On the Plastic Instability of a Circular Plate under Compression in the Case of Simple Flow

Abstract The loss of stability of a circular plate under uniform compression by a dead load is studied in a quasi-static setting. The plate is modeled as a multicomponent elastoviscoplastic medium. The problem is formulated for a multicomponent medium. The subcritical stress-strain state is defined in a cylindrical coordinate system. From the general solutions of the linearized equations of three-dimensional stability theory, a particular solution is considered that satisfies the boundary conditions of rigid plate restraint. A transcendental equation for determining the critical force is derived. For a thin-walled plate, it is presented in analytical form.