基于杂交应力元法的颗粒增强复合材料Monte-Carlo模拟

杂交应力元假设的高阶应力场可以用较疏的网格获得较高的计算精度.采用四叉树网格离散非均质计算域，四叉树杂交应力单元悬挂节点的位移协调条件自动满足，且得益于单元类型数量有限，单元刚度矩阵可以预计算，以便在实际计算时直接读取调用，大幅提高了计算效率.考虑夹杂的随机性对颗粒增强复合材料力学性能的影响，采用均匀化方法和Monte-Carlo方法，研究了随机夹杂的体积比、数量、长宽比对材料均质等效模量的影响，结果表明，复合材料的等效弹性模量随夹杂体积比、数量、长宽比的增大而增大，且对体积比最敏感.

Monte-Carlo Simulation of Particle Reinforced Composites Based on Hybrid Stress Elements

Based on the assumed high-order stress field, the hybrid stress finite element method has higher calculation accuracy with sparse grids. The quadtree meshes were used to discretize heterogeneous computing domains with advantages of the displacement coordination conditions for hanging nodes automatically satisfied. Moreover, all quadtree elements can be divided into a limited number of types, and the stiffness matrices of these elements can be pre-computed and stored in the memory, retrieved and scaled as required during computations, which greatly improves the computational efficiency. In view of the randomness of inclusions, the effects of the volume ratio, the number and the aspect ratio of random inclusions on the homogeneous equivalent modulus of the composite were discussed with the Monte-Carlo method and the homogenization method. The results show that, the equivalent elastic modulus of the composite increases with the volume ratio, the number and the aspect ratio of inclusions, and is most sensitive to the volume ratio.