A rigid-body-qualified plate theory for the nonlinear analysis of structures involving torsional actions

If a nonlinear plate theory is to be valid, it should work in the extreme case of rigid displacements. For this case, the strain energy vanishes as the strains are zero, but the instability potential of the initial forces acting on the plate does not. This is idea for deriving the instability potential of an initially stressed plate using the updated Lagrangian coordinates. For given real rigid displacements, an instability potential was derived for the plate based on the rigid body rule. Next, for given virtual rigid displacements, another instability potential was derived for the plate utilizing the equilibrium equations for the boundary tractions at the C1 and C2 states. By comparing the two instability potentials for the real and virtual rigid displacements, the total instability potential was recovered, which differs from the existing ones in the inclusion of the torsional terms. The total instability potential derived, along with the strain energy available, was adopted in the nonlinear analysis of structures involving torsional actions, by which the superiority of the present theory was demonstrated. The present theory is featured by the fact that virtually no kinematic hypothesis was adopted in the formulation.