应用数学和力学2024，Vol.45Issue(4)：400-415,16.DOI:10.21656/1000-0887.440241
含椭圆孔有限大二十面体准晶板平面弹性问题的边界元分析
Boundary Element Analysis for the Plane Elasticity Problems of Finite Icosahedral Quasicrystal Plates Containing Elliptical Holes
摘要
Abstract
Based on the extended Stroh method,a boundary element analysis was conducted for the plane elas-ticity 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 solu-tions 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 e-quations 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 infi-nite-sized plate to demonstrate that,the analytical solution of the infinite-sized plate cannot be used for the a-nalysis 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 ana-lyzed 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 per-pendicular to the vertical tensile direction,the inclination of the elliptical hole will mitigate the degree of stress concentration at the hole boundary.关键词
二十面体准晶/Stroh方法/椭圆孔/有限尺寸/应力集中系数Key words
icosahedral quasicrystal/Stroh method/elliptical hole/finite size/stress concentration factor分类
力学引用本文复制引用
王会苹,王桂霞,陈德财..含椭圆孔有限大二十面体准晶板平面弹性问题的边界元分析[J].应用数学和力学,2024,45(4):400-415,16.基金项目
国家自然科学基金(11962026) （11962026）
内蒙古自治区自然科学基金重点项目(2022ZD05) （2022ZD05）
内蒙古自治区高校科研项目(NJZZ21003) （NJZZ21003）
