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 Variants of determining correlations of deformation theory of plasticity in the calculation of shell of rotation on the basis of finite element method

2019 ◽  
Vol 15 (4) ◽  
pp. 315-322
Author(s):  
Yuriy V. Klochkov ◽  
Anatoliy P. Nikolaev ◽  
Olga V. Vakhnina ◽  
Mikhail Yu. Klochkov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cylindrical Shell ◽  
Deformation Theory ◽  
Plastic State ◽  
Plastic Deformations ◽  
Theory Of Plasticity ◽  
Is Development ◽  
Element Method

Relevance. The problems of decline of resource-demanding of objects of building and engineer dictate the necessity of consideration of processes of deformation of constructions at the resiliently-plastic state. The widely in-use theory of account of practical properties of material is a deformation theory of plasticity. The aim of the research is development of variants of receipt of determining correlations on the step of ladening at deformation of material outside a resiliency. Methods. Algorithms over of receipt of determining correlations of theory of small resiliently-plastic deformations are brought on the step of ladening in two variants. In the first they turn out differentiation of expressions of tensions as functions of deformations on the basis of deformation theory of plasticity; in the second determining correlations turn out on the basis of hypothesis about the proportion of components of deviators increases of tensions to components of deviators increases of deformations. Results. On the test example of calculation of the jammed cylindrical shell realization of the got determining correlations is presented.

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.

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.

Plastic Deformation Theory Application in Finite Element Analysis

2012 ◽  
Vol 594-597 ◽  
pp. 2723-2726
Author(s):  
Wen Shan Lin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Deformation Theory ◽  
Three Dimensional ◽  
Constitutive Laws ◽  
Constitutive Law ◽  
Element Analysis ◽  
Finite Element Program ◽  
Theory Of Plasticity ◽  
Element Program

In the present study, the constitutive law of the deformation theory of plasticity has been derived. And that develop the two-dimensional and three-dimensional finite element program. The results of finite element and analytic of plasticity are compared to verify the derived the constitutive law of the deformation theory and the FEM program. At plastic stage, the constitutive laws of the deformation theory can be expressed as the linear elastic constitutive laws. But, it must be modified by iteration of the secant modulus and the effective Poisson’s ratio. Make it easier to develop finite element program. Finite element solution and analytic solution of plasticity theory comparison show the answers are the same. It shows the derivation of the constitutive law of the deformation theory of plasticity and finite element analysis program is the accuracy.

Limit Dependences in Stability Calculations With Account for Physical Nonlinearity

2016 ◽  
Vol 33 (2) ◽  
pp. 157-160
Author(s):  
J. Rutman ◽  
V. Ulitin
Keyword(s):  
Critical State ◽  
Physical Nonlinearity ◽  
Solution Algorithm ◽  
Stability Calculation ◽  
Plastic Deformations ◽  
Thin Walled Structures ◽  
Calculated Stress ◽  
Thin Walled ◽  
Deformation Stress ◽  
Proportionality Limit

AbstractStability of bars, plates, shells, and other thin-walled structures in conditions of small physical nonlinearity is considered, when stresses exceed the proportionality limit, the amount of deformations being limited. Shanley's concept is used. The critical state is determined by means of some limit dependences. In a large number of cases, when creating efficient highly-stressed constructions, limited plastic deformations are allowed in them. When analysing stability in the critical state, the calculated stresses turn out to exceed the proportionality limit and the Young's modulus of elasticity turns out to be greater than the tangent modulus corresponding to the calculated stress on the diagram “deformation-stress”. The objective of this work is to show that stability calculation beyond the proportionality limit is reduced to the analysis of some limit dependences as well as to develop a general solution algorithm for similar problems.

scholarly journals Spatial thin-walled reinforced concrete structures taking into account physical nonlinearity in SCAD software. Rod finite element

2019 ◽  
Author(s):  
Sergiy Fialko ◽  
Viktor Karpilowskyi
Keyword(s):  
Finite Element ◽  
Reinforced Concrete ◽  
Plastic Flow ◽  
Deformation Theory ◽  
Numerical Solutions ◽  
Experimental Studies ◽  
Particle Method ◽  
Reinforced Concrete Beams ◽  
Principal Stresses ◽  
Theory Of Plasticity

This paper considers a spatial frame bar finite element for modeling reinforced concrete beams and columns. Both concrete and reinforcement are described by the equations of the deformation theory of plasticity and the theory of plastic flow. Degradation of concrete during cracking is modeled by the descending branch of the σ – ε diagram (the deformation theory of plasticity), as well as the compression of the yield surface and its displacement in the space of principal stresses (the plastic flow theory). The longitudinal reinforcement is considered discretely. It is assumed that there is no reinforcement slipping in concrete. The paper provides the results of the studies that reveal the causes of computational instability related to the presence of a descending branch of the σ – ε diagram for concrete, and proposes ways to overcome it. The reliability of the obtained results is confirmed by comparing them with the results of experimental studies performed by other researchers, as well as with the results of numerical solutions obtained by the particle method. This paper also provides an example of the nonlinear analysis of the fragment of a multi-storey building from the SCAD Soft collection of problems (www.scadsoft.com).

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