INVESTIGATION OF THE SCATTERING OF HARMONIC ELASTIC WAVES BY TWO COLLINEAR SYMMETRIC CRACKS USING THE NON-LOCAL THEORY  

作　　者：ZHOU Zhen-gong(周振功) WANG Biao(王彪) 

机构地区：[1]Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, P R China Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, P R China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2001年第7期766-775,共10页应用数学和力学（英文版）

基　　金：theNationalFoundationforExcellentYoungInvestigations ( 1 972 5 2 0 9) ;thePostDoctoralScienceFoundationofHeilongjiangProvince

摘　　要：The scattering of harmonic waves by two collinear symmetric cracks is studied using the non-local theory. A one-dimensional non-local kernel was used to replace a two-dimensional one for the dynamic problem to obtain the stress occurring at the crack tips. The Fourier transform was applied and a mixed boundary value problem was formulated. Then a set of triple integral equations was solved by using Schmidt's method. This method is more exact and more reasonable than Eringen's for solving this problem. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the lattice parameter and the circular frequency of incident wave.The scattering of harmonic waves by two collinear symmetric cracks is studied using the non-local theory. A one-dimensional non-local kernel was used to replace a two-dimensional one for the dynamic problem to obtain the stress occurring at the crack tips. The Fourier transform was applied and a mixed boundary value problem was formulated. Then a set of triple integral equations was solved by using Schmidt's method. This method is more exact and more reasonable than Eringen's for solving this problem. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the lattice parameter and the circular frequency of incident wave.

关 键 词：the non-local theory Schmidt's method the triple-integral equation 

分 类 号：O345.21[理学—固体力学]