scholarly journals Plane stress state of a strip weakened by a crack

2019 ◽  
pp. 182-185
Author(s):  
V. V. Reut ◽  
Yu. V. Molokanov
Keyword(s):  
Stress State ◽  
Plane Stress ◽  
Integral Transform ◽  
Longitudinal Crack ◽  
Singular Integral Equations ◽  
Infinite Strip ◽  
Infinite Plane ◽  
Transform Method ◽  
One Dimensional ◽  
The One

The plane stress elastic infinite strip problem of a finite longitudinal crack is investigated. The method that can be applied to calculate the stress state and the displacements for an infinite and semi-infinite strip with the longitudinal crack and arbitrary configuration of the boundary conditions is proposed. The main advantage of this method lies in the absence of necessity for use of the apparatus of the matrix differential calculus. Initial problem is reduced to the one-dimensional boundary value problem with the help of the generalized scheme of the integral transform method. By using the inverse integral Fourier transform, the one-dimensional problem is reduced to solving of the system of singular integral equations on a finite interval. The solution of this system was constructed with the help of the method of orthogonal polynomials by means of the second kind Chebyshev polynomials series expansion of the unknown functions. A graph of dependence of the stress intensity factor (SIF) on the geometric parameters of the problem is plotted. It is shown that the SIF for the case of the said strip tends to the SIF for the case of an infinite plane as the width of the strip approaches infinity.

scholarly journals On the Stress State of the Semi-Strip with a Longitudinal Crack

2018 ◽  
Vol 10 (2) ◽  
pp. 104
Author(s):  
Natalya Vaysfeld ◽  
Zinaida Zhuravlova
Keyword(s):  
Stress State ◽  
Integral Equations ◽  
Singular Integral ◽  
Mechanical Load ◽  
Longitudinal Crack ◽  
Singular Integral Equations ◽  
Dimensional Problem ◽  
Green Matrix ◽  
One Dimensional ◽  
The One

The stress state of the elastic semi-strip is investigated in the paper. The lateral sides of the semi-strip are fixed and the semi-strip’s short edge is under the mechanical load. The longitudinal crack is located inside the semi-strip. The problem is reduced to the one-dimensional problem with the help of Fourier sin-, cos- transformation, which was applied directly to the Lame’s equilibrium equations and the boundary conditions. The one-dimensional problem is formulated is a vector form. Its solution is constructed with the help of the matrix differential calculation and the Green matrix-function, which was constructed in the bilinear form. The solution of the problem is reduced to the solving of three singular integral equations. The first equation in this system contains two fixed singularities in its kernel. To consider them the corresponding transcendental equation is constructed, and its roots are found. The special generalized method is applied to solve the system of singular integral equations. The stress intensity factors are calculated.

Longitudinal Impact of Semi-Infinite Elastic Bars: Plane Any Time Solution

2013 ◽  
Vol 81 (5) ◽  
Author(s):  
M. A. Malkov
Keyword(s):  
Analytical Solution ◽  
Exact Analytical Solution ◽  
The Other ◽  
Longitudinal Impact ◽  
Infinite Plane ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
Contact Surfaces ◽  
The One ◽  
The Impact

Using the Sobolev–Smirnov method, we have found the exact analytical solution of a longitudinal impact of semi-infinite plane elastic bars for any time after the impact. After collision, there are loading waves from contact surfaces of bars and unloading waves from lateral surfaces. Then the unloading waves reach the opposite surface of the bars and create the reflected loading waves. These loading waves reach the other surface of the bars and generate new unloading waves. The number of waves grows exponentially. The sum of waves tends to the wave of the one-dimensional approximation.

A Semi-Infinite Elastic Strip Bonded to an Infinite Strip

1980 ◽  
Vol 47 (4) ◽  
pp. 789-794 ◽  
Author(s):  
G. G. Adams
Keyword(s):  
Shear Stress ◽  
Stress Intensity ◽  
Singular Integral ◽  
Integral Transform ◽  
Singular Integral Equations ◽  
Infinite Strip ◽  
Elastic Strip ◽  
Stress Distributions ◽  
Intensity Factors ◽  
Concentrated Forces

The solution is obtained for the plane strain problem of a semi-infinite elastic strip whose end is bonded to and pressed against an infinite elastic strip. The infinite strip is supported by a pair of symmetrically located, concentrated forces. Using integral transform techniques, the solution is reduced to a set of singular integral equations of the second kind. The order of the singularity is determined and the equations are then solved numerically. The results show the normal and shear stress distributions as well as the stress-intensity factors for a range of support locations corresponding to various width ratios and material combinations.

Variational principle of the one-dimensional convection–dispersion equation with fractal derivatives

2021 ◽  
pp. 2150195
Author(s):  
Pin-Xia Wu ◽  
Wei-Wei Ling ◽  
Xiu-Mei Li ◽  
Liang-Jin Xie
Keyword(s):  
Dispersion Equation ◽  
Variational Formula ◽  
Nonsmooth Boundary ◽  
Transform Method ◽  
One Dimensional ◽  
Solution Structures ◽  
Fractal Space ◽  
Pollutant Migration ◽  
The One ◽  
The Given

The convection–dispersion equation has always been a classic equation for studying pollutant migration models. There are certain deviations in scientific research because of the existence of the impurity of the medium and the nonsmooth boundary. In this paper, we introduced the one-dimensional convection–dispersion equation with fractal derivatives in fractal space, and established the fractal variational formula of the equation through the semi-inverse method. The fractal variational formula we have obtained can provide the conservation laws in an energy form in the fractal space and possible solution structures of the given equation. An analytical solution is obtained through the two-scale transform method and Laplace transform.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Adiabatic large polarons in anisotropic molecular crystals

2011 ◽  
Vol 35 (1) ◽  
pp. 15-27
Author(s):  
Zoran Ivić ◽  
Željko Pržulj
Keyword(s):  
Energy Transfer ◽  
Effective Mass ◽  
Molecular Crystals ◽  
Single Chain ◽  
Proper Understanding ◽  
One Dimensional ◽  
Interchain Coupling ◽  
Large Polaron ◽  
The One

Adiabatic large polarons in anisotropic molecular crystals We study the large polaron whose motion is confined to a single chain in a system composed of the collection of parallel molecular chains embedded in threedimensional lattice. It is found that the interchain coupling has a significant impact on the large polaron characteristics. In particular, its radius is quite larger while its effective mass is considerably lighter than that estimated within the one-dimensional models. We believe that our findings should be taken into account for the proper understanding of the possible role of large polarons in the charge and energy transfer in quasi-one-dimensional substances.

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