Papers by Keyword: Self-Similar Function

Abstract: By the theory of complex functions, symmetrical dynamic propagation problems of mode Ⅲ interface crack were investigated. The problems considered can be very easily translated into Riemann-Hilbert problem by the methods of self-similar functions, and the universal expressions of analytical solutions for the surfaces of symmetrical mode Ⅲ interface crack subjected to moving alterable loadings Pt3/x3 and Px4/t3 were obtained, respectively. After those solutions were utilized by superposition theorem, the solutions of arbitrary complex problems could be acquired.

Abstract: Dislocation distribution functions of the edges of mode III propagation crack subjected to Moving unit step load from a point was studied by the methods of the theory of complex variable functions.By the methods, the problems researched can be facilely transformed into Riemann-Hilbert problems and Keldysh-Sedov mixed boundary value problems. Analytical solutions of stresses, displacements, dynamic stress intensity factor and dislocation distribution function were obtained by the methods of the theory of self-similar functions.In terms of the relationship between dislocation distribution functions and displacements, analytical solutions of dislocation distribution functions were attained.

Abstract: By means of the complex variable functions, dynamic expension problems on symmetrical mode Ⅲ interface crack were researched. The problems considered can be very facilely transformed into Riemann-Hilbert problem by the measures of self-similar functions, and the general expressions of analytical solutions for the edges of mode Ⅲ symmetrical interface crack subjected to motive variable loadings Px²/t³ and Pt⁴/x³ were obtained by means of self-similar functions, respectively. After those solutions were utilized by superposition theorem, the solutions of arbitrary complex problems could be readily attained.

Abstract: By the approaches of complex variable functions, two dynamic propagation problems of mode Ⅲ interface crack were researched. The problems considered can be very facilely changed into Riemann-Hilbert problem by means of self-similar functions, and analytical solutions of the stresses, displacements, dynamic stress intensity factors for the edges of mode Ⅲ symmetrical dynamix interface crack subjected to moving increasing loads Pt2/x2 and Px3/t2, respectively, were obtained by the methods of self-similar functions. After those solutions were utilized by superposition theorem, the solutions of arbitrary complex problems can be readily attained.

Abstract: By application of the theory of complex functions, the problem for mode Ⅲ dynamic crack under concentrated force were researched. The Riemann-Hilbert problem is formulated according to relationships of self-similar functions. Analytical solutions of stresses, displacements and dynamic stress intensity factors were obtained by the measures of self-similar functions and corresponding differential and integral operation.

Abstract: Dislocation distribution functions of mode I dynamic crack subjected to two loads were studied by the methods of the theory of complex variable functions. By this way, the problems researched can be translated into Riemann-Hilbert problems and Keldysh-Sedov mixed boundary value problems. Analytical solutions of stresses, displacements and dynamic stress intensity factors were obtained by the measures of self-similar functions and corresponding differential and integral operation. The analytical solutions attained relate to the crack propagation velocity and time, but the solutions have nothing to the other parameters. In terms of the relationship between dislocation distribution functions and displacements, analytical solutions of dislocation distribution functions were gained, and variation rules of dislocation distribution functions were depicted.

Abstract: By the theory of complex functions, dynamic propagation problems on symmetrical mode Ⅲ interface crack were researched. The problems considered can be very facilely transformed into Riemann-Hilbert problem by the methods of self-similar functions, and the general expressions of analytical solutions for the surfaces of mode Ⅲ symmetrical interface crack subjected to motive variable loadings Px²/t² and Pt³/x² were obtained, respectively. After those solutions were utilized by superposition theorem, the solutions of arbitrary complex problems could be attained.

Abstract: By means of the built dynamic fracture model of bridging fiber pull-out of composite materials, the problems considered will be transformed into Riemann-Hilbert problem in terms of the theory of complex functions. Analytical solutions of the stresses displacements, dynamic stress intensity factors, strain energy release rate and bridging fibrous fracture speeds under the conditions of an moving increasing loads, Pt/x, Px2/t, respectively, can be facilely obtained by the approaches of self-similar functions. After those solutions were utilized by superposition theorem, the solutions of arbitrary complex problems can be attained.

Abstract: By the approaches of the theory of complex functions, two dynamic propagation problems of symmetrical mode Ⅲ crack were researched. The problems considered can be very facilely changed into Riemann-Hilbert problem by means of self-similar functions, and the general representations of analytical solutions of the stress, the displacement and dynamic stress intensity factor under the conditions of moving variable loads Pt and Px2/t2 which were applied the edges of mode Ⅲ crack, respectively, were readily acquired.

Abstract: By the approaches of the theory of complex functions, propagation problems concerning mode Ⅲ asymmetrical dynamic interface crack were studied. The problems can be transformed into Riemann-Hilbert problem easily by the measures of self-similar functions, and the universal expressions of analytical solutions of the edges of mode Ⅲ asymmetrical dynamics interface crack subjected to variable loads and respectively, were attained.