Asymptotic Theory of Multilayer Thin Plates

A theory of thin multilayer anisotropic plates is offered. The theory is constructed on the basis of equations of the general three-dimensional theory of elasticity by means of introducing asymptotic expansions with respect to a small parameter defined as a ratio of a thickness to the characteristic length without involvement of any hypotheses regarding a nature of distribution of displacements and stresses along the thickness. Recurrent sequences of local problems are formulated and their solutions are obtained in the explicit form. It is shown that the global (averaged by certain rules) problem of theory ofplates turns out in the developed theory to be close to the Kirchhoff-Love theory of plates. The offered method makes it possible to calculate all six components of the tensor of stresses including the transverse normal stresses and stresses of multilayer shear.