On the linear theory of micropolar plates

Source abstract

Abstract We discuss the general linear six‐parametric theory of plates based on the direct approach. We consider the plate as a deformable surface. Each material point of the surface can be regarded as an infinitesimal small rigid body with six degrees of freedom. The kinematics of the plate is described by using the vector of translation and the vector of rotation as the independent variables. The relations between the equilibrium conditions of a three‐dimensional micropolar plate‐like body and the two‐dimensional equilibrium equations of the deformable surface are established. Using the three‐dimensional constitutive equations of a micropolar material we discuss the determination of the effective stiffness tensors appearing in the two‐dimensional constitutive equations.