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 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 Modelling of elastic-plastic behavior of cables

2018 ◽  
Vol 174 ◽  
pp. 03001
Author(s):  
Oleksandr Shimanovsky
Keyword(s):  
Cross Section ◽  
Material Behavior ◽  
Structural Systems ◽  
Plastic Behavior ◽  
Rigid Plastic ◽  
Limit Values ◽  
Plastic Deformations ◽  
Linear Hardening ◽  
Elastic Plastic ◽  
Deflected Mode

The paper describes general calculation theory and elasticplastic behavior of cables - bearing elements of suspension structural systems. It is mentioned that this theory is based almost on the same assumptions as the theory of cable calculation at behavior of material in elastic range, excluding additional supposition in the part of idealization of real dependence between stresses and deformations on account of difficulties with using the latter in actual structures design. For that reason, this dependence is replaced with a model in the form of analytic curve or, as it is accepted to say in this case, a diagram, which is built according to some simple mathematic rule, reflecting element behavior conditions and characteristics of its material. It is stated that four main models of material behavior are used in practice: elastic-plastic, elastic-plastic with linear hardening, rigid-plastic and rigid-plastic with linear hardening. Conditions of occurrence of plastic deformations in all behavior stages of cable cross section are determined. Interrelations for geometrically and physically nonlinear task of the cable at active loading are provided. Methods are given and limit values of loads acting on the cable are determined. Equations defining parameters of cable deflected mode in all deformation phases and conditions of changing phases of cable behavior are given.

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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