New numerical methods based on collocation methods with the mechanical quadrature rules are proposed to solve some systems of singular integrodifferential equations that are defined on arbitrary smooth closed contours...New numerical methods based on collocation methods with the mechanical quadrature rules are proposed to solve some systems of singular integrodifferential equations that are defined on arbitrary smooth closed contours of the complex plane.We carry out the convergence analysis in classical Hölder spaces.A numerical example is also presented.展开更多
It is known that principal value plays vital roles in the study of singular integral.In this paper,one type of Cauchy–Fantappièintegral with multiple indexes is introduced.Since the structure of the kernel is co...It is known that principal value plays vital roles in the study of singular integral.In this paper,one type of Cauchy–Fantappièintegral with multiple indexes is introduced.Since the structure of the kernel is complexity,the Jacobian determinant included in the kernel is expanded for making clearly the expression of the kernel.Moreover,one differential operator is utilized for setting up relations between integrals with higher and usual orders.The work also concerns the convergent properties of the integral.In order to study Hadamard principal value and composite formula of this integral,finite and divergent parts will be estimated and separated.As an application,solvability of the system of integral equations with higher order singularity kernel is discussed.展开更多
This study presents the determination of the stress intensity factors （SIFs） at the edges of the cracks in an elastic strip weakened by N-collinear cracks. The problem of an orthotropic elastic strip is reduced to a...This study presents the determination of the stress intensity factors （SIFs） at the edges of the cracks in an elastic strip weakened by N-collinear cracks. The problem of an orthotropic elastic strip is reduced to a system of Cauchy type singular integral equations. The system of singular integral equations is approached by a Quadrature technique. Under two different loading conditions, the results are obtained for the different cases of crack numbers. The resistance of the strip is examined by considering the orthotropic properties of the strip material. Finally, the crack interactions are clarified during the analysis.展开更多
In this paper, the first fundamental problem for an infinite elastic plane bonded by different anisotropic materials with cracks of arbitrary shape is discussed. The problem is reduced to a certain system of singular ...In this paper, the first fundamental problem for an infinite elastic plane bonded by different anisotropic materials with cracks of arbitrary shape is discussed. The problem is reduced to a certain system of singular integral equations with several undetermined constants, which is proved to be uniquely solvable when these constants are suitably and uniquely chosen.展开更多
基金This research of Iurie Caraus was supported by a Fulbright Grant.The First author would like to thank the Department of Mathematics,North Carolina State University,and Dr.Zhilin Li for the support and the hospitality during his visitThe second author is partially supported by the US ARO grants 550694-MA,the AFSOR grant FA9550-09-1-0520,the US NSF grant DMS-0911434,the US NIH grant 096195-01,and the CNSF grant 11071123.
文摘New numerical methods based on collocation methods with the mechanical quadrature rules are proposed to solve some systems of singular integrodifferential equations that are defined on arbitrary smooth closed contours of the complex plane.We carry out the convergence analysis in classical Hölder spaces.A numerical example is also presented.
基金Supported by the National Natural Science Foundation of China(Grant No.11771357)。
文摘It is known that principal value plays vital roles in the study of singular integral.In this paper,one type of Cauchy–Fantappièintegral with multiple indexes is introduced.Since the structure of the kernel is complexity,the Jacobian determinant included in the kernel is expanded for making clearly the expression of the kernel.Moreover,one differential operator is utilized for setting up relations between integrals with higher and usual orders.The work also concerns the convergent properties of the integral.In order to study Hadamard principal value and composite formula of this integral,finite and divergent parts will be estimated and separated.As an application,solvability of the system of integral equations with higher order singularity kernel is discussed.
文摘This study presents the determination of the stress intensity factors （SIFs） at the edges of the cracks in an elastic strip weakened by N-collinear cracks. The problem of an orthotropic elastic strip is reduced to a system of Cauchy type singular integral equations. The system of singular integral equations is approached by a Quadrature technique. Under two different loading conditions, the results are obtained for the different cases of crack numbers. The resistance of the strip is examined by considering the orthotropic properties of the strip material. Finally, the crack interactions are clarified during the analysis.
文摘In this paper, the first fundamental problem for an infinite elastic plane bonded by different anisotropic materials with cracks of arbitrary shape is discussed. The problem is reduced to a certain system of singular integral equations with several undetermined constants, which is proved to be uniquely solvable when these constants are suitably and uniquely chosen.
