1 研究背景幂律奇异性是材料灾变破坏及地震发生时的一个典型前兆特征(Voight,1989;Xue et al,2018)。在灾变破坏发生时,系统的响应函数R=du/dU发散到无穷大,表现出临界幂律奇异性(Xue et al,2018)。其中,u是系统响应量,U是系统的加载...1 研究背景幂律奇异性是材料灾变破坏及地震发生时的一个典型前兆特征(Voight,1989;Xue et al,2018)。在灾变破坏发生时,系统的响应函数R=du/dU发散到无穷大,表现出临界幂律奇异性(Xue et al,2018)。其中,u是系统响应量,U是系统的加载控制量。响应函数R的临界幂律奇异性是灾变破坏能量准则的体现,对大理岩、花岗岩试样进行的准静态单轴压缩实验表明,响应函数幂律奇异性指数分布在-1/2到-1之间。展开更多
The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitut...The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitution method （VSM）, and steepest descent integration method （SDIM） were used to evaluate this type of Green＇s function. For SDIM, the complex domain was restricted only on the 0-plane. Meanwhile, the integral along the real axis was computed by use of the VSM to avoid the complication of a numerical search of the steepest descent line. Furthermore, the steepest descent line was represented by the B-spline function. Based on this representation, a new self-compatible integration method corresponding to parametric t was established. The numerical method was validated through comparison with other existing results, and was shown to be efficient and reliable in the calculation of the velocity potentials for the 3D seakeeping and hydrodynamic performance of floating struc- tures moving in waves.展开更多
The authors define the directional hyper Hilbert transform and give ita mixed norm estimate. The similar conclusions for the directional fractional integral of one dimension are also obtained in this paper. As an appl...The authors define the directional hyper Hilbert transform and give ita mixed norm estimate. The similar conclusions for the directional fractional integral of one dimension are also obtained in this paper. As an application of the above results, the authors give the Lp-boundedness for a class of the hyper singular integrals and the fractional integrals with variable kernel. Moreover, as another application of the above results, the authors prove the dimension free estimate for the hyper Riesz transform. This is an extension of the related result obtained by Stein.展开更多
Fracture analysis of a plane crack problem under chemo-mechanical loading is presented based on a linear chemo-elasticity model.The flux conductivity is introduced to characterize the influence of the crack defect on ...Fracture analysis of a plane crack problem under chemo-mechanical loading is presented based on a linear chemo-elasticity model.The flux conductivity is introduced to characterize the influence of the crack defect on the diffusion process.Using Fourier transform and the dislocation density functions,the crack problem is reduced to a set of singular integral equations,which are solved numerically by the Lobatto-Chebyshev method.Parametric studies are conducted to reveal the effects of flux conductivity,geometric configuration,chemical and mechanical loads on the crack tip field.The numerical results show that the stress singularity at the crack tip is usually a mixture of mode Ⅰ and mode Ⅱ types.展开更多
文摘1 研究背景幂律奇异性是材料灾变破坏及地震发生时的一个典型前兆特征(Voight,1989;Xue et al,2018)。在灾变破坏发生时,系统的响应函数R=du/dU发散到无穷大,表现出临界幂律奇异性(Xue et al,2018)。其中,u是系统响应量,U是系统的加载控制量。响应函数R的临界幂律奇异性是灾变破坏能量准则的体现,对大理岩、花岗岩试样进行的准静态单轴压缩实验表明,响应函数幂律奇异性指数分布在-1/2到-1之间。
基金Project supported by the National Natural Science Foundation of China （No. 50879090）, and the Key Research Program of Hydrody- namics of China （No. 9140A 14030712JB 11044）
文摘The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitution method （VSM）, and steepest descent integration method （SDIM） were used to evaluate this type of Green＇s function. For SDIM, the complex domain was restricted only on the 0-plane. Meanwhile, the integral along the real axis was computed by use of the VSM to avoid the complication of a numerical search of the steepest descent line. Furthermore, the steepest descent line was represented by the B-spline function. Based on this representation, a new self-compatible integration method corresponding to parametric t was established. The numerical method was validated through comparison with other existing results, and was shown to be efficient and reliable in the calculation of the velocity potentials for the 3D seakeeping and hydrodynamic performance of floating struc- tures moving in waves.
基金the 973 Project of China(No.G1999075105)the National Natural ScienceFoundation of China(No.19631080,No.10271016)the Zhejiang Provincial Natural ScienceFoundation of China(No.RC97017,No.197042).
文摘The authors define the directional hyper Hilbert transform and give ita mixed norm estimate. The similar conclusions for the directional fractional integral of one dimension are also obtained in this paper. As an application of the above results, the authors give the Lp-boundedness for a class of the hyper singular integrals and the fractional integrals with variable kernel. Moreover, as another application of the above results, the authors prove the dimension free estimate for the hyper Riesz transform. This is an extension of the related result obtained by Stein.
基金supported by the National Natural Science Foundation of China(Grant Nos.11932005 and 11772106).
文摘Fracture analysis of a plane crack problem under chemo-mechanical loading is presented based on a linear chemo-elasticity model.The flux conductivity is introduced to characterize the influence of the crack defect on the diffusion process.Using Fourier transform and the dislocation density functions,the crack problem is reduced to a set of singular integral equations,which are solved numerically by the Lobatto-Chebyshev method.Parametric studies are conducted to reveal the effects of flux conductivity,geometric configuration,chemical and mechanical loads on the crack tip field.The numerical results show that the stress singularity at the crack tip is usually a mixture of mode Ⅰ and mode Ⅱ types.
