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Plastic Behaviour of Circular Plates Under Transverse Impulse Loadings of Gaussian Distribution

An analytical study of the plastic response of a circular plate of uniform thickness
subjected to a normal axisymmetric impulse of Gaussian distribution is presented. The
Gaussian impulse loading is assumed initially to impart a momentum to the plate. The
plate is thereafter prescribed as free from external loads. The kinetic energy of motion
is assumed to be dissipated in plastic deformation. The radial and circumferential
strain and strain—rate distributions of the plastically deforming plate are determined as
a function of time and space from derived deflection expressions. Only the bending
action of the plate is taken into account and the plate material is assumed to behave as a
perfectly plastic—rigid continuum.
The possibility of a fracture or separation of the plate material occurring during
deformation is discussed. Maximum values of strain and strain rate are shown to occur
in the circumferential components, and a mode of failure by radial fractures is indicated.
The impingement and fracture of the main wall of a space vehicle by meteoroids
are of major concern to the spacecraft designer. Protective devices, such as meteoroid
bumpers, have been proposed to shatter the impinging meteoroid and to lessen its pene-
trating potential. It has been shown both theoretically and experimentally (refs. 1 and 2)
that the resulting cloud of meteoroid and bumper debris passes on to the main wall of the
space vehicle as an impulsive loading having a general Gaussian distribution. A study
of the dynamic response of a plate under this impulsive type loading could well classify
the mode or manner of fracture at failure recently observed experimentally on double
sheet models of a bumper and main wall configuration. (See refs. 3 and 4.)
The information presented herein was included in a thesis submitted in partial ful-
fillment of the requirements for the degree of Doctor of Philosophy, Virginia Polytechnic
Institute, Blacksburg, Va., 1966.
A thorough analysis of the behavior of an impulsively loaded plate should include
not only the plastic but also the elastic response of the plate material. Because of the
complex time-dependent properties of the problem, however, most analyses consider
only the rigid—plastic response of the plate and neglect its elastic behavior entirely.