Asymptotics of the solution of the problem of deformation of an arbitrary locally periodic thin plate
Е. А. Акімова, С. А. Назаров, Gregory Aleksandrovich Chechkin · Transactions of the Moscow Mathematical Society · 2004
This paper is concerned with a problem in the theory of elasticity for a thin composite plate. The principal terms are constructed for the asymptotics of the solution, with only local periodicity of the elastic moduli of the material and the shape of the plate assumed. The asymptotic expression is justified with the help of a weighted anisotropic Korn’s inequality, which is proved by means of the “tetris” procedure for constructing a supporting set.