Homogenization Limits of the Equations of Elasticity in Thin Domains
A. Damlamian, M. Vogelius · SIAM Journal on Mathematical Analysis · 1987
We study pure bending of a flat, linearly elastic three-dimensional plate with rapidly varying composition. Under appropriate coercivity—and boundedness—assumptions, it is shown that all limiting vertical displacement, coming from the equations of three-dimensional elasticity with plate thickness approaching 0, must necessarily satisfy a fourth order, two-dimensional “plate” equation. This analysis does not require any special structure of the composition, such as periodicity or quasiperiodicity.