模拟含随机分布椭圆形夹杂弹性体的边界元法

BEM simulation of 2D solids with randomly distributed elliptic inclusions

为了模拟含随机分布椭圆形夹杂固体的等效力学特性 ,根据椭圆形夹杂积分区域的相似性 ,提出了求解此类问题的边界元计算方案。通过利用著名的有限元商用软件MSC.Marc和边界元程序对含有两个非常接近椭圆夹杂板材的对比计算分析 ,表明该文提出的边界元方案比有限元法具有更高的计算精度和计算效率。最后 ,对含有 5 0个随机分布椭圆夹杂的板材进行了计算分析 ,从而为长纤维状复合材料宏观等效力学特性的研究提供了可靠的数值模拟方法。

A new boundary element method (BEM) scheme was developed to simulate the effective mechanical properties of 2D solids with random elliptical inclusions by comparing the area of the elliptical inclusions. The predictions of the finite element software MSC.Marc were compared with those of the BEM scheme for a square sheet with two very close elliptic inclusions. The comparision showed that the BEM scheme was much more accurate and efficient than the FEM scheme. The BEM scheme was then used to successfully analyzed a square sheet with 50 randomly distributed elliptical inclusions. Thus, the BEM scheme can reliably simulate effective the macroscopic mechanical properties of long fibrous reinforced composite materials.