有限覆盖无单元法在裂纹扩展数值分析问题中的应用

有限覆盖无单元法是一种基于有限覆盖技术和无单元法的数值计算方法。有限覆盖技术是数值流形方法的基础,由于数值流形方法具有统一处理连续与非连续问题的能力,而无单元法的前处理比较简单。因此有限覆盖无单元法综合了数值流形方法与无单元方法的优点,能够更有效地处理非连续性问题。本文简要阐述了有限覆盖无单元法的基本理论,着重将这种方法应用于应力强度因子计算和裂纹扩展模拟问题。若干算例数值计算结果表明了这种方法的有效性。

Applications of the finite-cover element-free method in numerical analyses of crack-expansion

Finite cover based element free method is a numerical method based on finite cover concept and element free method. Finite cover is fundamental technique in manifold method which can deal with both continuous and discontinuous problems in a universal form. The prior process of the element free method is relatively simple. Finite cover based element free method can integrates merits of both numerical manifold method and element free method. At the same time, it can overcome their individual shortcomings. This method can handle discontinuous problems in a fairly effective way and it is easily implemented. In this paper, fundamental theory of the finite cover based element free method developed by the authors is briefly presented. The proposed method is successfully applied in the computations of stress intensity factor and numerical simulations of crack expansion. The effectiveness of the present method is verified by some numerical examples.