scholarly journals Thermoelastic plastic deformation of a functional gradient material under conditions of central symmetry

2020 ◽  
pp. 238-246
Author(s):  
Евгений Павлович Дац ◽  
Евгений Валерьевич Мурашкин ◽  
Алексей Михайлович Буруруев ◽  
Тимофей Константинович Нестеров ◽  
Никита Эдуардович Стадник
Keyword(s):  
Plastic Deformation ◽  
Analytical Solution ◽  
Residual Stresses ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Gradient Material ◽  
Functional Gradient Material ◽  
Heated Object ◽  
Elastic Unloading ◽  
Thermoelastic Plastic

В работе рассматривается ряд краевых задач теории термоупругопластического деформирования материала в условиях тороидальной симметрии. Рассмотрен процесс упругой разгрузки предварительно нагретого объекта. Рассчитаны поля остаточных напряжений и перемещений. Получены точные формулы для аналитического решения поставленной краевой задачи A number of boundary value problems of the theory of thermoelastoplastic deformation of a material under conditions of toroidal symmetry are presented. The process of elastic unloading of a heated object is considered. The fields of residual stresses and displacements are calculated. Exact formulas are obtained for the analytical solution of the stated boundary value problem.

scholarly journals Calculation of residual stresses in the state of elastic unloading of a preheated inhomogeneous thermoelastoplastic material under conditions of toroidal symmetry

2021 ◽  
pp. 105-113
Author(s):  
Евгений Павлович Дац ◽  
Евгений Валерьевич Мурашкин ◽  
Алексей Михайлович Буруруев ◽  
Тимофей Константинович Нестеров ◽  
Никита Эдуардович Стадник
Keyword(s):  
Residual Stresses ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Analytical Approximation ◽  
Stress And Strain ◽  
Temperature Stresses ◽  
Strain Fields ◽  
Static Approximation ◽  
Toroidal Coordinates ◽  
Elastic Unloading

Статья посвящена численному моделированию остаточных напряжений в неоднородном торе. Материал тора полагается термоупругопластическим. Расчет температурных напряжений происходит в рамках квазистатического приближения. Рассчитываются поля остаточных напряжений и деформаций. Приводятся численные результаты решения краевой задачи в тороидальных координатах. Рассматриваются случаи длинного тора и возможность аналитического приближения исходной краевой задачи. The article is devoted to the numerical simulation of residual stresses in an inhomogeneous torus. The torus material is assumed to be thermoelastoplastic. The calculation of temperature stresses is carried out within the framework of the quasi-static approximation. Residual stress and strain fields are calculated. Numerical results of solving the boundary value problem in toroidal coordinates are presented. The cases of a long torus and the possibility of an analytical approximation of the original boundary value problem are considered

scholarly journals On the covergence of an iteration method for solving the boundary value problem in tile theory of elasto - platic deformation processes

1985 ◽  
Vol 7 (3) ◽  
pp. 6-12
Author(s):  
Dao Huy Bich ◽  
Nguyen Cong Hop
Keyword(s):  
Plastic Deformation ◽  
Boundary Value Problem ◽  
Iteration Method ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Uniqueness Of Solution ◽  
Deformation Processes ◽  
Tile Theory

In this paper is proposed an iteration method, as the Iliousin' s method for solving the boundary value problem in the theory of elasto - plastic deformation processes. The convergence of this method, i. e. the existence and uniqueness of  solution of the boundary value problem are also considered. 

scholarly journals The analytical solution of the 3D model with Robin's boundary conditions for 2 peat layers

2015 ◽  
Vol 3 ◽  
pp. 186
Author(s):  
Ērika Teirumnieka ◽  
Ilmārs Kangro ◽  
Edmunds Teirumnieks ◽  
Harijs Kalis
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Stationary Problem ◽  
Elliptic Type ◽  
Exponential Spline ◽  
Initial Boundary Value

<p>In this paper we consider averaging methods for solving the 3-D boundary value problem in domain containing 2 layers of the peat block. We consider the metal concentration in the peat blocks. Using experimental data the mathematical model for calculation of concentration of metal in different points in every peat layer is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for elliptic type partial differential equations of second order with piece-wise diffusion coefficients in every direction and peat layers.</p><p>The special parabolic and exponential spline, which interpolation middle integral values of piece-wise smooth function, are considered. With the help of this splines is reduce the problems of mathematical physics in 3-D with piece-wise coefficients to respect one coordinate to problems for system of equations in 2-D. This procedure allows reduce the 3-D problem to a problem of 2-D and 1-D problems and the solution of the approximated problem is obtained analytically.</p><p>The solution of corresponding averaged 2-D initial-boundary value problem is obtained also numerically, using for approach differential equations the discretization in space applying the central differences. The approximation of the 2-D non-stationary problem is based on the implicit finite-difference and alternating direction (ADI) methods. The numerical solution is compared with the analytical solution.</p>

scholarly journals Analytical Solution for the Boundary Value Problem of Elastic Beams Subjected to Distributed Load

2021 ◽  
Vol 17 (1) ◽  
pp. 75-93
Author(s):  
Mustapha Adewale Usman ◽  
Nur Nabilah Afja Mohd Afandi ◽  
Fatai Akangbe Hammed ◽  
Debora Oluwatobi Daniel
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Boundary Value Problem ◽  
Moving Load ◽  
Boundary Value ◽  
Elastic Beam ◽  
Beam Deflection ◽  
Elastic Beams ◽  
Distributed Load ◽  
Order Four

Analytical solution for the boundary value problem (BVP) of elastic beams subjected to distributed load was investigated. Based on the study, dynamic application curves are developed for beam deflection. The partial differential equation of order four were analysed to determine the dynamic response of the elastic beam under consideration and solved analytically. Effects of different parameters such as the mass of the load, the length of the moving load, the distance covered by the moving load, the speed of the moving and the axial force were considered. Result revealed that the values of the deflection with acceleration being considered are higher than the system where acceleration of the moving load is negligible. These obtained results are in agreement with the existing results.

Analytical Solution of Forced Vibration of a Column Subjected to Conservative and Nonconservative Forces

2001 ◽  
Author(s):  
Zhixiang Xu ◽  
Kunisato Seto ◽  
Hideyuki Tamura
Keyword(s):  
Analytical Solution ◽  
Boundary Value Problem ◽  
Integral Transform ◽  
Boundary Value ◽  
Suspension Bridge ◽  
Follower Force ◽  
Analysis Process ◽  
Finite Integral ◽  
Excitation Force ◽  
Integral Transform Technique

Abstract This paper presents analytical results of forced transverse vibration of a column with a mass attached at free-end subjected to a tangential follower force and a transverse distributed excitation force, that is a simplified model of some structures in civil and mechanical engineering, e.g., a column of a suspension bridge, a launched rocket in the atmosphere. Because the tangential follower force is nonconservative, it is very difficult to get the analytical solution of the problem by usually-used analysis methods with which the adjoint boundary value problem can not be directly obtained. However, by applying the finite integral transform technique, we directly obtained the adjoint boundary value problem in the analysis process, and successfully obtained the analytical solution of the column’s vibration excited by the transverse distributed force.

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