基于光滑扩展有限元的平板裂纹参数不确定性反求

Uncertain Inversion of Crack Parameters for Plates Based on the SmXFEM

裂纹位置和尺寸等是工程监测需掌握的非常重要的信息.光滑扩展有限元是近年来发展起来的一种模拟裂纹的有效方法,即使采用极度不规则单元仍可获得精确的模拟结果,无需单元"质量"要求.因此在单元自动划分方面具有突出的优势,这一特点也使得该方法适用于裂纹反求过程的实时调用和含裂纹仿真模型的网格自动划分.研究基于光滑扩展有限元的不确定反求方法,用于识别平面弹性板中直裂纹位置和尺寸参数,即采用光滑扩展有限元法进行拉伸工况的正问题分析,通过测量平板边缘的节点位移建立优化模型,调用遗传算法实现裂纹参数的反求.反求过程中将材料的弹性模量和Poisson(泊松)比作为区间不确定变量,采用一阶Taylor(泰勒)公式实现了平板裂纹参数的不确定性反求.

The crack parameters of positions and sizes are very important information for engineering monitoring.The smoothed extended finite element method（SmXFEM） was an effective method developed for the simulation of crack problems in recent years.The SmXFEM works well without high demand on the element quality,and gives accurate simulation results even with extremely irregular elements.The great advantages of the SmXFEM make it very suitable for automatic mesh generation of crack models in the real time calculation of crack inversion.An approach of uncertain inversion based on the SmXFEM was proposed to indentify the positions and sizes of straight cracks in elastic plane plates.In this approach,the SmXFEM,used to solve the forward problem of the crack model under tension,was called repeatedly by the genetic algorithm.Then an optimization model was established through measurement of the displacements of selected key nodes at the edge of the plate.Finally,with the elastic modulus and Poisson＇s ratio as uncertain interval variables,the 1st-order Taylor formula was used for the identification of crack parameters in the plates.The results show the correctness and applicability of the present method.