边界元法计算切口多重应力奇性指数

Calculation of multiple stress singularity exponents of notches by boundary element method

提出采用边界元法直接计算V形切口的多重应力奇性指数。首先在切口尖端挖出一微小扇形域,在该域边界列常规边界积分方程,后将扇形域内的位移场和应力场表示成关于切口尖端距离ρ的渐近级数展开式,回代入切口边界积分方程,离散后得到关于切口奇性指数的代数特征方程,从而求解获得V形切口的应力奇性指数。该法避免了常规边界元法和有限元法在切口尖端附近布置细密单元的缺陷,并可同时求得多阶应力奇性指数。

A new technique about the calculation of stress singularity exponents of V-notches with boundary element method is proposed. Based on the theory of linear elasticity, the asymptotic displacement and stress field in the V-notch tip region are expressed as a series expansion with respect to the radial coordinate from the tip. The series expansion of the asymptotic field is then substituted into the boundary integral equation of the V-notched structure. After the discretization, the boundary integral equation is transformed to the eigen equation with the stress singularity orders. By solving the algebraic eigen equation, the eigenvalues which are the singularity exponents can be obtained. Hence, the use of very fine elements near the V-notch tip in the conventional boundary element method is unnecessary in present new method. The multiple singularity exponents of V-notchs can be obtained simultaneously in the present method.