scholarly journals Plastic Flow in a Thin Layer: New Formulation of the Boundary-Value Problem and Its Solution

2019 ◽  
Vol 224 ◽  
pp. 01001
Author(s):  
Vagid Kadymov ◽  
Eugenе Sosenushkin
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Thin Sheet ◽  
Mathematical Formulation ◽  
Contact Boundary ◽  
Plastic Layer ◽  
Structural Elements ◽  
Sheet Rolling ◽  
Thin Plastic ◽  
New Formulation

The paper is dedicated to the theory of flow in a thin plastic layer that has numerous applications in calculations of technological processes of material treatment by pressure, such as stamping and pressing of thin-walled structural elements, thin-sheet rolling, and others. Two-dimensional, averaged over the thickness of the layer mathematical formulation of the contact boundary value problem of the spreading of a plastic layer on the plane has been examined. In the framework of the general “viscous liquid” model, an approximate analytical solution has been obtained and evaluated against measurements. This solution is in good agreement with the experimental results in the area far from the free boundary and the central part of the sample.

scholarly journals Plastic Flow in a Thin Layer: the Theory, Formulations of the Boundary- Value Problems and the Applications

2021 ◽  
Vol 248 ◽  
pp. 01018
Author(s):  
Vagid Kadymov ◽  
Elena Yanovskaya
Keyword(s):  
Heat Transfer ◽  
Boundary Value Problem ◽  
Mathematical Theory ◽  
Tensile Force ◽  
Boundary Value ◽  
Initial Time ◽  
Plastic Layer ◽  
Two Dimensional ◽  
Compression Force ◽  
Thin Plastic

Two-dimensional, averaged over the thickness of the layer, mathematical theory of the spreading of a plastic layer on the plane has been studied. General and simplified mathematical formulations of boundary value problem were presented. The problem of plastic stretching of a strip by forces applied on its “clamped” ends was investigated. The analysis of various modes of the process was carried out, which are determined by both the total compression force of the ends and the total tensile force. Mathematical analogy between the process of the free spreading of a plastic layer on the plane and the process of heat transfer was studied. For known forms of a domain occupied by a thin plastic layer at the initial time and for a given law of convergence of the plates, the evolution of the boundary of a plastic layer spreading was described. The exact particular solutions of the aforementioned problem was obtained.

scholarly journals AMPLITUDE – FREQUENCY CHARACTERISTICS OF SEISMIC IMPACT ON THE BUILDING WITH THE GROUND BASE AND THE COMPARISON OF THEORETICAL ESTIMATION WITH THE REAL EVENTS FROM THE DA TA BASE SMDB CGI

2015 ◽  
Author(s):  
К.С. Харебов ◽  
И.Д. Музаев ◽  
Н.И. Музаев
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Ground Surface ◽  
Frequency Characteristics ◽  
Contact Boundary ◽  
Soil Layers ◽  
Reflected Waves ◽  
Seismic Vibrations ◽  
Seismic Impact

В статье поставлена и решена многослойная контактная краевая задача сейсмических колебаний системы, состоящей из упруго-вязких слоев под застройкой. Краевая задача состоит из nдифференциальных уравнений описывающих поперечные сдвиговые колебания слоев грунта. На каждой поверхности контакта слоев грунта дифференциальные уравнения взаимосвязаны двумя граничными условиями, выражающими равенство перемещений и касательных напряжений в смежных слоях грунта. Последний глубинный слой считается полуограниченным. На бесконечности ставится условие ограниченности перемещения и частных производных перемещения. Поставленная краевая задача решена методом суперпозиции прямых и отраженных волн.Получены расчетные формулы для амплитуд сейсмических колебаний каждого слоя, в том числе и для дневной поверхности. Составлена соответствующая программа расчета на компьютере. Проведена расчетная оценка частотных характеристик грунта при сейсмическом воздействии. Проведено сравнение результатов расчетов с частотными параметрами реальных землетрясений на реальных площадках. The multilayer contact boundary-value problem of the seismic vibrations of the system, consisting of the elastic-viscous layers under the building, is set and solved. Boundary-value problem consists of n differential equations describing transversalshear vibrations of soil layers. On each contact surface of soil layers differential equations are interconnected by two boundary conditions, which express the equality of displacements and shearing stresses in the adjacent of soil layers. The last deep layer is considered semi-bounded. At infinity the limitedness of displacement and partial derivatives of displacement is stipulated.The presented boundary-value problem is solved by the method of the forward and reflected waves superposition. Calculation formulas for the seismic vibrations amplitudes of each layer, including for the ground surface are obtained.The corresponding program of calculation on the computer is created. The frequency characteristics evaluation of the seismic impact on the building is carried out. The comparison of results with the parameters of real earthquakes from the data base SMDB CGI is carried out.

The effect of focal depth on the spectra of P waves I. Theoretical formulation

1970 ◽  
Vol 60 (5) ◽  
pp. 1437-1456 ◽  
Author(s):  
Shyamal K. Guha
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Mathematical Formulation ◽  
Focal Depth ◽  
Point Sources ◽  
Body Waves ◽  
Elastic Plane ◽  
Theoretical Formulation ◽  
P Waves ◽  
Homogeneous Half Space

Abstract Since the Earth's free surface acts as a reflector, one may except the spectra of seismic body waves to be influenced by the focal depth of an earthquake. In order to investigate this effect, a boundary value problem has been formulated involving (n − 1) homogeneous, isotropic, perfectly elastic plane layers overlying a homogeneous half-space. The sources of the elastic waves are represented as discontinuities of stress across a conceptual interface inside the medium. Certain functions of the wave potentials which govern the solution of the boundary value problem are denoted as the source functions in the mathematical formulation of the problem. Expressions for the source functions for P and SV waves are derived for different kinds of point sources, including a double couple point source oriented in an arbitrary manner inside the medium.

Solving Unsteady Boundary Value Problems Using Discrete-Analytic Method for Non-Iterative Simulation of Temperature Processes in Time

2016 ◽  
Vol 685 ◽  
pp. 211-216 ◽  
Author(s):  
Vladimir N. Sidorov ◽  
Sergei M. Matskevich
Keyword(s):  
Heat Conduction ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Mathematical Formulation ◽  
Iterative Solution ◽  
Normal System ◽  
Matrix Functions ◽  
Unsteady State ◽  
State Heat ◽  
Different Types

Method for solving a boundary value problem of inhomogeneous unsteady-state heat conduction transfer is considered. This physical process can be described by a boundary value problem for a partial differential equation of the 2nd order. Discrete-analytical method, which turns out the mathematical formulation of the initial problem to be normal system of differential equations, was used. There is the non-iterative solution of such system, which is the set of analytic functions. The theory of matrix functions, particularly the properties of matrix exponential, was applied to get the solution. This approach allows us to model the unsteady-state heat conduction processes with unstationary boundary conditions of different types, defined as time-dependent functions. Such modeling describes the real physical processes in structural materials more accurately.

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