2024,
45(4):
400-415.
doi: 10.21656/1000-0887.440241
Abstract:
Based on the extended Stroh method, a boundary element analysis was conducted for the plane elasticity problem of finitesized icosahedral quasicrystal plates with elliptical holes. Firstly, the extended Stroh method was used to study Green’s function for the icosahedral quasicrystal, to obtain the fundamental solutions of displacements and stresses of the plane elasticity problem about infinitesized icosahedral quasicrystal plates with elliptical holes. With these fundamental solutions, the weighted residual method was employed to establish the integral equations within the domain and on the boundary, and the linear interpolation functions and the Gaussian integration were used to discretize the boundary integral equations and the domain integral equations with unknown variables, respectively. Furthermore, the stress at the hole boundary was numerically solved, and the numerical results of the finitesized plate were compared with the analytical solution of the infinitesized plate to demonstrate that, the analytical solution of the infinitesized plate cannot be used for the analysis of the finitesized plate with the ratio of the plate size to the hole size below a certain threshold. Finally, the effects of the plate size, the hole size, and the inclination angle on the stress at the hole boundary were analyzed under tensile loading in the vertical direction. The results show that, the variation of the plate size along the vertical tensile direction has a more significant effect on the stress at the hole boundary. As the elliptical hole size increases, the stress concentration phenomenon becomes more pronounced. If the major axis is perpendicular to the vertical tensile direction, the inclination of the elliptical hole will mitigate the degree of stress concentration at the hole boundary.
