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.

Dynamic Stress and Deformation of Non-Homogeneous Poroelastic Shells of Revolution Saturated in Viscous Fluid

2009 ◽  
Vol 407-408 ◽  
pp. 305-308 ◽  
Author(s):  
Takeshi Gonda ◽  
Katsumi Tao ◽  
Shigeru Otsuka ◽  
Masaki Yakabe
Keyword(s):  
Viscous Fluid ◽  
Shell Thickness ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Elastic Solid ◽  
Shells Of Revolution ◽  
Difference Formula ◽  
Difference Form ◽  
Stress And Deformation ◽  
Fundamental Equations

This paper describes an analytical formulation and a numerical solution of the elastic dynamic problems of non-homogeneous poroelastic shells of revolution saturated in viscous fluid. The porosity and porous diameter of the material are assumed to be continuously varied along the shell thickness. The equations of motion and the relations between strains and displacements are derived by extending the Sanders shell theory. As the constitutive relations, the consolidation theory of Biot for models of fluid-solid mixtures is employed. The flow of viscous fluid through a porous elastic solid is governed by Darcy's law. In the numerical analysis of the fundamental equations an usual finite difference form is employed for the spatial derivatives and the inertia terms are treated with the backward difference formula proposed by Houbolt. As a numerical example, the simply supported cylindrical shell under a semi-sinusoidal internal load with respect to time is analyzed. Numerical computations are carried out by changing porosity and mean void radius along the shell thickness, and the variations of pore pressure, displacements and internal forces with time are analyzed.

Dynamic Stress and Deformation of Non-Homogeneous Poroelastic Moderately Thick Shells of Revolution Saturated in Viscous Fluid

2013 ◽  
Vol 652-654 ◽  
pp. 1466-1470
Author(s):  
Takeshi Gonda ◽  
Shigeru Otsuka ◽  
Masaki Yakabe ◽  
Katsumi Tao
Keyword(s):  
Viscous Fluid ◽  
Shell Thickness ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Elastic Solid ◽  
Shells Of Revolution ◽  
Difference Formula ◽  
Naghdi Shell ◽  
Stress And Deformation ◽  
Thick Shells

This paper describes an analytical formulation and a numerical solution of the elastic dynamic problems of non-homogeneous poroelastic moderately thick shells of revolution saturated in viscous fluid. The porosity and porous diameter of the material are assumed to be continuously varied along the shell thickness. The equations of motion and the relations between strains and displacements are derived from the Reissner-Naghdi shell theory. As the constitutive relations, the consolidation theory of Biot for models of fluid-solid mixtures is employed. The flow of viscous fluid through a porous elastic solid is governed by Darcy's law. In the numerical analysis of the fundamental equations an usual finite difference form is employed for the spatial derivatives and the inertia terms are treated with the backward difference formula proposed by Houbolt. As a numerical example, the simply supported cylindrical shell under a semi-sinusoidal internal load with respect to time is analyzed. Numerical computations are carried out by changing porosity and mean void radius along the shell thickness, and the variations of pore pressure, displacements and internal forces with time are analyzed.

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.

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

Calculation of the primary trajectories of seeds and other particles in strong winds

1983 ◽  
Vol 219 (1215) ◽  
pp. 217-217
Keyword(s):  
Equations Of Motion ◽  
Aerodynamic Resistance ◽  
Reynolds Numbers ◽  
Spherical Particles ◽  
Spores And Pollen ◽  
General Terms ◽  
Wide Range ◽  
Strong Winds ◽  
Dispersal Distances ◽  
Enormous Number

The movement of variously dense spherical particles representing a variety of seeds, fruits, spores and pollen, and released from rest into arbitrary winds and a gravitational field is discussed in general terms that account in detail for changes in the quasi-static aerodynamic resistance to motion experienced by such particles during aerial flight. A hybrid analytical-empirical law is established which describes this resistance fairly accurately for particle Reynolds numbers in the range 0—60 000 and that allows for the numerical integration of the equations of motion so as to cover a very wide range of flight conditions. This makes possible the provision of a set of four-parameter universal range tables from which the dispersal distances for an enormous number of practical cases may be estimated. One particular case of particle movement in a region of pseudo-thermal convection is also discussed and this shows how a marked degree of deposition concentration may be induced in some circumstances by such a flow. Botanists and ecologists concerned with seed and particle dispersal in the environment may find the universal range tables of particular interest and use. This is because the tables obviate the need for the integration of the equations of motion when dealing with individual cases and permit an estimation of range purely on the basis of the specified quantities of particle size, density and altitude of release, atmospheric wind speed, density and viscosity, and the acceleration due to gravity.

Atomistic Aspects of Fracture Modelling in the Framework of Continuum Mechanics

1998 ◽  
Vol 538 ◽  
Author(s):  
F. Cleri
Keyword(s):  
Continuum Mechanics ◽  
Constitutive Relations ◽  
Point Of View ◽  
Atomic Scale ◽  
Continuum Models ◽  
Cohesive Law ◽  
Macroscopic Models ◽  
Scale Models ◽  
Level Information ◽  
Set Up

AbstractThe validity and predictive capability of continuum models of fracture rests on basic informations whose origin lies at the atomic scale. Examples of such crucial informations are, e.g., the explicit form of the cohesive law in the Barenblatt model and the shear-displacement relation in the Rice-Peierls-Nabarro model. Modem approaches to incorporate atomic-level information into fracture modelling require to increase the size of atomic-scale models up to millions of atoms and more; or to connect directly atomistic and macroscopic, e.g. finite-elements, models; or to pass information from atomistic to continuum models in the form of constitutive relations. A main drawback of the atomistic methods is the complexity of the simulation results, which can be rather difficult to rationalize in the framework of classical, continuum fracture mechanics. We critically discuss the main issues in the atomistic simulation of fracture problems (and dislocations, to some extent); our objective is to indicate how to set up atomistic simulations which represent well-posed problems also from the point of view of continuum mechanics, so as to ease the connection between atomistic information and macroscopic models of fracture.

Uncertainty in Collapse Strength Prediction of Sandwich Pipelines

2021 ◽  
Author(s):  
U. Bhardwaj ◽  
A. P. Teixeira ◽  
C. Guedes Soares
Keyword(s):  
Probabilistic Models ◽  
Uncertainty Propagation ◽  
Simulation Method ◽  
External Pressure ◽  
Design Parameters ◽  
Collapse Strength ◽  
Parameters Uncertainty ◽  
Wide Range ◽  
Model Predictions ◽  
Strength Models

Abstract This paper assesses the uncertainty in the collapse strength of sandwich pipelines under external pressure predicted by various strength models in three categories based on interlayer adhesion conditions. First, the validity of the strength models is verified by comparing their predictions with sandwich pipeline collapse test data and the corresponding model uncertainty factors are derived. Then, a parametric analysis of deterministic collapse strength predictions by models is conducted, illustrating insights of models’ behaviour for a wide range of design configurations. Furthermore, the uncertainty among different model predictions is perceived at different configurations of outer and inner pipes and core thicknesses. A case study of a realistic sandwich pipeline is developed, and probabilistic models are defined to basic design parameters. Uncertainty propagation of models’ predictions is assessed by the Monte Carlo simulation method. Finally, the strength model predictions of sandwich pipelines are compared to that of an equivalent single walled pipe.

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