A rational approach to Cosserat continua, with application to plate and beam theories

• Develops a new approach to the formulation of the mechanics of generalized continua.
• Suggests a natural definition of classes of generalized continua.
• Provides a direct deduction of plate and beam theories from the 3D Cosserat continuum.

In a recently proposed approach, a generalized continuum is defined by the specification of the form of the external power, plus some regularity assumptions on the system of the contact actions. Under these assumptions the power can be expressed as a volume integral, the internal power. The conditions of indifference to rigid virtual velocities lead to a reduced form of the internal power, which determines the internal forces and generalized deformations to be related by constitutive equations and to be specified in the boundary conditions. Further restrictions, imposed by kinematic constraints, determine special subclasses of continua. In this context, the equations of some classical plate and beam theories are deduced from those of the three-dimensional Cosserat continuum in a quite simple and natural way.