摘要
板切口尖端的奇异应力场影响结构安全,需要对含切口板进行强度计算。文章首先根据中厚板的弹性控制方程,利用切口特征渐近展开理论,推演出中厚板切口的奇性特征方程,引入插值矩阵法进行求解,获得板切口的奇异性指数、特征角函数及其导数。之后使用边界元法,求解切口板内离切口尖端等距离圆弧上点的位移,并将其代入切口尖端位移渐近展开式,形成一组非正定方程组,采用超定法求解,获得渐近展开式的幅值系数,据此进一步计算出切口板的应力强度因子。文章分别计算了板切口在对称荷载、反对称荷载以及复合型荷载作用下的应力强度因子。
The singular stress field near the vertex of a notched plate will affect the safety of structure.It is necessary to evaluate the strength of a notched plate.The singular characteristic equation of the notch in a plate is firstly established,basing on the elastic governing equation of a plate and the asymptotic expansion theory near the notch tip.The interpolating matrix method is then introduced to solve it for getting the singularity orders,characteristic angle functions and their derivatives of the notch.The boundary element method is thereafter applied to determine the displacements of the inner points on the arc around the notch tip.The displacement values are substituted into the asymptotic expansion to form a set of non-positive definite equations,which are solved by the over-deterministic method to obtain the amplitude coefficients in the asymptotic expansion.The stress intensity factors are further given out basing on the amplitude coefficients.The stress intensity factors of the notched plate under the symmetrical load,anti-symmetric load and mixed-mode load are respectively investigated.
作者
刘静雯
程长征
黄一帆
王飞炀
李腾岳
LIU Jingwen;CHENG Changzheng;HUANG Yifan;WANG Feiyang;LI Tengyue(School of Civil and Hydraulic Engineering,Hefei University of Technology,230009 Hefei,China)
出处
《应用力学学报》
CAS
CSCD
北大核心
2022年第6期1086-1095,共10页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金资助项目(No.12172114)
安徽省杰出青年自然科学基金资助项目(No.2208085J25)。
关键词
板切口
应力强度因子
超定法
边界元法
notched plate
stress intensity factors
over-deterministic method
boundary element method