scholarly journals Calculation of thin isotropic shells beyond the elastic limit by the method of elastic solutions

2018 ◽  
Vol 196 ◽  
pp. 01014 ◽  
Author(s):  
Avgustina Astakhova
Keyword(s):  
Elastic Limit ◽  
Physical Nonlinearity ◽  
Elasticity Tensor ◽  
Thin Shells ◽  
Equilibrium Equations ◽  
Spherical Shells ◽  
Plastic Deformations ◽  
Elastic Plastic ◽  
Internal Forces

The paper focuses on the model of calculation of thin isotropic shells beyond the elastic limit. The determination of the stress-strain state of thin shells is based on the small elastic-plastic deformations theory and the elastic solutions method. In the present work the building of the solution based on the equilibrium equations and geometric relations of linear theory of thin shells in curved coordinate system α and β, and the relations between deformations and forces based on the Hirchhoff-Lave hypothesis and the small elastic-plastic deformations theory are presented. Internal forces tensor is presented in the form of its expansion to the elasticity tensor and the additional terms tensor expressed the physical nonlinearity of the problem. The functions expressed the physical nonlinearity of the material are determined. The relations that allow to determine the range of elastic-plastic deformations on the surface of the present shell and their changing in shell thickness are presented. The examples of the calculation demonstrate the convergence of elastic-plastic deformations method and the range of elastic-plastic deformations in thickness in the spherical shell. Spherical shells with the angle of half-life regarding 90 degree vertical symmetry axis under the action of equally distributed ring loads are observed.

scholarly journals Plastic deformations in the ring spherical shells

2018 ◽  
Vol 251 ◽  
pp. 04060
Author(s):  
Avgustina Astakhova
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Thin Shells ◽  
Stress Dependence ◽  
Strain Intensity ◽  
Spherical Shells ◽  
Plastic Deformations ◽  
Linear Hardening ◽  
Elastic Plastic ◽  
Development Area

In the present work the results of the study of plastic deformations distribution in the thickness in ring spherical shells are presented. Resolving differential equations system is based on the Hirchhoff-Lave hypothesis, linear thin shells theory and small elastic-plastic deformations theory. The studying of the development area of plastic deformations in shells thickness are performed with using the results of the elastic solutions method. The basic relations of elastic solutions method that allow to determine the distribution areas of plastic deformations in shells thickness and along the generatrix are presented. The diagram of intense stress dependence from the strain intensity with linear hardening is received. The numerical solution is performed by orthogonal run method. Long and short spherical shells under the operation of three evenly distributed ring loads are observed. The shells have a tough jamming along the contour at the bottom and at the top. Dependency between tension intensity and deformations intensity is accepted for the case of a material linear hardening. Area of plastic deformations in shells thickness for three kinds of ring spherical shells are shown. The results for the loads differed by the value in twice are presented.

scholarly journals An analytical solution for static problems of curved composite beams

2019 ◽  
Vol 6 (1) ◽  
pp. 105-116 ◽  
Author(s):  
István Ecsedi ◽  
Ákos József Lengyel
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Radial Displacement ◽  
Fundamental Solutions ◽  
Composite Beams ◽  
Shear Stresses ◽  
Equilibrium Equations ◽  
Euler Beam ◽  
Internal Forces

AbstractAn analytical solution is presented for the determination of deformation of curved composite beams. Each cross-section is assumed to be symmetrical and the applied loads are acted in the plane of symmetry of curved beam. In-plane deformations are considered of composite curved beams. Assumed form of the displacement field assures the fulfillment of the classical Bernoulli-Euler beam theory. The curvature of beam is constant and the internal forces in a cross-section is replaced by an equivalent forcecouple system at the origin of the cylindrical coordinate system used. The internal forces are expressed in terms of two kinematical variables, which are the radial displacement and the rotation of the cross-sections. The determination of the analytical solutions of the considered static problems are based on the fundamental solutions. Linear combination of the fundamental solutions which are filling to the given loading and boundary conditions, gives the total solution. Closed form formulae are derived for the radial displacement, cross-sectional rotation, nomral and shear forces and bending moments. The circumferential and radial normal stresses and shear stresses are obtained by the integration of equilibrium equations. Examples illustrate the developed method.

On the Accuracy of Some Shell Solutions

1959 ◽  
Vol 26 (4) ◽  
pp. 577-583
Author(s):  
G. D. Galletly ◽  
J. R. M. Radok
Keyword(s):  
Negative Curvature ◽  
Numerical Solutions ◽  
Asymptotic Solutions ◽  
Thin Shells ◽  
Shells Of Revolution ◽  
Equilibrium Equations ◽  
Influence Coefficients ◽  
Bending Loads ◽  
Edge Influence

Abstract R. B. Dingle’s method [1] for finding asymptotic solutions of ordinary differential equations of a type such as occur in the bending theory of thin shells of revolution is presented in outline. This method leads to the same results as R. E. Langer’s method [2], recently used for problems of this kind, and permits a simple analytical and less formal interpretation of the asymptotic treatment of such equations. A comparison is given of edge influence coefficients due to bending loads, obtained by use of these asymptotic solutions and numerical integration of the equilibrium equations, respectively. The particular shells investigated are of the open-crown, ellipsoidal, and negative-curvature toroidal types. The results indicate that the agreement between these solutions is satisfactory. In the presence of uniform pressure, the use of the membrane solutions for the determination of the particular integrals appears to lead to acceptable results in the case of ellipsoidal shells. However, in the case of toroidal shells, the membrane and the numerical solutions disagree significantly.

scholarly journals Problems in the strength and stability of inhomogeneous structures of rocket and space hardware with account for plasticity and creep

2021 ◽  
Vol 2021 (1) ◽  
pp. 3-15
Author(s):  
V.S. Hudramovich ◽  
◽  
V.N. Sirenko ◽  
E.L. Hart ◽  
D.V. Klimenko ◽  
...  
Keyword(s):  
High Cycle Fatigue ◽  
Physical Nonlinearity ◽  
Approximation Schemes ◽  
Stress And Strain ◽  
Structural Elements ◽  
Equilibrium Equations ◽  
Early Failure ◽  
Creep Deformations

Shell structures provide a compromise between strength and mass, which motivates their use in rocket and space hardware (RSH). High and long-term loads cause plastic and creep deformations in structural elements. RSH structures feature inhomogeneity: design inhomogeneity (polythickness, the presence of reinforcements, openings, etc.) and technological inhomogeneity (defects produced in manufacturing, operation, storage. and transportation, defects produced by unforeseen thermomechanical effects, etc.). These factors, which characterize structural inhomogeneity, are stress and strain concentrators and may be responsible for an early failure of structural elements and inadmissible shape imperfections. In inhomogeneous structures, different parts thereof are deformed by a program of their own and exhibit a different stress and strain level. In accounting for a physical nonlinearity, which is governed by plastic and creep deformations, the following approach to the determination of the stress and strain field is efficient: the calculation is divided into stages, and at each stage parameters that characterize the plastic and creep deformations developed are introduced: additional loads in the equilibrium equations or boundary conditions, additional deformations, or variable elasticity parameters (the modulus of elasticity and Poisson’s ratio). Successive approximation schemes are constructed: at each stage, an elasticity problem is solved with the introduction of the above parameters. Special consideration is given to the determination of the launch vehicle and launch complex life. This is due to damages caused by alternate high-intensity thermomechanical loads. The basic approach relies on the theory of low- and high-cycle fatigue. The plasticity and the creep of a material are the basic factors in the consideration of the above problems. This paper considers various aspects of the solution of RSH strength and stability problems with account for the effect of plastic and creep deformations.

scholarly journals Calculation of thin-walled axisymmetrically loaded structures of the AIC taking into account FEM-based physical nonlinearity

2020 ◽  
Vol 17 ◽  
pp. 00199
Author(s):  
Arsen Dzhabrailov ◽  
Anatoly Nikolaev ◽  
Natalya Gureeva
Keyword(s):  
Finite Element ◽  
Comparative Analysis ◽  
Shell Structure ◽  
Deformation Theory ◽  
Physical Nonlinearity ◽  
Plastic Deformations ◽  
Conjugation Conditions ◽  
Elastic Plastic ◽  
Theory Of Plasticity ◽  
Thin Walled

The article describes an algorithm for calculating an axisymmetrically loaded shell structure with a branching meridian, taking into account elastic-plastic deformations when loading based on the deformation theory of plasticity without assuming that the material is incompressible during plastic deformations. The correct relations which determine the static conjugation conditions of several revolution shells in the joint assembly are used. A comparative analysis of finite element solutions is presented for various options plasticity matrix development at the loading stage.

scholarly journals The method of determining internal forces at any cross section of links in mechanisms

2004 ◽  
Vol 26 (2) ◽  
pp. 110-121
Author(s):  
Do Sanh ◽  
Do Dang Khoa
Keyword(s):  
Cross Section ◽  
Analytical Mechanics ◽  
Equilibrium Equations ◽  
Closed Loops ◽  
Equal Zero ◽  
Mechanical Constraints ◽  
Reaction Forces ◽  
Internal Forces ◽  
The Cross

In the paper it is introduced a method of determining internal forces at any cross section of the links of mechanisms. As known, so far it is used the method of D'Alembert, which consists of two steps, the determination of the acceleration states of links and the establishment of the equilibrium equations for the set of forces including the forces of inertia and the internal forces at the cross section. A. I. Lurie proposed a method of analytical mechanics for this problem. Its concept is to make a new system called the released one by cutting the link at a cross section under consideration and adding some coordinates. Only one condition putting restriction on the released system is the additional coordinates must equal zero. Under this restriction the new created system is coincided to the original one. This restriction is equivalent to put the mechanical constraints, whose reaction forces are the components of internal forces at the cross section under consideration. It is necessary emphasize that the Lurie's method is convenient only for opened loops, but is not applied for closed ones. Moreover, the Lagrange's multiplier equations applied by A. I. Lurie are unsuitable. In this paper it is presented the generalized Lurie's method, which is applied for the opened and closed loops by using the Principle of Compatibility.

Determination of Internal Forces in End Plates of Simple End Plate Joints

2009 ◽  
Vol 12 (-1) ◽  
pp. 83-94
Author(s):  
Stefan Dominikowski ◽  
Piotr Bogacz
Keyword(s):  
End Plate ◽  
Internal Forces

scholarly journals Symmetric Nature of Stress Distribution in the Elastic-Plastic Range of Pinus L. Pine Wood Samples Determined Experimentally and Using the Finite Element Method (FEM)

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 39
Author(s):  
Łukasz Warguła ◽  
Dominik Wojtkowiak ◽  
Mateusz Kukla ◽  
Krzysztof Talaśka
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Stress Distribution ◽  
Moisture Content ◽  
Tool Geometry ◽  
Wood Fibers ◽  
Data Set ◽  
Plastic Deformations ◽  
Pine Wood ◽  
Elastic Plastic

This article presents the results of experimental research on the mechanical properties of pine wood (Pinus L. Sp. Pl. 1000. 1753). In the course of the research process, stress-strain curves were determined for cases of tensile, compression and shear of standardized shapes samples. The collected data set was used to determine several material constants such as: modulus of elasticity, shear modulus or yield point. The aim of the research was to determine the material properties necessary to develop the model used in the finite element analysis (FEM), which demonstrates the symmetrical nature of the stress distribution in the sample. This model will be used to analyze the process of grinding wood base materials in terms of the peak cutting force estimation and the tool geometry influence determination. The main purpose of the developed model will be to determine the maximum stress value necessary to estimate the destructive force for the tested wood sample. The tests were carried out for timber of around 8.74% and 19.9% moisture content (MC). Significant differences were found between the mechanical properties of wood depending on moisture content and the direction of the applied force depending on the arrangement of wood fibers. Unlike other studies in the literature, this one relates to all three stress states (tensile, compression and shear) in all significant directions (anatomical). To verify the usability of the determined mechanical parameters of wood, all three strength tests (tensile, compression and shear) were mapped in the FEM analysis. The accuracy of the model in determining the maximum destructive force of the material is equal to the average 8% (for tensile testing 14%, compression 2.5%, shear 6.5%), while the average coverage of the FEM characteristic with the results of the strength test in the field of elastic-plastic deformations with the adopted ±15% error overlap on average by about 77%. The analyses were performed in the ABAQUS/Standard 2020 program in the field of elastic-plastic deformations. Research with the use of numerical models after extension with a damage model will enable the design of energy-saving and durable grinding machines.

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