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Green's function for T-stress of semi-infinite plane crack

Applied Mathematics and Mechanics(English Edition) 2011年第8期32卷 973-980页

作者：崔元庆杨卫仲政 School of Aerospace Engineering and Applied Mechanics Tongji University Office of the Presidents Zhejiang University

Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Green’s function for the T-stress is obtained in a straightforward manner. Furthermore, Green’s functions are derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimposing method. Then, Green’s function is used to predict the domain-switch-induced T-stress in a ferroelectric double cantilever beam （DCB） test. The T-stress induced by the electromechanical loading is used to judge the stable and unstable crack growth behaviors observed in the test. The prediction results generally agree with the experimental data.

关键词： Green’s function T-stress complex variable function semi-infinite crack fracture mechanics

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AN ITERATION METHOD FOR INTEGRAL EQUATIONS ARISING FROM GRAVITY FLOWS WITH FREE SURFACE

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Acta Mechanica Sinica 1987年第2期3卷 123-138页

作者： Wen Xianyun Wu Chigong (Chengdu University of Science and Technology) Chengdu University of Science and Technology Chengdu China

Gravity potential flows with free surface still present considerable difficulties in non-linear mathematical *** researchers using analytic function theory could consideronly simple geometrical *** curvilinear solid boundaries by means of analytictheory is a difficult problem that has not been *** this paper,using Muskhelishvili’s singularintegral equation theory,we turn the gravity flow problem into the Riemann-Hilbert *** the length of the streamline of the boundary as the independent variable and the velocitypotential of the boundary as the function to be determined,we avoid the difficulty that the angle ofthe curved fixed part is *** the difference method and the finite element method,we develop a new numerical method that is suitable for complex solid boundaries and overcome thedifficulties encountered in applying analytic function *** known discharge,the conver-g(?)nee and stability of the method have been proved and an estimation of error has been *** method has been successfully applied to the calculation of the flow past spillway *** values agree well with the measured results.

关键词： gravity flow with free surface complex variable function boundary-integral equation convergence stability estimation of error

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DYNAMIC ANALYSIS FOR SHALLOW ELASTIC CYLINDRICAL INCLUSION NEAR MULTIPLE SEMI-CYLINDRICAL HILLS IMPACTED BY SH-WAVE

DYNAMIC ANALYSIS FOR SHALLOW ELASTIC CYLINDRICAL INCLUSION N...

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第三届全国压电和声波理论及器件技术研讨会

作者： Xiao-tang L Department of Civil Engineering,Hefei University,373 Huangshan Street,Hefei,Anhui 230601,China Zai-lin YANG,Dian-kui LIU College of Civil Engineering,Harbin Engineering University,145 Nantong Street,Harbin,Heilongjiang 150001,China

complex variable function and moving coordinates were introduced to investigate the dynamic stress concentration of a subsurface elastic cylindrical inclusion below multiple semi-cylindrical hills under *** whole model was divided into two ***Ⅰwas composed of multiple circular domains which include the boundaries of multiple hills, and all the rest can be considered as partⅡ.Therefore the lower half boundaries of multiple circular domains were"common boundaries"of two *** next process was constructing the suitable displacement solutions in two parts *** the boundary conditions of common boundaries and the elastic inclusion,a series infinite algebraic equation for dynamic stress concentration factors(DSCF) can be ***,the calculating results are provided to show the influence of different parameters on DSCF.

关键词： Dynamic stress concentration multiple semi-cylindrical hills elastic cylindrical inclusion scattering of SH wave complex variable function

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