Buckling Analysis of an Orthotropic Elliptical Toroidal Shell

2009 ◽  
Author(s):  
D. Redekop
Keyword(s):  
Differential Quadrature Method ◽  
External Pressure ◽  
Buckling Analysis ◽  
Toroidal Shell ◽  
Shells Of Revolution ◽  
Good Correspondence ◽  
Elliptical Cross ◽  
Wide Range ◽  
Orthotropic Shells ◽  
Toroidal Shells

A theoretical solution is given for the linearized buckling problem of an orthotropic toroidal shell with an elliptical cross-section under external pressure loading. The solution is based on the Sanders-Budiansky shell theory, and makes use of the harmonic differential quadrature method. Theory developed earlier for the buckling of orthotropic shells of revolution, and the vibration of orthotropic elliptical toroidal shells, is incorporated in the present work. Numerical results obtained from the solution are compared with results given in the literature, and good correspondence is generally observed. A parametric study is then conducted, covering a wide range of material and geometric parameters. Regression formulas are derived, indicating the variation of the buckling pressure with the degree of orthotropy of the material. Overall, the study introduces a new tool for the buckling analysis of elliptical toroidal shells, and extends the information available for orthotropic toroidal shells.

Experimental and numerical buckling analysis of toroidal shell segments under uniform external pressure

2020 ◽  
Vol 150 ◽  
pp. 106689 ◽  
Author(s):  
Jian Zhang ◽  
Xin Wang ◽  
Wenxian Tang ◽  
Fang Wang ◽  
Baoji Yin
Keyword(s):  
External Pressure ◽  
Buckling Analysis ◽  
Toroidal Shell ◽  
Uniform External Pressure

Nonlinear Finite Element Analysis of a Toroidal Shell With Ring-Stiffened Ribs

2010 ◽  
Author(s):  
Qing-Hai Du ◽  
Wei-Cheng Cui ◽  
Zheng-Quan Wan
Keyword(s):  
Finite Element ◽  
Cylindrical Shell ◽  
Circular Cylindrical Shell ◽  
Structural Characteristics ◽  
External Pressure ◽  
Nonlinear Finite Element ◽  
Toroidal Shell ◽  
Shells Of Revolution ◽  
Element Analysis ◽  
Stiffened Cylindrical Shell

The toroidal shell is a special type of shells of revolution, which is hardly solved by analytical method. To show the nonlinear structural characteristics of a circular toroidal shell with ring-stiffened ribs due to external pressure, both material nonlinear and geometric nonlinear Finite Element Analyses (FEA) have been presented in this paper, especially for the stability to the type of pressure hull. In the presented Finite Element Method (FEM), the elastic-plastic stress-strain relations have been adopted, and the initial deflection of toroidal shell created by manufacture was also taken into account. The analytic results eventually indicate that by nonlinear FEA such a new type of ring-stiffened circular toroidal shell could be used to a main pressure hull as the traditional ring-stiffened circular cylindrical shell, which could obtain kinds of performance in underwater engineering, such as better stability and more reserve buoyancy to the classical ring-stiffened cylindrical shell.

Buckling of Externally Pressurized Toroidal Shell With Stiffened Ribs

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Yongmei Zhu ◽  
Bo Zhao ◽  
Binbin Chen ◽  
Xilu Zhao ◽  
Wenxian Tang ◽  
...  
Keyword(s):  
Cross Sections ◽  
Shell Thickness ◽  
External Pressure ◽  
Toroidal Shell ◽  
Single Wire ◽  
Test Models ◽  
Buckling Behavior ◽  
Practical Engineering ◽  
Discrete Ribs ◽  
Toroidal Shells

Abstract The buckling characteristics of toroidal shells with closed circular cross sections loaded with a static external pressure were investigated. Eight toroidal shell test models were developed: two ribless, two semicircular discrete ribs, two rectangular discrete ribs, and two rectangular continuous ribs. The geometry, toroidal shell thickness, buckling load, and failure of each model were measured and compared. The effects of different ribbing methods (discrete, continuous unidirectional single-wire, continuous unidirectional multiwire wound, and continuous bidirectional wound ribs) on the buckling behavior of a ribbed toroidal shell were investigated, and the results provide guidance for practical engineering.

scholarly journals Buckling Analysis of Orthotropic Thick Cylindrical Shells Considering Geometrical Imperfection Using Differential Quadrature Method (DQM)

2018 ◽  
Vol 48 (4) ◽  
pp. 45-60
Author(s):  
A. Maleki ◽  
A. Ahmadi
Keyword(s):  
Differential Quadrature Method ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Reduction Factor ◽  
Differential Quadrature ◽  
Buckling Load ◽  
Quadrature Method ◽  
Linear System Of Equations ◽  
Geometrical Properties ◽  
Orthotropic Shells

Abstract This paper presented a three dimensional analysis for the buckling behavior of an imperfect orthotropic thick cylindrical shells under pure axial or external pressure loading. Critical loads are computed for different imperfection parameter. Both ends of the shell have simply supported conditions. Governing differential equations are driven based on the second Piola–Kirchhoff stress tensor and are reduced to a homogenous linear system of equations using differential quadrature method. Buckling loads reduction factor is computed for different imperfection parameters and geometrical properties of orthotropic shells. The sensitivity is established through tables of buckling load reduction factors versus imperfection amplitude. It is shown that imperfections have higher effects on the buckling load of thin shells than thick ones. Results show that the presented method is very accurate and can capture the various geometrical imperfections observed during the manufacturing process or transportation.

scholarly journals About applicability of the winkler model for contact interaction of cylindrical elastoplastic shells with an elastic filler at external pressure

2020 ◽  
pp. 3-8
Author(s):  
Валентин Георгиевич Баженов ◽  
Елена Владимировна Нагорных ◽  
Дарья Анатольевна Самсонова
Keyword(s):  
Contact Interaction ◽  
Continuum Mechanics ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
External Pressure ◽  
Isotropic Hardening ◽  
Shells Of Revolution ◽  
Plastic Properties ◽  
Wide Range ◽  
Elastic Filler

Представлено сравнение результатов расчетов контактного взаимодействия и потери устойчивости упругопластических цилиндрических оболочек с упругим толстостенным заполнителем, выполненных на основе двух подходов: с позиций механики сплошных сред и теории оболочек типа Тимошенко с основанием Винклера. Оба подхода позволяют решать задачи деформирования и устойчивости непологих оболочек с учетом геометрических нелинейностей. Постановка с позиций механики сплошных сред позволяет аппроксимировать оболочку по толщине рядом слоев конечных элементов. Определяющие соотношения формулируются в переменных Лагранжа с использованием в качестве отсчетной неподвижной декартовой или цилиндрической системы координат. Кинематические соотношения записываются в метрике текущего состояния. Упругопластические свойства оболочек описываются теорией пластического течения с изотропным упрочнением. Уравнения движения следуют из баланса виртуальных мощностей работ. В первом подходе контактное взаимодействие оболочки и упругого тела моделируется условиями непроникания по нормали и свободного проскальзывания вдоль касательной. Во втором подходе контактное взаимодействие упругого заполнителя с оболочкой моделируется основанием Винклера. Оба подхода позволяют описать нелинейное докритическое деформирование оболочек вращения с упругим заполнителем, определить предельные (критические) нагрузки в широком диапазоне скоростей нагружения с учетом геометрических несовершенств формы. Оценивается область применимости гипотезы Винклера при контактном взаимодействии оболочки с упругой средой в зависимости от жесткости и толщины основания. Comparison of the results of calculations of contact interaction and loss of stability of elastoplastic cylindrical shells with an elastic thick-walled filler, performed on the basis of two approaches: from the standpoint of continuum mechanics and the theory of Timoshenko-type shells with a Winkler base is presented. Both approaches allow solving the problems of deformation and stability of non-sloping shells, taking into account geometric nonlinearities. The statement from the perspective of continuum mechanics makes it possible to approximate the shell in thickness by a number of layers of finite elements. The constitutive relations are formulated in Lagrange variables using a fixed Cartesian or cylindrical coordinate system as a reference. Kinematic relations are recorded in the metric of the current state. The elastic-plastic properties of shells are described by the theory of plastic flow with isotropic hardening. The equations of motion follow from the balance of the virtual powers of the jobs. In the first approach, the contact interaction of a shell and an elastic body is modeled by the conditions of nonpenetration along the normal and free slip along the tangent. In the second approach, the contact interaction of the elastic filler with the shell is modeled by the Winkler base. Both approaches allow one to describe the nonlinear subcritical deformation of shells of revolution with an elastic filler, to determine the limiting (critical) loads in a wide range of loading rates, taking into account the geometric imperfections of the shape. The area of applicability of the Winkler hypothesis is estimated for the contact interaction of a shell with an elastic medium, depending on the stiffness and thickness of the base.

scholarly journals Analysis of the fracture toughness parameters at the free edge in layered composites

2020 ◽  
pp. 49-59
Author(s):  
D. A Bondarchuk ◽  
B. N Fedulov ◽  
A. N Fedorenko ◽  
E. V Lomakin
Keyword(s):  
Contact Interaction ◽  
Continuum Mechanics ◽  
Constitutive Relations ◽  
External Pressure ◽  
Isotropic Hardening ◽  
Winkler Foundation ◽  
Shells Of Revolution ◽  
Plastic Properties ◽  
Elastic Core ◽  
Wide Range

The problem of deformation and elastoplastic buckling of shells of revolution with a thick-walled elastic core under combined static and dynamic loading is formulated in a two-dimensional planar formulation based on two approaches: full-scale modeling within the framework of continuum mechanics and a simplified formulation based on the hypotheses of the theory of shells of the Timoshenko type and the Winkler foundation. Both approaches allow solving the problems of deformation and stability of non-shallow shells on the basis of Timoshenko's hypotheses, taking into account geometric nonlinearities. The statement from the perspective of continuum mechanics makes it possible to approximate the shell in thickness by a number of layers of finite elements. The constitutive relations are formulated in Lagrange variables using a fixed Cartesian coordinate system as a reference one. Kinematic relations are recorded in the metric of the current state. The elastic-plastic properties of shells are described by the theory of plastic flow with isotropic hardening. The equations of motion follow from the balance of the virtual powers of the work. In the first approach, the contact interaction of a shell and an elastic body is modeled by the conditions of nonpenetration along the normal and free slip along the tangent. The nonpenetration conditions are satisfied only in the active phase of the contact interaction; if the contact is broken, they are replaced by conditions on the free surface. In the second approach, the contact interaction of the elastic core with the shell is modeled by the Winkler foundation. Both approaches allow one to describe the nonlinear subcritical deformation of shells of revolution with an elastic core, to determine the limiting (critical) loads in a wide range of loading rates, taking into account the geometric imperfections of the shape. Using both approaches, a numerical simulation of contact interaction problem of an elastoplastic cylindrical shell with a thick-walled elastic core at a quasi-static uniform external pressure is carried out. The study of the influence of the thickness and initial deflection of the shell, as well as the stiffness and thickness of the core, on the value of the critical pressure and the form of buckling has been carried out. Based on these calculations, a conclusion was made about a wide range of applicability of the Winkler foundation model.

scholarly journals Investigation of the Winkler foundation model applicability for describing the contact interaction of elastoplastic shells with a core under external pressure

2020 ◽  
pp. 36-48
Author(s):  
V. G Bazhenov ◽  
E. V Nagornykh ◽  
D. A Samsonova
Keyword(s):  
Contact Interaction ◽  
Continuum Mechanics ◽  
Constitutive Relations ◽  
External Pressure ◽  
Isotropic Hardening ◽  
Winkler Foundation ◽  
Shells Of Revolution ◽  
Elastic Core ◽  
Wide Range ◽  
Foundation Model

The problem of deformation and elastoplastic buckling of shells of revolution with a thick-walled elastic core under combined static and dynamic loading is formulated in a two-dimensional planar formulation based on two approaches: full-scale modeling within continuum mechanics and a simplified formulation based on the hypotheses of the theory of shells of the Timoshenko type and the Winkler foundation. Both approaches allow solving the problems of deformation and stability of non-shallow shells on the basis of Timoshenko's hypotheses, taking into account geometric nonlinearities. The statement from the perspective of continuum mechanics makes it possible to approximate the shell in thickness by a number of layers of finite elements. The constitutive relations are formulated in Lagrange variables using a fixed Cartesian coordinate system as a reference one. Kinematic relations are recorded in the metric of the current state. The elastic-plastic properties of shells are described by the theory of plastic flow with isotropic hardening. The equations of motion follow from the balance of the virtual powers of the work. In the first approach, the contact interaction of a shell and an elastic body is modeled by the conditions of nonpenetration along the normal and free slip along the tangent. The nonpenetration conditions are satisfied only in the active phase of the contact interaction; if the contact is broken, they are replaced by conditions on the free surface. In the second approach, the contact interaction of the elastic core with the shell is modeled by the Winkler foundation. Both approaches allow one to describe the nonlinear subcritical deformation of shells of revolution with an elastic core, to determine the limiting (critical) loads in a wide range of loading rates, taking into account the geometric imperfections of the shape. Using both approaches, a numerical simulation of epy contact interaction problem of an elastoplastic cylindrical shell with a thick-walled elastic core at a quasi-static uniform external pressure is carried out. The study of the influence of the thickness and initial deflection of the shell, as well as the stiffness and thickness of the core, on the value of the critical pressure and the form of buckling has been carried out. Based on these calculations, a conclusion was made about a wide range of applicability of the Winkler foundation model.

scholarly journals Differential Quadrature and Differential Transformation Methods in Buckling Analysis of Nanobeams

2019 ◽  
Vol 6 (1) ◽  
pp. 68-76 ◽  
Author(s):  
Subrat Kumar Jena ◽  
S. Chakraverty
Keyword(s):  
Boundary Conditions ◽  
Differential Quadrature Method ◽  
Nonlocal Parameter ◽  
Transformation Method ◽  
Nonlocal Theory ◽  
Buckling Analysis ◽  
Differential Quadrature ◽  
Load Parameter ◽  
Computationally Efficient ◽  
Differential Transformation

AbstractIn this paper, two computationally efficient techniques viz. Differential Quadrature Method (DQM) and Differential Transformation Method (DTM) have been used for buckling analysis of Euler-Bernoulli nanobeam incorporation with the nonlocal theory of Eringen. Complete procedures of both the methods along with their mathematical formulations are discussed, and MATLAB codes have been developed for both the methods to handle the boundary conditions. Various classical boundary conditions such as SS, CS, and CC have been considered for investigation. A comparative study for the convergence of DQM and DTM approaches are carried out, and the obtained results are also illustrated to demonstrate the effects of the nonlocal parameter, aspect ratio (L/h) and the boundary condition on the critical buckling load parameter.

Free vibrations of orthotropic shells of revolution with variable parameters

1978 ◽  
Vol 14 (8) ◽  
pp. 820-825
Author(s):  
E. I. Bespalova ◽  
Ya. M. Grigorenko ◽  
A. B. Kitaigorodskii ◽  
A. I. Shinkar'
Keyword(s):  
Free Vibrations ◽  
Shells Of Revolution ◽  
Variable Parameters ◽  
Orthotropic Shells
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