A COMPLETE STABILITY THEORY FOR THE KIRCHHOFF THIN PLATE UNDER ALL KINDS OF ACTIONS

A complete stability theory for a plate can be constructed by an incremental virtual work equation describing instability effects induced by all kinds of actions. Besides, this incremental virtual work equation should satisfy the rigid body rule, i.e., it should objectively obey the rigid body rule no matter what coordinates systems are adopted. In this paper, a complete nonlinear stability theory for the Kirchhoff thin plate is proposed by using the principle of virtual work and the update Lagrangian formulation. Then, a rigid body motion testing method is developed for examining the incremental virtual work equation. In developing such a theory, three key procedures are especially considered. First of all, the virtual strain energy contributed from all six nonlinear strain components are clearly identified and then, two actions on the effective transverse edge per unit length, namely the Kirchhoff's forces and moment per unit length in the currently deformed configuration (2 C state) are especially considered here in contrast to be ignored in previous literatures. Finally, nonlinear terms of the virtual work done by boundary moments per unit length in the 2 C state are also derived. Advantages of this new theory not only come from passing the rigid body rule, which is seldom found in the nonlinear theory of the plate, but also owing to the completeness of the proposed theory.