Exact Solutions of Some Shear Dislocation Problems Involving a Stopping Effect

1997 ◽  
Vol 64 (1) ◽  
pp. 183-192
Author(s):  
Gwolong Lai ◽  
A. R. Robinson
Keyword(s):  
Exact Solutions ◽  
Analytical Approach ◽  
Circular Region ◽  
Self Similar ◽  
Superposition Technique ◽  
Stretching Effect ◽  
Elliptical Region

An analytical approach is developed for dealing with the sudden stopping of a shear dislocation that acts over an expanding circular or elliptical region. The analysis begins with the case of circular region. Despite the fact that this problem is not self-similar, it has been possible to express the solution as a superposition of several self-similar problems that have different degrees of homogeneity. The use of a new rotational superposition technique that includes a stretching effect developed by the authors allows the extension to elliptical shear dislocation problems.

scholarly journals Self-similar cosmological solutions in f(R,T) gravity theory

2021 ◽  
pp. 2150206
Author(s):  
José Antonio Belinchón ◽  
Carlos González ◽  
Sami Dib
Keyword(s):  
Exact Solutions ◽  
The Self ◽  
Exact Form ◽  
Field Equations ◽  
Self Similarity ◽  
Similarity Hypothesis ◽  
Geometrical Quantity ◽  
Cosmological Solutions ◽  
Self Similar ◽  
Matter Collineation

We study the [Formula: see text] cosmological models under the self-similarity hypothesis. We determine the exact form that each physical and geometrical quantity may take in order that the field equations (FE) admit exact self-similar (SS) solutions through the matter collineation approach. We study two models: the case[Formula: see text] and the case [Formula: see text]. In each case, we state general theorems which determine completely the form of the unknown functions [Formula: see text] such that the FE admit SS solutions. We also state some corollaries as limiting cases. These results are quite general and valid for any homogeneous SS metric[Formula: see text] In this way, we are able to generate new cosmological scenarios. As examples, we study two cases by finding exact solutions to these particular models.

Exact Solutions for Vibration of Multi-Span Rectangular Mindlin Plates

2002 ◽  
Vol 124 (4) ◽  
pp. 545-551 ◽  
Author(s):  
Y. Xiang ◽  
G. W. Wei
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Analytical Approach ◽  
Solution Method ◽  
Plate Boundary ◽  
Vibration Frequencies ◽  
Type Solution ◽  
Simply Supported ◽  
Space Technique ◽  
Benchmark Solutions

This paper presents the first-known exact solutions for the vibration of multi-span rectangular Mindlin plates with two opposite edges simply supported. The Levy type solution method and the state-space technique are employed to develop an analytical approach to deal with the vibration of rectangular Mindlin plates of multiple spans. Exact vibration frequencies are obtained for two-span square Mindlin plates with varying span ratios and two-, three- and four-equal-span rectangular Mindlin plates. The influence of the span ratios, the number of spans and plate boundary conditions on the vibration behavior of square and rectangular Mindlin plates is examined. The presented exact vibration results may serve as benchmark solutions for such plates.

scholarly journals Stability plate with longitudinal constructive discontinuity

2011 ◽  
Vol 9 (1) ◽  
pp. 23-33
Author(s):  
Snezana Mitic ◽  
Ratko Pavlovic
Keyword(s):  
Exact Solutions ◽  
Analytical Approach ◽  
Plate Theory ◽  
Elastic Stability ◽  
The Other ◽  
Uniform Thickness ◽  
Simply Supported ◽  
Thin Plate Theory ◽  
The Stability ◽  
Different Thickness

The influence of longitudinal constructive discontinuity on the stability of the plate in the domain of elastic stability is solved based on the classical thin plate theory. The constructive discontinuities divide the plate into fields of different thickness. The plate has two opposite edges simply supported while the other two edges can take any combination of free, simply supported and clamped conditions. The Levy method is used for the solution of the problem of stability, with the aim of developing an analytical approach when researching the stability of plates with longitudinal constructive discontinuities and also with the aim of obtaining exact solutions for plates with non-uniform thickness. The exact solutions for stability presented herein are very valuable as they may serve as benchmark results for researches in this area.

Self-similar elastic regime of filtration through moving boundary

2018 ◽  
Vol 13 (3) ◽  
pp. 64-72 ◽  
Author(s):  
S.V. Khabirov ◽  
S.S. Khabirov
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Boundary Problem ◽  
Moving Boundary ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Elastic Regime ◽  
Self Similar ◽  
The One ◽  
The Relationship

The one-dimensional problem of elastic filtration of fluid through moving boundary is considered. The boundary conditions for invariant problem is introduced. The problem is reduced to overdetermine boundary problem for Veber equation. The exact solutions are obtained. For arbitrary invariant filtration law the relationship between overdetermine invariant boundary conditions is obtained.

scholarly journals Self similar collapse and the Raychaudhuri equation

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
Shibendu Gupta Choudhury ◽  
Soumya Chakrabarti ◽  
Ananda Dasgupta ◽  
Narayan Banerjee
Keyword(s):  
Scalar Field ◽  
Exact Solutions ◽  
Gravitational Collapse ◽  
Similar Distribution ◽  
Raychaudhuri Equation ◽  
Conformally Flat ◽  
Flat Spacetime ◽  
Imperfect Fluid ◽  
Self Similar

AbstractThe role of the Raychaudhuri equation in studying gravitational collapse is discussed. A self-similar distribution of a scalar field along with an imperfect fluid in a conformally flat spacetime is considered for the purpose. The general focusing condition is found out and verified against the available exact solutions. The connection between the Raychaudhuri equation and the critical phenomena is also explored.

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