NON-HOMOGENIZATION APPROACH TO THE ANALYSIS OF PERIODIC ELASTIC SYSTEMS: APPLICATIONS TO FRACTURE MECHANICS AND TOPOLOGICAL OPTIMIZATION

摘要

The representative cell method is employed for the analysis of periodic elastic domains. The method is based on the discrete Fourier transform and reduces the analysis of an arbitrarily loaded domain possessing translational symmetry to the analysis of a single repetitive cell. In the case of topological optimization of periodic structures the problem for the cell is solved numerically by the use of the finite element method. As an example of a fracture problem the analysis of a 2D regular beam lattice with a flaw is presented. In this case the cell problem is solved analytically. Crack nucleation and propagation for different layouts with triangular, square and hexagonal cells is also considered.