Thin elastic and periodic plates

Source abstract

Abstract This paper is devoted to the study of a three dimensional model of elastic periodic plate when the thickness e of the plate and the size ω of the periods are small. In the three studied limits ( e → 0 then ω → 0), (ω → 0 then e → 0) and lately ( e and ω → 0 together) the three dimensional equation of elasticity are approached by the two dimensional general equations of a linear anisotropic plate, the stretching and bending being coupled. This study points out the importance of the ratio of the two small parameters, indeed the moduli occuring in the two dimensional equations are different in the three limits. In each case a convergence proof is carried out.