Etude de la déformée hors-plan d’une membrane microstructurée 2 par une approche discrète et non-locale

Abstract

In this paper, the static behavior of a finite microstructured rectangular membrane is studied. The 17 microstructured membrane model comprises a given number of elastic springs in both directions 18 forming a rectangular lattice membrane. We consider the out-of-plane displacement of each node of 19 this two-dimensional lattice. The rectangular lattice membrane is fixed at its boundary. A nonlocal 20 continuous membrane model is developed to approximate the behavior of the finite lattice model. A 21 continualization procedure is applied to the discrete equations where the difference operators are 22 approximated by differential operators. The resulting nonlocal continuum is governed by some length 23 scales in each direction that depend on the size of the microstructure. A comparison of both discrete 24 (the reference lattice model) and continualized nonlocal responses brings out the effectiveness of this 25 micromechanics-based approach.