Mixed variational principle for micropolar elasticity and an accurate two-dimensional plate model

Abstract

A mixed variational principle for the micropolar elasticity theory is established in which the displacements, microrotations, force stresses and couple stresses are considered as independent fields. The presented mixed variational principle not only collects all the intrinsic features of the model in one statement, but, it helps to overcome some inconsistencies between introduced simple kinematic assumptions and the boundary conditions. The mixed variational statement is used to present improved 2D model for micropolar plates. A simple displacement vector accounting for shear deformation and normal stain effects is introduced, as well as, microrotations are taken varying linearly through the plate thickness. Furthermore, force stresses and couple stresses are assumed in complete consistent with the loading conditions on the external faces of the plates. Bending and free vibration applications are presented for micropolar homogenous and functionally graded (FG) plates with different edges conditions. The validity of the presented model is examined by comparing some present numerical results with other published results due to 2D and 3D micropolar plate models. Numerical and graphical analyses are presented to demonstrate the importance of the normal strain and microrotation effects on the bending and free vibration responses of the micropolar plates.