孔洞和夹杂问题有限元模拟的数学理论
首发时间:2006-09-14
摘要:本文阐述了一种模拟任意孔洞及夹杂问题的新方法,该方法无需考虑内部边界,并将该数值方法运用到扩展有限元(Extended Finite Element Method, XFEM)中。在XFEM里,用单位分解法通过附加函数来改进有限元形函数,利用水平集函数来表述孔洞和夹杂的位置及材料的分界面处单元形函数的改进。并给出了带孔洞及夹杂问题的二维线弹性力学系统的控制方程、扩展有限元弱形式及其离散系统和积分方法等,为进一步数值模拟此类问题建立了基础。
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NUMERICAL THEORY OF FINITE ELEMENT METHOD SIMULATION FOR HOLES AND INCLUSIONS
Abstract: A new method to model holes and interfaces is described, without meshing the internal boundaries, and applied in Extended Finite Element Method (XFEM). In the XFEM, the finite element shape function is enriched by additional functions through the notion of partition of unity, the level set function is used to represent the location of holes and interfaces, meanwhile, to develop the local enrichment function in material interfaces. In addition, this paper gives the control equations for two-dimensional elastostatics with holes and interfaces, two different approaches for the numerical integration of the weak form and so on, it supplied basis for numerical modeling.
Keywords: holes, inclusions, level set method, extended finite element method(XFEM)
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No.8349772571158206****
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