The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors(SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A confo...The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors(SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A conformal mapping is proposed and combined with the complex variable method. Due to some difficulties in the calculation of the stress function, the mapping function is approximated and simplified via the applications of the series expansion. To validate the obtained solution, several examples are analyzed with the proposed method, the finite element method, etc. In addition, the effects of the lengths of the cracks and the ratio of the semi-axes of the elliptical hole(a/b) on the SIFs are studied. The results show that the present analytical solution is applicable to the SIFs for small cracks.展开更多
The strength of composite plate with different hole-shapes is always one of the most important but complicated issues in the application of the composite material. The holes will lead to mutations and discontinuity to...The strength of composite plate with different hole-shapes is always one of the most important but complicated issues in the application of the composite material. The holes will lead to mutations and discontinuity to the structure. So the hole-edge stress concentration is always a serious phenomenon. And the phenomenon makes the structure strength decrease very quickly to form dangerous weak points. Most partial damage begins from these weak points. According to the complex variable functions theory, the accurate boundary condition of composite plate with different hole-shapes is founded by conformal mapping method to settle the boundary condition problem of complex hole-shapes. Composite plate with commonly hole-shapes in engineering is studied by several complex variable stress fimction. The boundary integral equations are founded based on exact boundary conditions. Then the exact hole-edge stress analytic solution of composite plate with rectangle holes and wing manholes is resolved. Both of offset axis loadings and its influences on the stress concentration coefficient of the hole-edge are discussed. And comparisons of different loads along various offset axis on the hole-edge stress distribution of orthotropic plate with rectangle hole or wing manhole are made. It can be concluded that hole-edge with continuous variable curvatures might help to decrease the stress concentration coefficient; and smaller angle of outer load and fiber can decrease the stress peak value.展开更多
By using the complex variable method and conformal mapping, the diffraction of flexural waves and dynamic stress concentrations in thick plates with a cavity have been studied. A general solution of the stress problem...By using the complex variable method and conformal mapping, the diffraction of flexural waves and dynamic stress concentrations in thick plates with a cavity have been studied. A general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of an arbitrary cavity is obtained. By employing the orthogonal function expansion technique, the dynamic stress problem can be reduced to the solution of an infinite algebraic equation series. As an example, the numerical results for the dynamic stress concentration factor in thick plates with a circular, elliptic cavity are graphically presented. The numerical results are discussed.展开更多
In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied....In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.展开更多
This study aims to investigate the feasibility of deriving in situ horizontal stresses from the breakout width and depth using the analytical method.Twenty-three breakout data with different borehole sizes were collec...This study aims to investigate the feasibility of deriving in situ horizontal stresses from the breakout width and depth using the analytical method.Twenty-three breakout data with different borehole sizes were collected and three failure criteria were studied.Based on the Kirsch equations,relatively accurate major horizontal stress(sH)estimations from known minor horizontal stress(sh)were achieved with percentage errors ranging from 0.33%to 44.08%using the breakout width.The Mogi-Coulomb failure criterion(average error:13.1%)outperformed modified Wiebols-Cook(average error:19.09%)and modified Lade(average error:18.09%)failure criteria.However,none of the tested constitutive models could yield reasonable sh predictions from known sH using the same approach due to the analytical expression of the redistributed stress and the nature of the constitutive models.In consideration of this issue,the horizontal stress ratio(sH/sh)is suggested as an alternative input,which could estimate both sH and sh with the same level of accuracy.Moreover,the estimation accuracies for both large-scale and laboratory-scale breakouts are comparable,suggesting the applicability of this approach across different breakout sizes.For breakout depth,conformal mapping and complex variable method were used to calculate the stress concentration around the breakout tip,allowing the expression of redistributed stresses using binomials composed of sH and sh.Nevertheless,analysis of the breakout depth stabilisation mechanism indicates that additional parameters are required to utilise normalised breakout depth for stress estimation compared to breakout width.These parameters are challenging to obtain,especially under field conditions,meaning utilising normalised breakout depth analytically in practical applications faces significant challenges and remains infeasible at this stage.Nonetheless,the normalised breakout depth should still be considered a critical input for any empirical and statistical stress estimation method given its significant correlation with horizontal stresses.The outcome of this paper is expected to contribute valuable insights into the breakout stabilisation mechanisms and estimation of in situ stress magnitudes based on borehole breakout geometries.展开更多
文摘The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors(SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A conformal mapping is proposed and combined with the complex variable method. Due to some difficulties in the calculation of the stress function, the mapping function is approximated and simplified via the applications of the series expansion. To validate the obtained solution, several examples are analyzed with the proposed method, the finite element method, etc. In addition, the effects of the lengths of the cracks and the ratio of the semi-axes of the elliptical hole(a/b) on the SIFs are studied. The results show that the present analytical solution is applicable to the SIFs for small cracks.
基金supported by National Natural Science Foundation of China(No.50675209)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,Ministry of Education of China(No.200724).
文摘The strength of composite plate with different hole-shapes is always one of the most important but complicated issues in the application of the composite material. The holes will lead to mutations and discontinuity to the structure. So the hole-edge stress concentration is always a serious phenomenon. And the phenomenon makes the structure strength decrease very quickly to form dangerous weak points. Most partial damage begins from these weak points. According to the complex variable functions theory, the accurate boundary condition of composite plate with different hole-shapes is founded by conformal mapping method to settle the boundary condition problem of complex hole-shapes. Composite plate with commonly hole-shapes in engineering is studied by several complex variable stress fimction. The boundary integral equations are founded based on exact boundary conditions. Then the exact hole-edge stress analytic solution of composite plate with rectangle holes and wing manholes is resolved. Both of offset axis loadings and its influences on the stress concentration coefficient of the hole-edge are discussed. And comparisons of different loads along various offset axis on the hole-edge stress distribution of orthotropic plate with rectangle hole or wing manhole are made. It can be concluded that hole-edge with continuous variable curvatures might help to decrease the stress concentration coefficient; and smaller angle of outer load and fiber can decrease the stress peak value.
文摘By using the complex variable method and conformal mapping, the diffraction of flexural waves and dynamic stress concentrations in thick plates with a cavity have been studied. A general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of an arbitrary cavity is obtained. By employing the orthogonal function expansion technique, the dynamic stress problem can be reduced to the solution of an infinite algebraic equation series. As an example, the numerical results for the dynamic stress concentration factor in thick plates with a circular, elliptic cavity are graphically presented. The numerical results are discussed.
文摘In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.
基金funded by the Australian Coal Industry’s Research Program(ACARP,Grant No.C26063).
文摘This study aims to investigate the feasibility of deriving in situ horizontal stresses from the breakout width and depth using the analytical method.Twenty-three breakout data with different borehole sizes were collected and three failure criteria were studied.Based on the Kirsch equations,relatively accurate major horizontal stress(sH)estimations from known minor horizontal stress(sh)were achieved with percentage errors ranging from 0.33%to 44.08%using the breakout width.The Mogi-Coulomb failure criterion(average error:13.1%)outperformed modified Wiebols-Cook(average error:19.09%)and modified Lade(average error:18.09%)failure criteria.However,none of the tested constitutive models could yield reasonable sh predictions from known sH using the same approach due to the analytical expression of the redistributed stress and the nature of the constitutive models.In consideration of this issue,the horizontal stress ratio(sH/sh)is suggested as an alternative input,which could estimate both sH and sh with the same level of accuracy.Moreover,the estimation accuracies for both large-scale and laboratory-scale breakouts are comparable,suggesting the applicability of this approach across different breakout sizes.For breakout depth,conformal mapping and complex variable method were used to calculate the stress concentration around the breakout tip,allowing the expression of redistributed stresses using binomials composed of sH and sh.Nevertheless,analysis of the breakout depth stabilisation mechanism indicates that additional parameters are required to utilise normalised breakout depth for stress estimation compared to breakout width.These parameters are challenging to obtain,especially under field conditions,meaning utilising normalised breakout depth analytically in practical applications faces significant challenges and remains infeasible at this stage.Nonetheless,the normalised breakout depth should still be considered a critical input for any empirical and statistical stress estimation method given its significant correlation with horizontal stresses.The outcome of this paper is expected to contribute valuable insights into the breakout stabilisation mechanisms and estimation of in situ stress magnitudes based on borehole breakout geometries.
基金The National Natural Science Foundation of China(11362018,11261045)the Specialized Research Fund for the Doctoral Program of Higher Education of China(20116401110002)the Natural Science Foundation of Ningxia University(ZR15026).
