Dissertation > Mathematical sciences and chemical > Mechanics > Solid Mechanics > Strength theory > Fracture theory

A Singular Integral Equation Method for the Branch Crack Problem in Antiplane Elasticity

Author WangFei
Tutor ChenYiZhou;WangZhongXian
School Jiangsu University
Course Solid Mechanics
Keywords Crack bifurcation Multiple cracks Periodic Cracks Anti- plane elasticity Dislocation Singular integral equation Stress intensity factor
CLC O346.1
Type Master's thesis
Year 2005
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In this paper, on the basis of previous studies , the use of complex function of knowledge and singular integral equations method , systematic study of anti- plane linear elastic branch crack problems and related numerical solution . This paper studied the infinite region where there is a single branch crack the case . Singular equation approach in the use of theoretical derivation , the use of the improvement over the integration scheme . Used to simulate the branch crack dislocations , the dislocations will focus placed on the bifurcation point , the distribution of dislocations are arranged at the crack of the branch. According to the boundary conditions established in order to concentrate the strength and continuous dislocation dislocation density of unknown function singular integral equations . And, by the displacement condition is a single value constraint equations . Numerical calculations, in the various branches of semi- open type of numerical integration formulas will be simplified as singular integral equations to solve algebraic equations , has been focused intensity dislocations and dislocation density functions of discrete values ??. And then come to work on the various branches of great concern to tip stress intensity factor values. In a single branch crack , based on the results of further anti- infinite plane elastic case , there are two large areas and periodic bifurcation branch crack crack answers. Quantitative analysis of the interaction between the crack and interact . Bifurcation in the periodic crack problem for numerical calculation of infinite series summation made ??effective approximation . This work was done using the method of singular integral equations and further study of anti-plane crack problem of providing a foundation. Programming with Fortran program very easy to implement the proposed numerical method . Accurate comparison of the results obtained . The paper also gives a number of examples , the numerical results and charts Sim can also be directly used in engineering practice .

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