Boundary Element Analysis for the Plane Elasticity Problems of Finite Icosahedral Quasicrystal Plates Containing Elliptical Holes

WANG Huiping; WANG Guixia; CHEN Decai

doi:10.21656/1000-0887.440241

Volume 45 Issue 4

Apr. 2024

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Article Navigation > Applied Mathematics and Mechanics > 2024 > 45(4): 400-415

WANG Huiping, WANG Guixia, CHEN Decai. Boundary Element Analysis for the Plane Elasticity Problems of Finite Icosahedral Quasicrystal Plates Containing Elliptical Holes[J]. Applied Mathematics and Mechanics, 2024, 45(4): 400-415. doi: 10.21656/1000-0887.440241

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Boundary Element Analysis for the Plane Elasticity Problems of Finite Icosahedral Quasicrystal Plates Containing Elliptical Holes

doi: 10.21656/1000-0887.440241

WANG Huiping^1
,,
WANG Guixia^{1, 2
,
,},
CHEN Decai¹

1.
College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, P.R.China
2.
Inner Mongolia Center of Applied Mathematics, Hohhot 010022, P.R.China

Received Date: 2023-08-14
Rev Recd Date: 2023-12-12
Publish Date: 2024-04-01

Abstract

Abstract

Based on the extended Stroh method, a boundary element analysis was conducted for the plane elasticity problem of finite-sized 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 infinite-sized 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 finite-sized plate were compared with the analytical solution of the infinite-sized plate to demonstrate that, the analytical solution of the infinite-sized plate cannot be used for the analysis of the finite-sized 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.
- icosahedral quasicrystal,
- Stroh method,
- elliptical hole,
- finite size,
- stress concentration factor

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References(34)

References

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