scholarly journals Theoretical Solutions to The Problem of Seepage and Consolidation in Saturated Clay Based on The Spatial Axisymmetric Model

2021 ◽  
Author(s):  
Zi-kun Gao ◽  
Jing-guo Wang
Keyword(s):  
Boundary Conditions ◽  
Time Variation ◽  
Fundamental Equation ◽  
Seepage Flow ◽  
Step Function ◽  
Series Expansions ◽  
Initial Condition ◽  
Series Solutions ◽  
Saturated Clay ◽  
Mathematical Justification

Abstract The series solutions to the problem of spatial axisymmetric consolidation are deduced under non-homogeneous boundary conditions. Firstly, differentiable step function is introduced to construct the homogeneous operation function. Secondly, the operation function is used to superimpose the non-homogeneous boundaries to obtain homogeneous boundaries, non-homogeneous fundamental equation and new initial condition. Finally, the method of variables separation is used to construct the eigenfunction, and due to the mathematical justification of complete orthogonality of the eigenfunction, the series expansions of the fundamental equation and initial condition are carried out to obtain solutions for the seepage and consolidation in saturated clay with a borehole boundary. The correctness of the theoretical solutions are verified by the strict mathematical and mechanics derivation and the law of space-time variation in seepage flow.

scholarly journals Short-time heat diffusion in compact domains with discontinuous transmission boundary conditions

2015 ◽  
Vol 26 (01) ◽  
pp. 59-110 ◽  
Author(s):  
Claude Bardos ◽  
Denis Grebenkov ◽  
Anna Rozanova-Pierrat
Keyword(s):  
Asymptotic Expansion ◽  
Boundary Conditions ◽  
Order Term ◽  
Heat Content ◽  
Resistance Coefficient ◽  
Small Time ◽  
Heat Diffusion ◽  
Heat Problem ◽  
Short Time ◽  
Mathematical Justification

We consider a heat problem with discontinuous diffusion coefficients and discontinuous transmission boundary conditions with a resistance coefficient. For all bounded (ϵ, δ)-domains Ω ⊂ ℝn with a d-set boundary (for instance, a self-similar fractal), we find the first term of the small-time asymptotic expansion of the heat content in the complement of Ω, and also the second-order term in the case of a regular boundary. The asymptotic expansion is different for the cases of finite and infinite resistance of the boundary. The derived formulas relate the heat content to the volume of the interior Minkowski sausage and present a mathematical justification to the de Gennes' approach. The accuracy of the analytical results is illustrated by solving the heat problem on prefractal domains by a finite elements method.

Experimentally Measured Boundary and Initial Conditions for Simulations

2014 ◽  
Vol 1041 ◽  
pp. 293-296 ◽  
Author(s):  
Dušan Katunský ◽  
Marek Zozulák ◽  
Marián Vertaľ ◽  
Jozef Šimiček
Keyword(s):  
Boundary Conditions ◽  
Indoor Environment ◽  
Initial Conditions ◽  
Weather Data ◽  
Initial Condition ◽  
Dynamic Boundary Conditions ◽  
Climate Monitoring ◽  
Set Up ◽  
Water Profile

Real dynamic boundary conditions and initial condition has to be taken into an account when simulations need to be done. The most helpful are in situ measurement facilities with climate monitoring. Indoor environment operation modes with different air temperature and relative humidity made indoor boundary conditions. Measured weather data are used to create complete boundary conditions for the research locality. Initial condition of masonry water profile is set up. The initial and boundary conditions are considered for an individual locality simulation proposes.

Heat Transfer in a Couple Stress Fluid over a Continuous Moving Surface with Internal Heat Generation and Convective Boundary Conditions

2012 ◽  
Vol 67 (5) ◽  
pp. 217-224 ◽  
Author(s):  
Tasawar Hayat ◽  
Zahid Iqbal ◽  
Muhammad Qasim ◽  
Omar M. Aldossary
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Heat Generation ◽  
Couple Stress ◽  
Couple Stress Fluid ◽  
Physical Parameters ◽  
Series Solutions ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
Moving Surface

This investigation reports the boundary layer flow and heat transfer characteristics in a couple stress fluid flow over a continuos moving surface with a parallel free stream. The effects of heat generation in the presence of convective boundary conditions are also investigated. Series solutions for the velocity and temperature distributions are obtained by the homotopy analysis method (HAM). Convergence of obtained series solutions are analyzed. The results are obtained and discussed through graphs for physical parameters of interest.

scholarly journals Propagação do calor em uma barra homogênea com condições de fronteira e dependendo de um parâmetro real

1981 ◽  
Vol 3 (3) ◽  
pp. 01
Author(s):  
Lilian M. Kieling Reis ◽  
Vanilde Bisognin
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Initial Condition

In this work the permanent temperature, in one homogeneous bar with boundary conditions that depends of a real parameters, was determined. The problem to be resolved was find the analytical solution of the heat equation ut =α2 uxx with the initial condition u (x, 0) = 0, ≤ x ≤ L and the contours conditions u (0, t) = 0 and u (L, t) = sen t, t> 0.

scholarly journals A modified Tikhonov regularization method for a class of inverse parabolic problems

2020 ◽  
Vol 28 (1) ◽  
pp. 181-204
Author(s):  
Nabil Saouli ◽  
Fairouz Zouyed
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Parabolic Problem ◽  
Tikhonov Regularization Method ◽  
Parabolic Problems ◽  
Initial Condition ◽  
Ill Posed ◽  
Convergence Estimates

AbstractThis paper deals with the problem of determining an unknown source and an unknown initial condition in a abstract final value parabolic problem. This problem is ill-posed in the sense that the solutions do not depend continuously on the data. To solve the considered problem a modified Tikhonov regularization method is proposed. Using this method regularized solutions are constructed and under boundary conditions assumptions, convergence estimates between the exact solutions and their regularized approximations are obtained. Moreover numerical results are presented to illustrate the accuracy and efficiency of the proposed method.

scholarly journals A problem of coefficient determination in parabolic equations solved as moment problem

2017 ◽  
Vol 6 (4) ◽  
pp. 109
Author(s):  
Maria Beatriz Pintarelli
Keyword(s):  
Boundary Conditions ◽  
Real Number ◽  
Moment Problem ◽  
Parabolic Equations ◽  
Arbitrary Real Number ◽  
Initial Condition ◽  
Moments Problem ◽  
Inverse Moment

The problem is to find a(t) y w(x; t) such that wt = a(t) (wx)x+r(x; t) under the initial condition w(x; 0) =fi(x) and the boundary conditions w(0; t) = 0 ; wx(0; t) = wx(1; t)+alfa w(1; t) about a region D ={(x; t); 0 <x < 1; t >0}. In addition it must be fulfilled the integral of w (x, t) with respect to x is equal to E(t) where fi(x) , r(x; t) and E(t) are known functions and alfa is an arbitrary real number other than zero.The objective is to solve the problem as an application of the inverse moment problem. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on moments problem. In addition, the method is illustrated with several examples.

Elastic waves from a spherical source: Aperiodic solutions for Scholte's model

1964 ◽  
Vol 54 (3) ◽  
pp. 897-908
Author(s):  
Tomowo Hirasawa
Keyword(s):  
Time Variation ◽  
Elastic Waves ◽  
Step Function ◽  
Wave Form ◽  
Type I ◽  
Type Ii ◽  
Spherical Coordinates ◽  
Force System ◽  
Spherical Source ◽  
S Waves

Abstract The radiation patterns of P and S waves from a spherical cavity, in an infinite elastic medium on which the stress similar to a single couple force acts, were obtained by J. G. J. Scholte and A. R. Ritsema (1962). In this paper the solution for their model is presented in the case when a step function is assumed as the time variation of the stress. As a result, it is found that the wave form of S waves depends on θ in spherical coordinates (r, θ, ø). Generally speaking, the orbit of the particle motion of S waves is not linear. Also the radiation pattern of S waves is similar to that for Type II rather than for Type I force system.

scholarly journals THE REACTIONS OF THE «BEAM – FOUNDATION» SYSTEM TO THE SUDDEN CHANGE OF THE BOUNDARY CONDITIONS

2018 ◽  
Vol 188 ◽  
pp. 03008 ◽  
Author(s):  
Vladimir A. Gordon ◽  
Olga V. Pilipenko ◽  
Vladimir A. Trifonov
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions ◽  
Dynamic Process ◽  
Sudden Change ◽  
Static Problem ◽  
Forced Vibrations ◽  
Winkler Foundation ◽  
Initial Condition ◽  
Foundation Parameters ◽  
Beam Foundation

The authors constructed a mathematical model of a dynamic process in a loaded beam on the elastic Winkler foundation in a sudden formation of a defect in the form of a change in the boundary conditions. The solution of the static problem of bending of the beam pinched at the ends served as the initial condition for the process of forced vibrations hinged supported at the ends of a beam, which arose after a sudden break in the connections that prevented the rotation of the end sections. The authors determined the dynamic increments of stresses in a beam for various combinations of a beam and foundation parameters.

Free In-Plane Vibration Analysis of Annular Plates with General Boundary Conditions

2013 ◽  
Vol 572 ◽  
pp. 189-192
Author(s):  
Dong Yan Shi ◽  
Xian Jie Shi ◽  
Wen L. Li ◽  
Zheng Rong Qin
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Current Method ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Series Solutions ◽  
Plane Vibration ◽  
Annular Plates ◽  
Special Cases

An analytical method is derived for the free in-plane vibration analysis of annular plates with general boundary conditions. Under this framework, all the classical homogeneous boundary conditions can be treated as the special cases when the stiffness for each restraining springs is equal to either zero or infinity. The improved Fourier series solutions for the in-plane vibrations are obtained by employing the Rayleigh-Ritz method. A numerical example is presented to demonstrate the accuracy and reliability of the current method.

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