Dislocation Distribution Function of the Mode III Dynamic Crack Subjected to Moving Unit Step Load from a Point

2011 ◽  
Vol 314-316 ◽  
pp. 872-876
Author(s):  
Yun Tao Wang ◽  
Nian Chun Lü ◽  
Jin Kang Zheng ◽  
Jin Cheng
Keyword(s):  
Distribution Function ◽  
Analytical Solutions ◽  
Mixed Boundary ◽  
Dynamic Stress Intensity Factor ◽  
Distribution Functions ◽  
Dynamic Crack ◽  
Mode Iii ◽  
Dislocation Distribution ◽  
Unit Step ◽  
The Relationship

Dislocation distribution functions of the edges of mode III propagation crack subjected to Moving unit step load from a point was studied by the methods of the theory of complex variable functions.By the methods, the problems researched can be facilely transformed into Riemann-Hilbert problems and Keldysh-Sedov mixed boundary value problems. Analytical solutions of stresses, displacements, dynamic stress intensity factor and dislocation distribution function were obtained by the methods of the theory of self-similar functions.In terms of the relationship between dislocation distribution functions and displacements, analytical solutions of dislocation distribution functions were attained.

Dislocation Distribution Functions of the Edges of Mode I Crack under Several Boundary Conditions

2012 ◽  
Vol 619 ◽  
pp. 98-102
Author(s):  
Yun Tao Wang ◽  
Nian Chun Lü ◽  
Chao Ying Wang ◽  
Jin Cheng
Keyword(s):  
Analytical Solutions ◽  
Mixed Boundary ◽  
Distribution Functions ◽  
Mode I ◽  
Dynamic Crack ◽  
Dynamic Stress Intensity Factors ◽  
Dislocation Distribution ◽  
Crack Propagation Velocity ◽  
Self Similar ◽  
The Relationship

Dislocation distribution functions of mode I dynamic crack subjected to two loads were studied by the methods of the theory of complex variable functions. By this way, the problems researched can be translated into Riemann-Hilbert problems and Keldysh-Sedov mixed boundary value problems. Analytical solutions of stresses, displacements and dynamic stress intensity factors were obtained by the measures of self-similar functions and corresponding differential and integral operation. The analytical solutions attained relate to the crack propagation velocity and time, but the solutions have nothing to the other parameters. In terms of the relationship between dislocation distribution functions and displacements, analytical solutions of dislocation distribution functions were gained, and variation rules of dislocation distribution functions were depicted.

Dislocation Distribution Model of Mode I Dynamic Crack

2011 ◽  
Vol 214 ◽  
pp. 235-239
Author(s):  
Yun Tao Wang ◽  
Nian Chun Lü
Keyword(s):  
Analytical Solutions ◽  
Mixed Boundary ◽  
Distribution Functions ◽  
Distribution Model ◽  
Mode I ◽  
Dynamic Crack ◽  
Dynamic Stress Intensity Factors ◽  
Dislocation Distribution ◽  
Crack Propagation Velocity ◽  
The Relationship

Dislocation distribution functions of mode I dynamic crack subjected to two loads were studied by the methods of the theory of complex variable functions. By this way, the problems researched can be translated into Riemann-Hilbert problems and Keldysh-Sedov mixed boundary value problems. Analytical solutions of stresses, displacements and dynamic stress intensity factors were obtained by the measures of self-similar functions and corresponding differential and integral operation. The analytical solutions attained relate to the crack propagation velocity and time, but the solutions have nothing to the other parameters. In terms of the relationship between dislocation distribution functions and displacements, analytical solutions of dislocation distribution functions were gained, and variation rules of dislocation distribution functions were depicted.

Dislocation Distribution Function of the Surfaces of Mode III Dynamic Crack Subjected to Unit-Step Loads and Moving Increasing Loads

2006 ◽  
Vol 324-325 ◽  
pp. 101-104
Author(s):  
Xin Gang Li ◽  
Nian Chun Lü ◽  
Guo Zhi Song ◽  
Cheng Jin
Keyword(s):  
Distribution Function ◽  
Analytical Solution ◽  
Crack Propagation ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Mode Iii ◽  
Dislocation Distribution ◽  
Unit Step ◽  
Complex Functions ◽  
Self Similar

By the theory of complex functions, dislocation distribution function concerning mode dynamic crack propagation problem under the conditions of unit-step loads and moving increasing loads was studied respectively. Analytical solution representations are attained by the methods of self-similar functions. The problems investigated can be transformed into Riemann-Hilbert problems and their closed solutions are obtained rather simple by this approach.

scholarly journals DC3 Pairs and the Set of Discontinuities in Distribution Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Lidong Wang ◽  
Piotr Oprocha ◽  
Hui Wang
Keyword(s):  
Distribution Function ◽  
Distribution Functions ◽  
Continuous Map ◽  
The Relationship

We study the relationship between DC3 pairs and the set of discontinuities in distribution function. We also check relations between DC3 pairs for a continuous map and its higher iterates.

Mode III Yoffe Dynamic Crack Problem on the Interface between Dissimilar Materials

2007 ◽  
Vol 353-358 ◽  
pp. 42-45 ◽  
Author(s):  
Cheng Jin ◽  
Xin Gang Li ◽  
Li Zhang
Keyword(s):  
Crack Problem ◽  
Dynamic Stress Intensity Factor ◽  
Dissimilar Materials ◽  
Shear Loading ◽  
Dynamic Crack ◽  
Mode Iii ◽  
Moving Crack ◽  
Plane Shear ◽  
Shear Moduli ◽  
Laminated Material

A moving crack in a laminated structure with free boundary subjected to anti-plane shear loading is investigated in this paper. Using the bonding conditions of the interface between different media, all the quantities in our question have been represented with a single unknown function, and the problem is transformed into a dual integrated equation with the method of Fourier transform. The equation is solved using Schmidt method. Finally the numerical results show the relationships among the dynamic stress intensity factor and crack velocity, the height of different laminated material, shear moduli of different laminated material.

scholarly journals An Analysis of Relationship among Income Inequality, Poverty, and Income Mobility, Based on Distribution Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Jiandong Chen ◽  
Yaqing Si ◽  
Fengying Li ◽  
Aifeng Zhao
Keyword(s):  
Distribution Function ◽  
Income Inequality ◽  
Research Result ◽  
Distribution Functions ◽  
Logistic Distribution ◽  
Urban Residents ◽  
Income Mobility ◽  
Common Distribution ◽  
New Perspective ◽  
The Relationship

Many studies show that the relationship among income inequality, poverty, and income mobility needs to be further discussed. Meanwhile, some researches on Distribution Function offer new perspective and methods to analyze this issue. First, this paper expresses the relationship among the Gini coefficient, poverty ratio, and income mobility of 5 common Distribution Functions through math deduction; this finding cannot be found in relevant literatures. Furthermore, an empirical research result proves that the income distribution of urban residents in the period from 2005 to 2010 fits Log-Logistic Distribution. On the basis of the above analysis and empirical data, the paper explores the relations of income inequality, poverty, and income mobility of urban residents and draws some useful conclusions.

scholarly journals Comparable analysis of the distribution functions of runup heights of the 1896, 1933 and 2011 Japanese Tsunamis in the Sanriku area

2012 ◽  
Vol 12 (5) ◽  
pp. 1463-1467 ◽  
Author(s):  
B. H. Choi ◽  
B. I. Min ◽  
E. Pelinovsky ◽  
Y. Tsuji ◽  
K. O. Kim
Keyword(s):  
Distribution Function ◽  
Field Survey ◽  
Tsunami Wave ◽  
Distribution Functions ◽  
Statistical Characteristics ◽  
Statistical Independence ◽  
Wave Heights ◽  
Abstract Data ◽  
Log Normal ◽  
The Relationship

Abstract. Data from a field survey of the 2011 Tohoku-oki tsunami in the Sanriku area of Japan is used to plot the distribution function of runup heights along the coast. It is shown that the distribution function can be approximated by a theoretical log-normal curve. The characteristics of the distribution functions of the 2011 event are compared with data from two previous catastrophic tsunamis (1896 and 1933) that occurred in almost the same region. The number of observations during the last tsunami is very large, which provides an opportunity to revise the conception of the distribution of tsunami wave heights and the relationship between statistical characteristics and the number of observed runup heights suggested by Kajiura (1983) based on a small amount of data on previous tsunamis. The distribution function of the 2011 event demonstrates the sensitivity to the number of measurements (many of them cannot be considered independent measurements) and can be used to determine the characteristic scale of the coast, which corresponds to the statistical independence of observed wave heights.

Analytical Solutions of Mode III Moving Crack under Concentrated Force Boundary Condition

2011 ◽  
Vol 214 ◽  
pp. 271-275
Author(s):  
Yun Tao Wang ◽  
Nian Chun Lü ◽  
Cheng Jin
Keyword(s):  
Analytical Solutions ◽  
Dynamic Stress ◽  
Hilbert Problem ◽  
Dynamic Crack ◽  
Mode Iii ◽  
Moving Crack ◽  
Dynamic Stress Intensity Factors ◽  
Concentrated Force ◽  
Complex Functions ◽  
Self Similar

By application of the theory of complex functions, the problem for mode Ⅲ dynamic crack under concentrated force were researched. The Riemann-Hilbert problem is formulated according to relationships of self-similar functions. Analytical solutions of stresses, displacements and dynamic stress intensity factors were obtained by the measures of self-similar functions and corresponding differential and integral operation.

Scaling

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Distribution Function ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Power Law ◽  
Scaling Laws ◽  
Power Laws ◽  
Distribution Functions ◽  
Temporal Process ◽  
Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

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