一种分析二维任意分布多裂纹的求解方法

A Numerical Algorithm for Solving Two-dimensional Arbitrary Distribution of Multiple Cracks

摘要:

基于虚边界元最小二乘法求解多域组合问题的基本思想，将每一裂纹视为一对子域，并对每一子域的虚边界上虚拟源函数的近似构造借鉴了边界型无网格法中紧支径向基函数插值的基本思想，建立了用于分析二维多裂纹问题的一种虚边界无网格最小二乘的计算格式。依据文中的子域定义，在计算过程中无需像边界元直接法中“常规子域法”那样在裂纹面的延伸边界上额外增添附加子域，从而减少了计算量，尤其避免了由附加子域所引起的因划分单元数或配点数不足或不当而带来的计算误差。为数值论证本文方法的可行性和计算精度，以及讨论任意分布多裂纹间的相互影响，文中分别给出了单向受拉无限大板的中心裂纹、三等长共线且相邻间距不同的裂纹和一水平一倾斜角不同的裂纹等算例；由数值比较可知该方法具有较高的计算精度。

Abstract:

Based on the basic idea solving multi-domain combinations with virtual boundary element least square method, that each crack can be treated as a pair of sub-domains, and learning from the interpolation of the compactly supported radial basis function used in boundary-type meshless methods to approximately construct the virtual source function on the virtual boundary corresponding to each sub-domain, the computational scheme with the virtual boundary meshless least squares analyzing two-dimensional multi-crack problems is established. According to the definition about sub-domain in this paper, the added extra sub-domains on the boundary extended along the crack surface as “conventional sub-domain method” in the direct boundary element method do not have to be considered, thereby reducing the computational, especially avoiding this calculation error caused due to inadequate number of the elements or with the collocation points configured on the boundary of the additional sub-domains and its improper configuration. In order to verify feasibility and accuracy of the numerical algorithm proposed in the article and discuss the interaction between multiple cracks with arbitrary distribution, some examples, such as a single center crack, third-adjacent spacing of different length collinear cracks and one horizontal crack and one different inclined angle crack by one-way tension in infinite plate, are given. The results show that this method leads to higher accuracy in comparison with the other methods considered in this study.