带椭圆孔有限大二维八次对称准晶问题的应力分析  

Stress Analysis of Finite Octagonal Two-dimensional Quasicrystal Problem with Elliptical Hole

作　　者：陈德财 王桂霞[1,2] 李联和 CHEN Decai;WANG Guixia;LI Lianhe(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022;Inner Mongolia Center of Applied Mathematics,Hohhot 010022)

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022 [2]内蒙古自治区应用数学中心,呼和浩特010022

出　　处：《工程数学学报》2024年第5期897-914,共18页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11962026);内蒙古自治区自然科学基金(2022ZD05);内蒙古自治区高校科研项目(NJZZ21003);内蒙古师范大学研究生科研创新基金(CXJJS22099).

摘　　要：首先,利用扩展的Stroh方法,研究含椭圆孔无限大八次对称二维准晶板的格林函数,得到边界元法求解含椭圆孔有限大八次对称二维准晶板所需的基本解。其次,利用加权余量法,建立边界积分方程,采用线性插值函数及高斯积分对含未知量的边界积分方程进行离散并重新组织离散格式,形成变量统一的线性方程组。最后,对椭圆孔的孔边应力进行数值求解,并将有限大板的数值结果与无限大板的解析解进行对比验证,说明边界元法的有效性。进一步分析在垂向拉伸作用下,板材的尺寸、孔口的大小及倾斜角度对孔边应力的影响。数值实例结果表明,随着椭圆孔尺寸的增加,孔边应力集中现象越明显。若长轴垂直拉伸方向,椭圆孔倾斜会减缓孔边应力集中程度。而裂纹尖端的应力强度因子随着裂纹的增长而增加。Firstly,the extended Stroh formulism is used to study the Green’s function of an infinite octagonal two-dimensional quasicrystals plate with an elliptical hole.And the funda-mental solution of the boundary element method for solving the finite octagonal two-dimensional quasicrystals plate with an elliptical hole is obtained.Secondly,the boundary integral equation is established by using the weighted residual method.The boundary integral equation with unknown quantity is discretized by linear interpolation function and Gauss integral,and the discrete format is reorganized to form a linear system of equations with unified variables.Fina-lly,the hole edge stress of the elliptical hole is numerically solved,and the numerical results of the finite plate are compared with the analytical solution of the infinite plate to verify the effectiveness of the boundary element method.The influence of the size of the plate,the size of the hole and the inclination angle on the stress at the edge of the hole under vertical tension are further analyzed.The results of numerical examples show that the stress concentration at the edge of the hole is more obvious with the increase of the size of the elliptical hole.The inclination of the elliptical hole aggravates the stress concentration at the edge of the hole.The stress intensity factor at the crack tip increases with the growth of the crack.

关 键 词：边界元方法 八次对称二维准晶 有限尺寸 椭圆孔 应力集中因子 

分 类 号：O343.1[理学—固体力学] O343.4[理学—力学]