Numerical Analysis of the Stress-Strain State of a Body with Thin Inclusion by the Domain Decomposition Method

2016 ◽  
Vol 217 (3) ◽  
pp. 283-298
Author(s):  
A. O. Styahar ◽  
Ya. H. Savula ◽  
I. I. Dyyak
Keyword(s):  
Numerical Analysis ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Strain State ◽  
Domain Decomposition Method ◽  
Thin Inclusion ◽  
Stress Strain ◽  
Stress Strain State

scholarly journals On The Convergence of Domain Decomposition Algorithm for The Body with Thin Inclusion

2015 ◽  
Vol 9 (1) ◽  
pp. 27-32
Author(s):  
Andriy Styahar ◽  
Yarema Savula
Keyword(s):  
Domain Decomposition ◽  
Strain State ◽  
The Body ◽  
Decomposition Algorithm ◽  
Thin Inclusion ◽  
Stress Strain ◽  
Linear Elasticity Theory ◽  
Stress Strain State ◽  
Domain Decomposition Algorithm ◽  
Well Posed

Abstract We consider a coupled 3D model that involves computation of the stress-strain state for the body with thin inclusion. For the description of the stress-strain state of the main part, the linear elasticity theory is used. The inclusion is modelled using Timoshenko theory for shells. Therefore, the dimension of the problem inside the inclusion is decreased by one. For the numerical solution of this problem we propose an iterative domain decomposition algorithm (Dirichlet-Neumann scheme). This approach allows us to decouple problems in both parts and preserve the structure of the corresponding matrices. We investigate the convergence of the aforementioned algorithm and prove that the problem is well-posed.

Numerical Solution to the Contact Interaction Problem of Nuclear Fuel Element Components Using the Mortar Method and the Domain Decomposition Method

2021 ◽  
pp. 4-22
Author(s):  
P.S. Aronov ◽  
M.P. Galanin ◽  
A.S. Rodin
Keyword(s):  
Fuel Element ◽  
Domain Decomposition ◽  
Nuclear Fuel ◽  
Contact Interaction ◽  
Decomposition Method ◽  
Strain State ◽  
Domain Decomposition Method ◽  
Mortar Method ◽  
Stress Strain ◽  
Nuclear Fuel Element

The paper presents algorithms for solving axisymmetric contact interaction problems for several thermoelastic bodies using unmatched meshes. We employed the finite element method to obtain numerical solutions to problems of thermal conductivity and the theory of elasticity. We took contact interaction into account by applying the mortar method and the method of domain decomposition. The mortar method requires solving an ill-conditioned system of linear algebraic equations with a zero block at the main diagonal. To solve it numerically, we used a modified method of successive over-relaxation (MSSOR), which makes it possible to reduce solving the system of equations for all contacting bodies to sequentially solving systems of equations for each body separately. We showcase our algorithm results by solving an example problem simulating thermomechanical processes in a nuclear fuel element. We analyse the features of the stress-strain state in the structure and compare the results obtained using the mortar method and the domain decomposition method. The computational domain in the problem considered consisted of 10 nuclear fuel pellets and a cladding section. The analysis results showed that the quantitative stress-strain state properties in a system of bodies obtained by the two methods are quite close to each other. This confirms the fact that these algorithms may be correctly applied to solving similar problems

Numerical Analysis of Stress-Strain State and Crack Propagation in Welded Samples

2017 ◽  
Vol 265 ◽  
pp. 507-512
Author(s):  
M.S. Bisong ◽  
P.V. Sivtsev ◽  
V.V. Lepov
Keyword(s):  
Numerical Analysis ◽  
Crack Growth ◽  
Heat Affected Zone ◽  
Strain State ◽  
Stochastic Modelling ◽  
Hardness Test ◽  
Crack Size ◽  
Stress Strain ◽  
Mechanical Heterogeneity ◽  
Stress Strain State

The numerical analysis of stress-strain state of low-alloyed welded steel samples test has been considered. The mechanical heterogeneity has been estimated by the micro hardness test. The stress-strain state analysis is based on the models of linear elasticity, which are described by Lame equations for displacement. In this case the samples are considered as perfect welded samples without any welding defects. The discretization of the system of equations is done through the finite element method, and the numerical realization of the method is performed on collection of free software FEniCS. The defects influence has been estimated by stochastic modelling of viscous crack growth. The data for crack size in weld and heat affected zone was obtain from microscopic observation, and for mechanical properties from microhardness testing. The result obtained shows that, the distribution of displacement in all samples are almost the same. Between the welded zone, the heat affected zone and the external elliptic zone, the Von Mizes stress is almost the same in all three samples. Concerning the crack growth, the velocity of it propagation in welded zone is higher as much again than that in the heat affected zone. This research is beneficial to welders, modellers of structures, researches as a whole.

scholarly journals REGULARITIES OF THE LINING STRESS-STRAIN STATE DURING OF THE PYLON METRO STATION CONSTRUCTION

2021 ◽  
pp. 19-27
Author(s):  
D. O. BANNIKOV ◽  
V. P. KUPRII ◽  
D. YU. VOTCHENKO
Keyword(s):  
Finite Element ◽  
Numerical Analysis ◽  
Finite Elements ◽  
Strain State ◽  
Finite Element Models ◽  
Bending Moments ◽  
Stress Strain ◽  
Normal Forces ◽  
Stress Strain State ◽  
Station Structure

Purpose. Perform numerical analysis of the station structure. Take into account in the process of mathematical modeling the process of construction of station tunnels of a three-vaulted station. Obtain the regularities of the stress-strain state of the linings, which is influenced by the processes of soil excavation and lining construction. Methodology. To achieve this goal, a series of numerical calculations of models of the deep contour interval metro pylon station was performed. Three finite-element models have been developed, which reflect the stages of construction of a three-vaulted pylon station. Numerical analysis was performed on the basis of the finite element method, implemented in the calculation complex Lira for Windows. Modeling of the stress-strain state of the station tunnel linings and the soil massif was performed using rectangular, universal quadrangular and triangular finite elements, which take into account the special properties of the soil massif. Station tunnel linings are modeled by means of rod finite elements. Findings. Isofields of the stress-strain state in finite-element models reflecting the stages of construction are obtained. The vertical displacements and horizontal stresses that are characteristic of a three-vaulted pylon station are analyzed. The analysis of horizontal stresses proved that at the stage of opening of the middle tunnel the scheme of pylon operation is rather disadvantageous. The analysis of bending moments and normal forces was also carried out and the asymmetry of their distribution was noted. Originality. Based on the obtained patterns of distribution of stress-strain state and force factors, it is proved that numerical analysis of the station structure during construction is necessary to take measures to prevent or reduce deformation of frames that are in unfavorable conditions. Practical value. In the course of research, the regularities of changes in stresses, displacements, bending moments and normal forces in the models of the pylon station, which reflect the sequence of its construction, were obtained.

scholarly journals Numerical analysis of the stress-strain state of laminated springs

2009 ◽  
Vol 2 (2) ◽  
pp. 74-84
Author(s):  
V.M. Pestrenin ◽  
I.V. Pestrenina ◽  
N.F. Talantsev
Keyword(s):  
Numerical Analysis ◽  
Strain State ◽  
Stress Strain ◽  
Stress Strain State

Estimation of the accuracy of numerical analysis for the deformed state of power structures of technical objects

2018 ◽  
Author(s):  
А.Н. Рогалев ◽  
С.В. Доронин ◽  
В.В. Москвичев
Keyword(s):  
Finite Element ◽  
Numerical Analysis ◽  
Safety Factor ◽  
Stiffness Matrix ◽  
Strain State ◽  
Power Structures ◽  
Safety Factors ◽  
Rounding Errors ◽  
Stress Strain ◽  
Stress Strain State

Под силовыми конструкциями понимают технические устройства, составленные из различных частей, воспринимающие комплекс эксплуатационных нагрузок в штатных и аварийных режимах нагружения. При решении прикладных задач исследования напряженно-деформированных состояний силовых конструкций важна оценка степени близости к точному приближенного решения, полученного на вполне определенной сетке конечных элементов с конечной величиной шага сетки. С учетом влияния ошибок округления сходимость метода конечных элементов контролировать сложно: при большом числе конечных элементов решение может расходиться из-за накапливающихся ошибок округления, даже если условия сходимости выполняются. Описанное в статье применение методов обратного анализа ошибок позволяет достаточно точно контролировать точность численных оценок деформированного состояния силовых конструкций, что подтверждают расчеты, выполненные для практических задач. The solution of applied problems of technogenic safety, survivability, risk and protection is performed for structures which are close to limiting states. These states are characterized by decreasing safety factors down to one. In this case a mistaken estimation for safety factor may cause the situation when the calculated safety factor will be greater than one but the real safety factor will be less than one. Safety factors estimation is performed on the basis of calculation for stress-strain state characteristics. Thus, the issues of accuracy and reliability of determining stresses and deformations are an integral part of the problem of man-made safety. In the numerical analysis of the stress-strain state, the stiffness matrix of the design model is formed, the dimension of which reaches up to tens of millions. A large number of computations for tasks of this dimension is presumably leading to significant rounding errors. Ensuring the grid convergence of results by decreasing the grid spacing is inconsistent with the growth of computational errors due to rounding. For finite element analysis of power structures of technical objects, methods of a posteriori reverse error analysis are proposed that control the effect of rounding errors on the result when solving a solving system of linear algebraic equations. The coefficient matrix of this system is the stiffness matrix of the finite element model. The basic idea is to obtain and solve a system of equations with a known exact solution. Comparison of the results of exact and numerical solutions allows us to estimate the magnitude of the error.

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