Extended multiscale finite element method for large deflection analysis of thin-walled composite structures with complicated microstructure characteristics

An efficient multiscale finite element method is developed for large deflection analysis of thin-walled composite structures with complicated microstructure characteristics. The multiscale base functions are reconstructed to consider the coupling effects of thin-walled composite structures by introducing some additional coupling terms among translations and rotations. For the construction of multiscale base functions, two kinds of displacement boundary conditions are proposed for in-plane and out-plane degrees of freedom. Moreover, two kinds of relaxed decoupled displacement boundary conditions are constructed by adopting the oversampling technique to further improve the accuracy of the method. Then, the equivalent incremental/iterative equilibrium equations for each load step can be constructed and solved directly on the macro scale which will improve the computing efficiency significantly. The microscopic results can be obtained by downscale computation in which the incremental/iterative equilibrium equations on the micro scale are solved under the incremental boundary conditions updated by incremental macroscopic displacements. Several numerical examples demonstrate that the developed method possesses high computing accuracy and efficiency compared with the conventional finite element method.