用于非均质复合材料应力分析的交错网格有限体积法

Staggered Cell-Vertex Finite Volume Method for Analyzing Stress in Heterogeneous Composite Materials

针对非均质复合材料的应力问题,发展了一种交错网格有限体积法(SCV-FVM)。该方法基于非结构网格离散线弹性平衡方程,采用交错网格技术将材料的空间变化引入离散过程,从而不需要显式处理复合材料交界面。用SCV-FVM对宏观非均质复合材料应力场进行了数值模拟,结果与理论解吻合良好。与其他数值结果的对比表明,SCV-FVM能够避免材料物性突变引起的牵引力方向的应力数值波动及不连续现象,但是难以捕捉垂直于牵引力方向的应力跳跃现象,可以通过加密交界面网格来改善计算结果。用SCV-FVM对微观非均质复合材料应力场进行了数值模拟,结果不存在由物性参数空间变化引起的数值不连续现象及应力集中现象,表明SCV-FVM适合对微观非均质材料进行应力分析。

A staggered cell-vertex finite volume method （SCV-FVM） is developed for stress analysis in heterogeneous composite materials. The linear elastic equilibrium equation is discretized based on unstructured grids. The staggered grid technique is adopted to introduce the material variation into the discretization, so it is unnecessary to treat the material interfaces explicitly. SCV-FVM is taken to simulate the elastic fields of macrostructures and the results agree well with the analytical ones. Comparisons between different numerical results show that SCV-FVM is able to avoid numerical oscillation of the stress along traction direction, however it is hard for SCV-FVM to capture the stress jump vertical to the traction direction, which can be improved by refining the mesh around the material interface. The elastic performance of multi- layer composites with microstructures is discussed via SCV-FVM, and the numerical discontinuity and stress concentration due to variation of physical parameters do not appear in the predicted results, which demonstrates the feasibility of SCV-FVM for stress analysis of heterogeneous composite materials.