含裂纹体的数值模拟

不连续体的数值模拟一直是工程界的热点和难点问题,特别是动态裂纹的追踪问题,由于该问题具有重要的现实意义,一直是大家关注的问题。扩展有限元是近几年出现的一种可方便模拟静态、动态裂纹的数值方法。据此,给出了这种在常规有限元框架下可模拟强不连续问题(位移)和弱不连续问题(应变局部化)的数值方法。在常规有限元位移模式中,基于单位分裂的思想加进一个跳跃函数和渐进缝尖位移场,对不连续体附近的节点自由度局部加强,反映出位移的不连续性,这样不连续体和有限元网格可以互相独立。详细给出了扩展有限元的基本原理,导出了相应的公式,给出了一种求解不连续函数的积分方法和缝尖应力强度因子的计算。算例分析表明,扩展有限元能方便有效地模拟不连续性问题,且能大大缩短前处理时间,是一种具有应用前景的模拟不连续问题数值方法。

NUMERICAL SIMULATION OF A BODY WITH CRACKS

Numerical simulation of arbitrary discontinuities is a hot and difficult problem;especially for tracking the dynamic cracks,it has important practical meaning.A new numerical method,extended finite element method(XFEM),which may conveniently simulate static and dynamic cracks,was introduced several years ago.The numerical method for modeling strong(displacement) as well as weak(strain localization) discontinuities with a standard finite element framework is presented.In the XFEM,in order to model the discontinuities of displacements,the jump function and asymptotic crack-tip displacement fields are added to the finite element approximation for the local enrichment by using the framework of partition of unity.Thus,the discontinuities are independent of the mesh.The principles of XFEM are given;and some formulas are derived.The integral scheme of discontinuous function is presented;and the evaluation of stress intensity factor is discussed.Numerical simulations illustrate that XFEM can effectively model the discontinuities;and it has wonderful practical merits.