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.

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.

Dynamic Propagation of Mode III: Crack Concerning Surfaces Subjected to Variable Moving Concentrated Loads

2010 ◽  
Vol 139-141 ◽  
pp. 2312-2315
Author(s):  
Cheng Jin ◽  
Ying Ba ◽  
Min Lin ◽  
Bao Ke Guo
Keyword(s):  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Moving Loads ◽  
Concentrated Loads ◽  
Mode Iii ◽  
Mode Iii Crack ◽  
Dynamic Propagation ◽  
Complex Functions ◽  
Self Similar ◽  
Superposition Theorem

Asymmetric dynamic propagation of mode III: crack under variable moving loads on the crack surface is investigated using the theory of complex functions. Using the approach of self-similar function, the problems are readily transformed into Riemann-Hilbert problems. The paper presents a new mechanical model for dynamic crack propagation, in which the crack is under the conditions that the variable concentrated loads Pt3/x2 and Pt/x move along x-axial with velocity β. And then, analytical solutions of stress, displacement and stress intensity factors are attained, respectively. These solutions are utilizable to attain solutions of arbitrarily complex problems, using the superposition theorem

Dynamic Propagation of Mode Ⅲ Interfacial Crack Subjected to Variable Moving Concentrated Loads

2011 ◽  
Vol 197-198 ◽  
pp. 1712-1717
Author(s):  
Cheng Jin ◽  
Ying Ba ◽  
Min Lin ◽  
Bao Ke Guo
Keyword(s):  
Mechanical Model ◽  
Crack Surface ◽  
Interfacial Crack ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Moving Loads ◽  
Concentrated Loads ◽  
Dynamic Propagation ◽  
Complex Functions ◽  
Self Similar

Dynamic propagation of mode Ⅲ crack under variable moving loads on the crack surface is investigated using the theory of complex functions. Using the approaches of self-similar functions, the problems are readily transformed into Riemann-Hilbert problems. The paper presents a new mechanical model for dynamic crack propagation, in which the crack is under the conditions that the variable concentrated loads Pt3/x2 and Px/t move along x-axial with velocity β. At last, analytical solutions of stress, displacement and stress intensity factor are attained, respectively.

scholarly journals Dynamic Crack Propagation Problems of Fibre-Reinforced Concrete

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Y. H. Cheng ◽  
Lu Nian Chun ◽  
Li Xin-gang
Keyword(s):  
Analytical Solutions ◽  
Dynamic Stress ◽  
Dynamic Crack Propagation ◽  
Crack Model ◽  
Dynamic Crack ◽  
Dynamic Stress Intensity Factors ◽  
Fibre Concrete ◽  
Complex Functions ◽  
Self Similar ◽  
Superposition Theorem

Applying the built dynamic crack model of fibre concrete, bridging fiber segment is substituted by loads. When a crack propagates its fiber continues to break. By the approaches of the theory of complex functions, the problems dealt with can be translated into Riemann-Hilbert problems. Analytical solutions of the displacements, stresses, and dynamic stress intensity factors under the action of of moving variable loads and , respectively, are attained by the ways of self-similar measures. After those analytical solutions are utilized by superposition theorem, the solutions of arbitrary complex problems can be obtained.

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.

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