SH-wave Scatering Of Inclusions And A Crack With A Canyon In Elastic Semi-space

In this paper,based on the elastic wave theory,combined with the multi-polar coordinate and the method of tectonic cracks,the interaction problems with inclusion of a crack,circular cavity and inclusion subjected in semi-cylindrical canyon by SH wave were studied.First of all,a suitable Green's function which is a fundamental solution of displacement field for a semi-cylindrical gap containing circular cavity and inclusion while bearing out-of-plane harmonic line source force at any point is built for the current problem.Then constructing a linear crack near a circular cavity and inclusion,integration for solution is set up: while the scattering problems of SH-wave by circular cavity and inclusion with a linear crack is studied in semi-cylindrical gap.reverse stresses are applied along the cracks,out-of-plane harmonic line source forces which are equal in the size but opposite in the direction to the stresses produced due to SH-wave scattering by imperfection(circular cavity and inclusion)are loaded at the area where a crack comes out,so cracks can be built.So the expression of displacement and stress is solved while cavity and inclusion and a crack is existing in semi-cylindrical canyon.Dynamic stress concentration near the inclusion is studied by using the expression.The researches in detail have covered three areas:1.Green's Function is researched,which is the solution of displacement field for a semi-cylindrical canyon with inclusion of a crack,circular cavity and inclusion affected while bearing anti-plane harmonic line source force at any position.Using the method of multi-polar coordinate system,the expressions of displacement and stress are gained by utilizing the stress and displacement conditions of the circular cavities,inclusion and semi-cylindrical canyon.Then utilizing the expressions,the dynamic stress concentration factor at the margin of the inclusion is studied to the element of various parameters(.wave number,the radio of the shear modulus,and so on)by the concrete examples.2.It is researched which SH-wave scatters by circular inclusions,cavity in semi-cylindrical canyon.Utilizing the method of multi-polar coordinate system,the expressions of displacement and stress are gained by utilizing the stress and displacement condition of the cylindrical cavities,inclusion and semi-cylindrical canyon.Solving the expressions afterwards,the dynamic stress concentration factors at the margin of the inclusionare studied to the element of various parameters(.wave number,incident angles of SH-wave,the radio of the shear modulus,and so on)by the concrete examples.3.It is studied which SH-wave scatters by circular inclusions,cavity and a crack in semi-cylindrical canyon.First of all,we need solve the issue of SH-wave scattering by circular inclusions,cavity in semi-cylindrical canyon is researched.By finding Green's function which is fit to this problem and the construction of a crack,the expressions of displacement and stress are built.Employing the method of multi-polar coordinate system,the expressions of displacement and stress are gained by using the stress and displacement condition of the cavities,inclusion and semi-cylindrical canyon.Solving the expressions afterwards,the dynamic stress concentration factors at the margin of the inclusion are researched to the element of various parameters(.wave number,incident angles of SH-wave,the radio of the shear modulus,and so on).