Asymptotic Analysis of Second-Order Boundary Layer Correctors for Composite Plate with 3-D Small Periodic Configuration

Abstract

We consider a second order two scale (SOTS) approximate solution to the 3-D small periodic configuration composite plate. Classical two scale approximation yields a O( ) error in whole domain. We construct here a second-order mixed boundary layers corrections for the rectangle composite plate. Based on the boundary layers correctors, we prove that the optimal convergence order of the approximate solution to composite plate is O( ) in H1-norm. The numerical results for predicting the elastic parameters and the displacement and strains to composite plate made of 3-D 4-direction braided materials are demonstrated. Those show that the two scale approximation solution can capture the macroscopic phenomena caused from 3-D microcosmic configuration well.