Both surface motion and hole stress concentration have always been
concerned in anisotropic medium. In this paper, a theoretical approach
is used to study the scattering problem of circular holes under a
scalene trapezoid on the surface. The mapping function that anisotropic
medium to homogeneous medium is established, and the relationship
between the free boundary of anisotropic medium and the mapping of
homogeneous medium boundary is proved. In the space of homogeneous
medium mapping, the wave displacement function is obtained by solving
the equation of motion that meets the zero-stress boundary conditions by
separating the variable method and the symmetric method. Based on the
complex function, multi-polar coordinate method and region-matching
technique, algebraic equations are established at auxiliary boundary and
free boundary conditions in complex domain. Then according to sample
statistics, least square method is used instead of the Fourier expansion
method to solve the undetermined coefficient of the algebraic equations
by discrete boundary. Numerical results shows that the continuity of the
auxiliary boundary and the accuracy of the zero-stress boundary are
nice, and the displacement of the free surface and the stress of the
circular hole are related to the parameters of material medium, the
position of the circular hole, the direction of the incident wave and
the frequency content of the excitation. Finally the process of the wave
propagation and scattering around trapezoid and shallow circle are shown
in time domain through the inverse fourier transform.