A Semi-Analytical Solution for Elastic Analysis of Rotating Thick Cylindrical Shells with Variable Thickness Using Disk Form Multilayers (original) (raw)
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Using disk form multilayers, an elastic analysis is presented for determination of displacements and stresses of rotating thick truncated conical shells. The cone is divided into disk layers form with their thickness corresponding to the thickness of the cone. Due to the existence of shear stress in the truncated cone, the equations governing disk layers are obtained based on first shear deformation theory (FSDT). These equations are in the form of a set of general differential equations. Given that the truncated cone is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. The results obtained have been compared with those obtained through the analytical solution and the numerical solution.
Periodica Polytechnica Mechanical Engineering, 2015
Using multi-layers method (MLM), a semi-analytical solution have been derived for determination of displacements and stresses in a thick cylindrical shell with variable thickness under non-uniform pressure. Three different profiles (convex, linear and concave) are considered for the variable thickness cylinder. Given the existence of shear stress in the thick cylindrical shell due to thickness and pressure changes along the axial direction, the governing equations are obtained based on first-order shear deformation theory (FSDT). These equations are in the form of a set of general differential equations with variable coefficients. Given that the thick cylinder with variable thickness is divided into n homogenous disks, n sets of differential equations with constant coefficients are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. Finally, some numerical results are presented to study the effects of applied pressure, thickness profile type, and angular velocity on the mechanical behavior of the cylindrical shell. Keywords rotating thick cylindrical shell, variable thickness, hyperbolic profile, non-uniform pressure, multi-layers method (MLM) Period. Polytech. Mech. Eng. M. Z. Nejad, M. Jabbari, M. Ghannad
Journal of Solid Mechanics, 2017
In this paper, thermo-elastic analysis of a rotating thick truncated conical shell subjected to the temperature gradient, internal pressure and external pressure is presented. Given the existence of shear stress in the conical shell due to thickness change along the axial direction, the governing equations are obtained based on first-order shear deformation theory (FSDT). These equations are solved by using multi-layer method (MLM). The model has been verified with the results of finite element method (FEM). Finally, some numerical results are presented to study the effects of thermal and mechanical loading, geometry parameters of truncated conical shell.
Vibration analysis of thin rotating cylindrical shell
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I express my gratitude and sincere thanks to Prof. A. V. Asha, for her guidance and constant encouragement and support during the course of my work in the last one year. I truly appreciate and value her esteemed guidance and encouragement from the beginning to the end of this thesis, her knowledge and company at the time of crisis remembered lifelong.
— A cylindrical rectangular finite element is developed in this paper. The element has six nodal degrees of freedom at each of the four corner nodes, (Three general external degrees of freedom and three rotations). The displacement fields of the element satisfy the exact requirements of rigid body modes of motion. Shallow shell formulation is used and the element is based on an independent strain assumption insofar as it is allowed by the compatibility equations. A cylindrical shell problem for which a previous solution exists is first analyzed using the new element to test the efficiency of the element. The element is then used in the analysis of cylindrical shell subjected to uniformly distributed load varying sinusoidal along its length in addition to symmetric sinusoidal edge loads present along its longitudinal boundaries. The distribution of various components of stresses is obtained and the effect of radius-length ratio is also presented to give the designer an insight for the behavior of such structures.
Journal of Computational Applied Mechanics, 2024
In this paper, a thermo-elastic analysis is presented to obtain stresses, displacements, and the thermal field in the axisymmetric clamped-clamped rotating thick cylindrical shell with nonlinear variable thickness. This shell is subjected to mechanical and thermal load in two dimensions. The governing equations are formulated as a set of non-homogeneous ordinary differential equations with variable coefficients. The system of partial differential equations is semi-analytically solved by using (MLM). The solution of equations is obtained by applying boundary conditions and ensuring continuity between the layers. The problem is also solved, using the finite element method (FEM). The obtained results of the disk form multi-layers method (MLM) are compared with those of FEM.
Universal Journal of Mechanical Engineering, 2013
The objective of this work is to contribute with a simple and reliable numerical tool for the stress analysis of cylindrical vessels subjected to generalized forces using a mixed formulation. Variational techniques coupled with functional analysis are used to obtain an optimized solution for the shell displacement and further stress field evaluation using a combination of unknown analytic functions with Fourier expansions. A large cylindrical shell subjected to pinching loads is considered. These elements are intended to provide accurate modelling of the initially circular pipes response. Because of this behaviour, the bend's cross-section abandons its original roundness, turning into an oval or noncircular configuration. In addition, the initially plane cross-section, tends to deform out of its own plane. These two deformation patterns are termed ovalization and warping, respectively. In this work the results for the radial displacement and section ovalization are analysed where the solution has six terms for an acceptable accuracy. The transverse displacement presents important dependence on the shell thickness vs radius, where in the case of thin shells the ovalization is restricted to a local area and this is the case analysed. The proposed method leads to accurate results with low complex input data. The conclusions of this work are that the definition of the load system and boundary conditions are easily processed as the method has pre-defined possibilities for each load case or edge boundary conditions. An analytic solution is obtained and a low number of terms in the Fourier series show good accuracy as can be seen by a comparison with finite element methods.
Mathematical Problems in Engineering, 2009
The static buckling of a cylindrical shell of a four-lobed cross section of variable thickness subjected to non-uniform circumferentially compressive loads is investigated based on the thin-shell theory. Modal displacements of the shell can be described by trigonometric functions, and Fourier's approach is used to separate the variables. The governing equations of the shell are reduced to eight first-order differential equations with variable coefficients in the circumferential coordinate, and by using the transfer matrix of the shell, these equations can be written in a matrix differential equation. The transfer matrix is derived from the nonlinear differential equations of the cylindrical shells by introducing the trigonometric series in the longitudinal direction and applying a numerical integration in the circumferential direction. The transfer matrix approach is used to get the critical buckling loads and the buckling deformations for symmetrical and antisymmetrical shells....
Thermoelastic Analysis of Rotating Thick Truncated Conical Shells Subjected to Non-Uniform Pressure
Journal of Solid Mechanics, 2016
In the present work, a study of thermoelastic analysis of a rotating thick truncated conical shell subjected to the temperature gradient and non-uniform internal pressure is carried out. The formulation is based on first-order shear deformation theory (FSDT), which accounts for the transverse shear. The governing equations, derived using minimum total potential energy principle, are solved, using multi-layered method (MLM). The model has been verified with the results of finite element method (FEM) for several tapering angles of the truncated cone. The numerical results obtained are presented graphically and the effects of thermal and mechanical loading, tapering angle of truncated cone, and profile of internal pressure are studied in detail. © 2016 IAU, Arak Branch.All rights reserved.
Stress analysis of finite length cylinders of layered media
In this paper, we analyze an orthotropic, layered (0 • /90 •) and (0 • /core/0 •) sandwich cylinders under pressurized load with a diaphragm supported boundary conditions which is considered as a two dimensional (2D) plane strain boundary value problem of elasticity in (r, z) direction. A simplified numerical cum analytical approach is used for the analysis. Boundary conditions are satisfied exactly by using an analytical expression in longitudinal (z) direction in terms of Fourier series expansion. Resulting first order simultaneous ordinary differential equations (ODEs) with boundary conditions prescribed at r = r i , r o defines a two point boundary value problem (BVP), whose equations are integrated in radial direction through an effective numerical integration technique by first transforming the BVP into a set of initial value problems (IVPs). Numerical solutions are first validated for their accuracy with 1D solution of an infinitely long cylinder. Stresses and displacements in cylinders of finite lengths having various l/R and h/R ratios are presented for future reference.