Dynamic Plastic Response of Circular Plates With Transverse Shear and Rotatory Inertia

Abstract

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.

Shear and bending response of a rigid-plastic beam subjected to impulsive loading

“…The influence of transverse shear effects on the behaviour of circular plates was investigated by Jones and de Oliveira [15] and by Li and Jones [16].…”

Dynamic plastic behaviour of annular plates with transverse shear effects

“…In a similar study under taken by Jones and Oliveira [24] for circular plates subjected to blast loading idealized by an instantaneous uniform velocity, it was concluded that the velocity pattern depends on a parameter n ¼ RQ 0 =2M 0 . Following a procedure similar to that by Jones and Oliveira [24] the expressions for the shear force, bending moment and the plate deflection have been obtained. It appeared that the solution of the problem including shear showed greater radial moments throughout the plate when compared with the pure bending solution.…”

“…non-dimensional deflection w 0 ; w 1 ; w 2 transverse deflections at fixed points w f residual deflection W deflection a ¼ a=R non-dimensional coordinate g transverse shear ZðtÞ; Z 0 ðtÞ travelling hinges m mass per unit length n parameters r ¼ r=R non-dimensional coordinate s 0 ; t 0 yield stresses t 1 ; t 2 ; t 3 moments of time c rotation due to bending Jones and Oliveira [24] studied the influence of the rotatory inertia and shear forces on the dynamic plastic response of simply supported circular plates to impulsive loading. This study revealed the influence of shear forces on the behaviour of plates in the case of small values of the parameter n. Li and Jones [25] investigated clamped circular plates subjected to blast loading distributed uniformly over the entire area of the plate.…”

Analytical modelling of high-rate elasto-viscoplastic deformation of circular plates subjected to impulsive loads using pseudo-spectral collocation method

“…On the other hand, substituting equation (19) and equation (21) into equation (14) and considering the point that the maximum of plastic normal strain caused by bending moment occurs at z = h=2, the following is obtained…”