On the influence of radial displacements and bending strains on the large deflections of impulsively loaded circular plates

• A model of a blast loaded circular plate with a closed form solution is presented.
• The model includes radial displacements with coupled bending and membrane effects.
• The model shows why radial displacements may be ignored for deflection estimates.
• The model provides limits when bending and/or membrane effects are negligible.
• The model shows that initial non-monotonic plastic work is small.

This work considers the validity of the assumption that the influence of radial displacements and bending strains can be ignored when constructing closed form analytical solutions for the large displacement response of impulsively loaded circular plates. Three successive energy based analyses are presented. The first analysis considers only membrane strains, but includes radial displacements in addition to transverse displacements. It is shown that the inclusion of radial displacements alters the plastic strain distribution but does not alter the integral of the total energy dissipated due to plastic strain, and consequently, does not affect the final central deflection estimate. This result provides a rigorous justification for the assumption that radial displacements can be ignored. However, though neglectable, the radial displacements are not negligible and must be included in order to obtain realistic strain distributions. Thereafter, a model is presented that considers the interaction of bending and membrane strains. It is shown that at large displacements the membrane strains suppress the effect of bending strains. This result supports the assumption that bending strains can be ignored at large deflections. Furthermore, it provides an estimate for the displacement range in which the interaction between bending and membrane effects is significant and should not be ignored. Lastly, the non-monotonic nature of the strain history is considered and shown to have a small effect.