夹杂薄板扩展有限元分析

Inclusion Sheet Metal Analysis with Extended Finite Element Method

扩展有限元法在分析不连续问题中体现了比常规有限元法的优越性,能够分析规则夹杂的应力问题.然而实际夹杂大都是不规则的,为此,本文通过引进Mum-ford-Shah模型分割不规则夹杂,利用其水平集函数跟踪不规则夹杂的边界,对于任意形状夹杂建立扩展有限元的附加函数.另外,在网格划分时,采用图像像素作为有限单元,最后列举了两个实例.计算结果表明,该方法能够分析多个任意形状夹杂的应力,与常规有限元法比较,该方法的分析结果是精确的、可行的.

Extended finite element method shows more superiority than common finite element method（CFEM） in processing discontinuous problem.It can analyze regular inclusion.However,most inclusions are irregular.So this paper introduces Mumford-Shah model to divide irregular inclusions and uses level set function to track the boundary of irregular inclusions.To arbitrary shape inclusions,the enrichment function of XFEM is constituted.Moreover,in gridding division,a pixel is made as a finite element.Finally two examples are taken.The result shows that this method can analyze two or more arbitrary shape inclusions and it is accurate and feasible as CFEM.