疲劳多裂纹问题的Tayor级数解法

疲劳多裂纹问题是老龄结构可靠性分析中受到广泛关注的问题，在可靠性分析中需要反复求解多裂纹扩展方程，对计算方法的精度和效率提出了很高的要求。Taylor级数法是代数，微分方程的一种新的数值解法，其在线性问题中的理论和应用已经比较完善和成熟，本文将Taylor解法进一步用于非线性的疲劳多裂纹扩展方程的求解，对非线性项可以表达为多元多项式的问题，完善了Taylor级数方法的理论，通过计算实例验证了方法的精度和求解效率。

TAYLOR SERIES METHOD IN MULTIPLE FATIGUE CRACKS PROBLEM

The multiple fatigue cracks(MFC) problem is important for the reliability analysis of aging structures. It cries for a numerical method with higher precision and efficiency in the reliability analysis for repetitious calculation of the multi crack propagation equations. The Taylor series method is a new numerical method for the algebra and differential equations. The existed study shows that the Taylor series method has higher precision and efficiency. Its theory and application are mature and completed for linear problems but untried for nonlinear problems. This paper has established the Taylor series method theory for nonlinear problems, whose nonlinear items can be expressed by multi polynomials. The numerical results indicate that the Taylor series method is excellent for solving MFC problems whose nonlinear items can be expressed by multi polynomials.