By using the analytic theory of hypersingular integral equations in three- dimensional fracture mechanics, the interactions between two parallel planar cracks under arbitrary loads are investigated. According to the c...By using the analytic theory of hypersingular integral equations in three- dimensional fracture mechanics, the interactions between two parallel planar cracks under arbitrary loads are investigated. According to the concepts and method of finite- part integrals, a set of hypersingular integral equations is derived, in which the unknown functions are the displacement discontinuities of the crack surfaces. Then its numerical method is proposed by combining the finite-part integral method with the boundary element method. Based on the above results, the method for calculating the stress intensity factors with the displacement discontinuities of the crack surfaces is presented. Finally, several typical examples are calculated and the numerical results are satisfactory.展开更多
According to the constitutive relationship in linear piezoceramics, elliptical crack problems in the impermeable case are reconsidered with the hypersingular integral equation method. Unknown displacement and electric...According to the constitutive relationship in linear piezoceramics, elliptical crack problems in the impermeable case are reconsidered with the hypersingular integral equation method. Unknown displacement and electric potential jumps in the integral equations are approximated with a product of the fundamental density function and polynomials, in which the fundamental density function reflects the singular behavior of electroelastic fields near the crack front and the polynomials can be reduced to a real constant under uniform loading. Ellipsoidal coordinates are cleverly introduced to solve the unknown displacement and electric potential jumps in the integral equations under uniform loading. With the help of these solutions and definitions of electroelastic field intensity factors, exact expressions for mode Ⅰ, mode Ⅱ and mode Ⅲ stress intensity factors as well as the mode Ⅳ electric displacement intensity factor are obtained. The present results under uniform normal loading are the same as the available exact solutions, but those under uniform shear loading have not been found in the literature as yet.展开更多
By using the finite-part integral concepts and limit technique,the hypersingular inte- grodifferential equations ofthree-dimensional(3D)planar interface crack were obtained; then thedominant-part analysis of 2D hypers...By using the finite-part integral concepts and limit technique,the hypersingular inte- grodifferential equations ofthree-dimensional(3D)planar interface crack were obtained; then thedominant-part analysis of 2D hypersingular integral was further usedto investigate the stress fields near the crack front theoretically,and the accurate formulae were obtained for the singular stressfields and the complex stress intensity factors.展开更多
文摘By using the analytic theory of hypersingular integral equations in three- dimensional fracture mechanics, the interactions between two parallel planar cracks under arbitrary loads are investigated. According to the concepts and method of finite- part integrals, a set of hypersingular integral equations is derived, in which the unknown functions are the displacement discontinuities of the crack surfaces. Then its numerical method is proposed by combining the finite-part integral method with the boundary element method. Based on the above results, the method for calculating the stress intensity factors with the displacement discontinuities of the crack surfaces is presented. Finally, several typical examples are calculated and the numerical results are satisfactory.
基金Project supported by the Jiangxi Provincial Natural Science Foundation (No.0112001)the Japan Society for the Promotion of Science Postdoctoral Fellowship (No.P01205).
文摘According to the constitutive relationship in linear piezoceramics, elliptical crack problems in the impermeable case are reconsidered with the hypersingular integral equation method. Unknown displacement and electric potential jumps in the integral equations are approximated with a product of the fundamental density function and polynomials, in which the fundamental density function reflects the singular behavior of electroelastic fields near the crack front and the polynomials can be reduced to a real constant under uniform loading. Ellipsoidal coordinates are cleverly introduced to solve the unknown displacement and electric potential jumps in the integral equations under uniform loading. With the help of these solutions and definitions of electroelastic field intensity factors, exact expressions for mode Ⅰ, mode Ⅱ and mode Ⅲ stress intensity factors as well as the mode Ⅳ electric displacement intensity factor are obtained. The present results under uniform normal loading are the same as the available exact solutions, but those under uniform shear loading have not been found in the literature as yet.
基金the Foundation of Solid Mechanics Open Research Laboratory of State Education Commission at Tongji Universitythe National Natural Science Foundation
文摘By using the finite-part integral concepts and limit technique,the hypersingular inte- grodifferential equations ofthree-dimensional(3D)planar interface crack were obtained; then thedominant-part analysis of 2D hypersingular integral was further usedto investigate the stress fields near the crack front theoretically,and the accurate formulae were obtained for the singular stressfields and the complex stress intensity factors.
