Stability of the micropolar thin round plate


In this paper, a thin round plate of isotropic micropolar elastic material is considered, in which the elastic deflections are comparable with their thickness, and small in relation to the basic size, also both the angles of rotation of the normal elements to the middle plane before deformation and their free rotations are small. Thus, the strain tensor and tensor of bending-torsion takes into account not only linear but also the nonlinear terms in the gradients of displacement and rotation. The stability problem is solved in the case when the solid round plate is hinge supported along the contour and is under the action of radial compressive forces. After solving the obtained boundary value problem, the critical value of the external force is determined. The critical force of the micropolar problem is compared with the value of the classical solution. The important properties of micropolar material are established.