SELF-SIMILAR SOLUTIONS OF FRACTURE DYNAMICS PROBLEMS ON AXIALLY SYMMETRY  

作　　者：吕念春 程靳 程云虹 屈德志 

机构地区：[1]Department of Astronautics and Mechanics, Harbin Institute of Technology, Harbin 150001, P R China [2]Department of Civil Engineering, Northeastern University, Shenyang 110006, P R China [3]Compressive Vessel Manufacturer of Constructive Installation Group Company of Daqing, Daqing 163711, P R China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2001年第12期1429-1435,共7页应用数学和力学（英文版）

摘　　要：By the theory of complex functions, a penny-shaped crack on axially symmetric propagating problems for composite materials, was studied. The general representations of the analytical solutions with arbitrary index of self-similarity, were presented for fracture elastodynamics problems on axially symmetry by the ways of self-similarity under the ladder-shaped loads. The problems dealt with can be transformed into Riemann-Hilbert problems and their closed analytical solutions are obtained rather simple by this method. After those analytical solutions are utilized by using the method of rotational superposition theorem in conjunction with that of Smirnov-Sobolev, the solutions of arbitrary complicated problems can be obtained.By the theory of complex functions, a penny-shaped crack on axially symmetric propagating problems for composite materials, was studied. The general representations of the analytical solutions with arbitrary index of self-similarity, were presented for fracture elastodynamics problems on axially symmetry by the ways of self-similarity under the ladder-shaped loads. The problems dealt with can be transformed into Riemann-Hilbert problems and their closed analytical solutions are obtained rather simple by this method. After those analytical solutions are utilized by using the method of rotational superposition theorem in conjunction with that of Smirnov-Sobolev, the solutions of arbitrary complicated problems can be obtained.

关 键 词：penny-shaped crack axially symmetric composite materials analytical solutions 

分 类 号：O346.1[理学—固体力学]