced vibrations of a discretely reinforced cylindrical shell on an elastic foundation under distributed impulsive loading is stated. The dynamic behavior of the inhomogeneous cylindrical shell is analyzed using the Timoshenko-type theory of shells. The problem is solved with the finite-difference method. Numerical results are analyzed

Analytical solution of physically nonlinear problem for an inhomogeneous thick-walled cylindrical shell

Among the classical works devoted to Solid Mechanics a significant place is occupied by the studies taking into account the physical and geometric nonlinearity. Also there is enough of works, which concern linear problems taking into account the inhomogeneity of the material. At the same time there are very few publications, which take into account both effects (non-linearity and inhomogeneity). This is due to the lack of experimental data on the influence of various factors on the parameters defining the non-linear behavior of the materials. Thus it is of great importance to study the influence of inhomogeneity when solving the problems of structures made of physically nonlinear materials. This article provides a solution to one of the problems of the nonlinear theory of elasticity taking into account the inhomogeneity. The problem is solved in an axisymmetric formulation, i.e. all the parameters of the nonlinear relationship between the intensities of stresses and strains are functions of the radius. The article considers an example - the stress distribution in the inhomogeneous soil massif with a cylindrical cavity.

Solving the vibration problem of inhomogeneous orthotropic cylindrical shells with hoop-corrugated oval cross section

Based on the framework of Flügge's shell theory, transfer matrix approach and Romberg integration method, this paper investigates how corrugation parameters and material homogeneity affect the vibration behavior of isotropic and orthotropic oval cylindrical shells with sine-shaped hoop. Assume that the Young's moduli, shear moduli and density of the orthotropic material are continuous functions of the coordinate in the circumferential direction. The governing equations of non-homogeneous, orthotropic oval cylindrical shells with variable homogeneity along its circumference are derived and put in a matrix differential equation as a boundary-value problem. The trigonometric functions are used with Fourier's approach to approximate the solution in the longitudinal direction, and also to reduce the two-dimensional problem to a one-dimensional one. Using the transfer matrix approach, the equations can be written in a matrix differential equation of the first order and solved numerically as an initial-value problem. The proposed model is applied to get the vibration frequencies and mode shapes of the symmetric and antisymmetric vibration modes. The sensitivity of the vibration behavior to the corrugation parameters, homogeneity variation, ovality, and orthotropy of the shell is studied for different type modes of vibration.

New approach for the vibrations of inhomogeneous orthotropic cylindrical shells resting on step-wise Winkler foundations

In this paper, Flügge’s shell theory and solution for the vibration analysis of an inhomogeneous, orthotropic cylindrical shell resting on a circumferentially stepped Winkler foundation are carried out. The stepwise foundation consists of two regions having different stiffnesses and both regions are symmetric about the centrelines of the shell. The governing equations of the shell are formulated as a three-dimensional boundary-value problem and their solutions are obtained by a numerical–analytical approach. The trigonometric functions are used with Fourier’s approach to approximate the solution in the longitudinal direction and also to reduce the two-dimensional problem to one-dimensional one. Using the transfer matrix approach and based on the method of initial parameters, these equations can be written in a matrix differential equation of first order in the circumferential coordinate and solved numerically as an initial-value problem. The proposed model is applied to get the inverse vibration frequencies and the corresponding mode shapes of the shell vibrations. The sensitivity of the vibration behaviour and bending deformations to the geometry of Winkler foundation, homogeneity variation and shell orthotropy is investigated for different type-modes of vibration.

On a Problem of Truesdell for Anisotropic Elastic Shells

In this paper we study the equilibrium of cylindrical elastic shells under the action of resultant forces and moments on the end edges. We employ the linear the- ory of Cosserat surfaces to describe the deformation of anisotropic and inhomogeneous cylindrical shells with arbitrary (open or closed) cross-section. In this context, we prove a minimum energy characterization for the solution of the relaxed Saint-Venant's prob- lem determined previously. Then, we treat the problem of Truesdell associated to the deformation of cylindrical shells.

The homotopy analysis method for solving nonlinear wave propagation model in inhomogeneous cylindrical shells

The investigation of nonlinear wave propagation in cylindrical shells is of theoretical and realistic significance. In this work, using homotopy analysis method, we study a new model of nonlinear wave propagation in inhomogeneous cylindrical shells, and obtain approximate solitary wave solution and periodic wave solution with high accuracy. It shows that homotopy analysis method is one of the most effective methods for research into the problems of nonlinear wave propagation.