Linear theory of Cosserat surface and elastic plates of variable thickness

Abstract

AbstractWithin the scope of the linear isothermal theory of an elastic Cosserat surface, constitutive equations are derived for an initially flat Cosserat surface in which the initial director (along the normal to the initial surface) is allowed to depend on the surface coordinates. These constitutive equations correspond to those for bending and stretching of a transversely isotropic three-dimensional plate. Special attention is given to the relevance and applicability of the results to bending of (three-dimensional) plates of variable thickness and comparison is made with a set of equations for elastic plates of variable thickness obtained, by an approximation procedure, from the three-dimensional equations.