Dynamic Anti-plane Interaction Of Circular Cavities,inclusions And A Crack Under Stiffness Plane

During this paper,by applying Green's Function,the means of multi-polar coordinate and the means of crack-division,the interaction puzzle of multiple circular cavities and multiple circular inclusions with a linear crack under plane stiffness by SH-wave is discussed,Firstly,the right Green's functions for this problem are created,which are the solution of displacement field under plane stiffness with multiple inclusions and multiple circular cavities while enduring anti-plane harmonic line source load at any position.Then applying the method of crack-division.The specific method is that stresses are exerted along the cracks,out-of-plane harmonic line source loads which are equal in the amount but opposite in the orientation to the stresses brought for the cause of SH-wave scattering by flaws are loaded at the area where cracks will be produced.So cracks can be constructed.So the expression of displacement and stress is built while flaws and cracks exist simultaneously.Applying the expression dynamic stress concentration near the flaws is researched.The main work of the article is:1.Green's Function is studied,which is the solution of displacement field under plane stiffness with multiple inclusions and multiple circular cavities while bearing anti-plane harmonic line source force at any point.Applying the method of multi-polar coordinate system,the expression of displacement and stress is obtained.Then using the expressions,the dynamic stress concentration factor at the edge of the inclusion is discussed to the case of different parameters which is wave number,the radio of the shear modulus,the geometrical location of the circular inclusions and the line source.2.The problem of SH-wave scattering by multiple circular inclusions and multiple circular cavities near the inclusions under plane stiffness is investigated.By using the dynamic stress concentration at the edge of the circular inclusion is discussed to the case of different parameters which is the radio of the shear modulus,wave number,incident angles of SH-wave,and the geometrical location of the circular inclusions and the crack.3.The problem of SH-wave scattering by circular cavities and multiple circular inclusions with a crack of any limited lengths near the inclusions under plane stiffness is investigated.By using Green's function which is suitable to this problem and the method of crack-division,the expression of displacement and stress is established.Then the dynamicstress concentration at the edge of the circular cavities is discussed to the case of different parameters which is wave number,incident angles of SH-wave,and the geometrical location of the circular inclusions and the crack,the embedded depth of the circular inclusions and the crack.