A p-adaptive multi-node extended multiscale finite element method for 2D elastostatic analysis of heterogeneous materials

A multi-node extended multiscale finite element method is developed for 2D elastostatic analysis of the computational models with various microstructures. In addition, an adaptive algorithm is proposed for the coarse-scale mesh based on the developed multiscale method. Then, the basic principles of the multi-node extended multiscale finite element method are introduced in detail. To verify the effectiveness of the adaptive algorithm, some representative numerical experiments are carried out. By comparing with the reference solutions, which are obtained by the standard finite element method on the fine-scale mesh, it can be seen that multiscale solutions with high accuracy will be calculated by combining the developed multiscale method and the proposed adaptive algorithm. Finally, a nearly optimal distribution of macroscopic nodes on the fixed coarse-scale mesh can be found by using the proposed adaptive algorithm. Thus, the contradiction between the amount of calculation and computational accuracy, to some extent, can be balanced by using the adaptive multi-node extended multiscale finite element method.