The crushing analysis of rotationally symmetric plastic shells undergoing very large deflections is presented. A general methodology is developed and simple closed-form solutions are derived for the case of a conical shell, a spherical shell under point load, a spherical shell crushed between rigid plates and under boss loading, and a spherical cap under external uniform pressure.

The response of a simply supported circular plate made from a rigid perfectly plastic material and subjected to a uniformly distributed impulsive velocity is developed herein. Plastic yielding of the material is controlled by a yield criterion which retains the transverse shear force as well as bending moments and the influence of rotatory inertia is included in the governing equations. Various equations and numerical results are presented which may be used to assess the importance of transverse shear effects and rotatory inertia for this particular problem.

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The theoretical procedure presented herein examines the influence of retaining the transverse shear force in the yield criterion and rotatory inertia on the dynamic plastic response of beams. Exact theoretical rigid perfectly plastic solutions are presented for a long beam impacted by a mass and a simply supported beam loaded impulsively. It transpires that rotatory inertia might play a small, but not negligible, role on the response of these beams. The results in the various figures indicate that the greatest departure from an analysis which neglects rotatory inertia but retains the influence of the bending moment and transverse shear force in the yield condition is approximately 11 percent for the particular range of parameters considered.

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