论文部分内容阅读
基于扩展多尺度有限元法的基本思想,论文介绍了一种多节点扩展多尺度有限元法.为了可以模拟更加复杂的变形,提出了一种多节点宏观单元.随后,还介绍了一种新的方法来构造该宏观单元的数值基函数.该基函数可以有效反映出宏观单元内部的微观特性,可以将这些微观特性映射到宏观尺度上来.此外,对计算该宏观单元的等效刚度矩阵和等效外力向量的方法也进行了简要的介绍,然后就可以在宏观尺度上求解原问题,这大大地降低了计算量.最后用几个具有代表性的数值算例验证了方法的有效性.通过与传统有限元方法比较发现本文提出的方法可以得到足够精确的计算结果,而仅仅花费很小的计算资源.
Based on the basic idea of extended multi-scale finite element method, a multi-node extended multi-scale finite element method is introduced in this paper. In order to simulate more complex deformations, a multi-node macroscopic unit is proposed. The basis function can effectively reflect the microscopic characteristics of the macrocells and can map these microscopic characteristics to the macroscopic scale.In addition, to calculate the equivalent stiffness matrix of the macrocells and The method of equivalent external force vector is also briefly introduced, and then the original problem can be solved macroscopically, which greatly reduces the computational load.Finally, several representative numerical examples are used to verify the effectiveness of the method. Compared with the traditional finite element method, we find that the proposed method can get enough accurate results, but only spend a small amount of computational resources.