On Computational Strategies for Multiscale, Time-dependent, Nonlinear Structural Problems

摘要

This paper deals with multiscale computational strategies for nonlinear problems in structural mechanics, which are rather promising tools for solving several of today's engineering challenges. Following a review of the different approaches, we focus on a recently proposed multiscale computational strategy for the analysis of structures described on a refined space scale and a refined time scale. This strategy, which involves homogenization both in space and in time, requires no condition of periodicity. It is iterative and involves the resolution of problems on both a "micro" (fine) scale and a "macro" (homogenized) scale. In this overview, we present the bases of this approach and the numerical techniques used to solve the micro and macro problems. Finally, we discuss the efficiency of the method by giving numerical examples.