复合材料纤维内裂纹分析的随机边界元法

Stochastic Boundary Element Method of Analysis of Embeded Crack in the Fiber of the Composite Material

基于级数展开技术导出随机边界元法，并将随空间坐标随机变化的材料或几何参数模型化为随机变量或随机场，从而导出纤维内含圆盘状裂纹应力强度因子的均值和协方差的公式，并用来求解承受均匀拉伸的复合材料纤维内含圆盘状裂纹的同轴双圆柱体的应力强度因子，分析了基体与纤维的弹性模量比对应力强度因子的影响，算例表明本文方法是可行和有效的。

Based on the series expansion technique, the stochastic boundary element method is developed. The stochastic variational material or geometric parameter model with respect to the space coordinate is reduced to the stochastic variable or the stochastic field. The average value and covariance formulas of the stress intensity factor for a penny-shaped crack embedded in a fiber of the composite material are deduced. The stress intensity factor of coaxial bi-cylinder having a penny-shaped crack in the fiber of composite material under the action of uniform tension is solved. The influences of the elastic modulus ratio of the matrix to fiber on the stress intensity factor are also analyzed. The computed examples show that the method in this paper is reliable and efficient.