Interaction Of Cylindrical Inclusion And Crack In Right-angle Plane Impacted By SH Waves

The problems of SH waves scattering, which is caused by circular cavity (cylindrical inclusion) and crack of arbitrary position and arbitrary length in right-angle plane, are studied using the methods of complex variables, muti-polar coordinates and Green's Function. Firstly, a suitable Green's function is constructed, which is an essential solution to the displacement field for elastic right-angle plane possessing circular cavity (cylindrical inclusion) while bearing in-of-plane harmonic line source load at arbitrary point. Then using the Green's function, the scattering problem of SH waves is studied, which is caused by circular cavity (cylindrical inclusion) and crack of arbitrary position and arbitrary length in right-angle plane. Then using the method of crack division, the crack is established: reverse stresses are inflicted along the crack, that is, in-of-plane harmonic line source loads, which are equal in the quantity but opposite in the direction to the stresses produced for the reason of SH waves scattering by circular cavity (cylindrical inclusion), are loaded at the region where crack will appear, thus the crack can be made out. Thus expressions of displacement and stress are established while circular cavity (cylindrical inclusion) and crack are both in existent. Using the expressions, the dynamic stress concentration around the circular cavity (cylindrical inclusion), the ground motion of right-angle plane and the dynamic stress intensity factor at crack tip are discussed. The work in detail is as follows:1. The problem of SH waves scattering caused by circular cavity in right-angle plane is investigated. The key point of the work is that: based on the symmetry of SH waves scattering and the method of multi-polar coordinate system, a scattering field which satisfies the stress-free conditions at the surfaces of right-angle plane caused by the circular cavity is constructed. Then the expression of scattering field can be determined by the stress-free boundary condition of circular cavity. Finally, the solution of this problem can be reduced to a series of algebraic equations, which can be solved numerically by truncating the infinite algebraic equations to the finite ones. Numerical examples are provided for cases, and some influencing factors to the problem are discussed, such as the wave number, the incident angle of SH waves andt he position of circular cavity.2. The Green's function is constructed compatibly, which is an essential solution to the displacement field for the elastic right-angle plane possessing a circular cavity (cylindrical inclusion) while bearing in-of-plane harmonic line source load at arbitrary point. The continuity, singularity and some other characteristics of the Green's function are discussed as well.3. The problem of scattering of SH waves by a circular cavity and a beeline crack of arbitrary position and arbitrary length in right-angle plane is investigated. Using the Green's function which is suitable to the present problem, the expressions of displacement and stress are deduced with crack-division technique while the circular cavity and the crack are both in existent. The dynamic stress concentration around the circular cavity and the dynamic stress intensity factor at the crack tip are discussed. Furthermore, some examples and results are given. Finally, some influencing factors to the problem are discussed, such as the wave number, the incident angle of SH-wave, the position of circular cavity , and the position, angle and length of crack.4. The problem of scattering of SH waves by a cylindrical inclusion and a beeline crack of arbitrary position and arbitrary length in right-angle plane is investigated. Using the Green's function which is suitable to the present problem, the expressions of displacement and stress are deduced with crack-division technique while the interaction of the cylindrical inclusion and crack are both in existent. The dynamic stress concentration around the circular cavity and the dynamic stress intensity factor at the crack tip are discussed. Furthermore, some examples and results are given. Finally, some influencing factors to the problem are discussed, s such as the wave number, the incident angle of SH-wave, the shearing modulus of cylindrical inclusion medium, the position of cylindrical inclusion , and the position, angle and length of crack.