Multi-scale Finite Element Method and its Application

In order to improve the computing precision and computing efficiency of strength of woven composite material, the strength of woven composite material based on multi-scale finite element method (MsFEM) is simulated. The periodical boundary conditions are applied to the finite element method analyses to ensure stress continuous and strain continuous on boundary surfaces. The method can efficiently capture the large scale behavior of the solution without resolving all the small scale features by constructing the multi-scale finite element base functions that are adaptive to the local property of the differential operator. The characteristic difference between MsFEM and the conventional finite element method is attributed to base function. The applications demonstrate that the advantages of the multi-scale finite element method for numerical simulation of strength problem of woven composite material, i.e. significantly reducing computational efforts, and improving the accuracy of the solutions.