A basis reduction method using proper orthogonal decomposition for lower bound shakedown analysis of composite material

摘要

In this paper, a new basis reduction method for the construction of residual stress fields being capable of reducing the computational scale of lower bound shakedown analysis of composite based on the proper orthogonal decomposition is proposed. The method is based on calculation of snapshots of plastic strain field of RVE due to the previously selected loading history by using finite element analysis and the construction of bases of plastic strain field using the proper orthogonal decomposition. The bases of residual stress field are then obtained by solving the elastic problem having the initial strain as the computed bases of the plastic strain field. Numerical examples illustrate that the method can significantly decrease the number of bases for the shakedown analysis while maintaining good quality of the results compared to the reference solution.