| Summary: | The failure of unstiffened and stiffened mild steel plates subjected to blast loads is
investigated. The three failure modes identified in the literature, as the load intensity
increases, are; mode I (large ductile deformation), mode II (tensile-tearing) and mode III
(transverse shear). The prediction of failure for a large structure subjected to air blasts is a
complex problem involving non-linear response in both geometry and material properties. In
addition, the effect of high rates of strain on material properties is not well understood. An
accurate analysis using finite elements currently requires a very detailed element grid with a
large number of elements and the associated volume of input and output data. In the
preliminary stages of design this is not practical. The present work develops simplified
analysis tools to allow engineering level accuracy for preliminary design of blast loaded plates.
The analysis tools consist of an analytical formulation used to predict when material
separation has occurred, by either tensile tearing (mode II) or shear failure (mode III), in
conjunction with a numerical formulation which models the large inelastic (mode I) behaviour
of the plates when subjected to air blasts. This numerical formulation is capable of modelling
a large structure with relatively few elements and yet obtain a reasonable overall accuracy but
with a resulting loss of detail at the local level.
The numerical formulation employed for the square plates employs existing super finite
elements. These elements contain all the basic modes of deformation response (mode I) which
occur in orthogonally stiffened plates. This allows stiffened plate structures to, be modelled
with only one plate element per bay and one beam element per stiffener span, greatly
simplifying the input and output data, A regular finite element formulation is also developed to
model axisymmetric plates.
Both these formulations use von Karman large deflection theory and the von Mises
yield criterion and associated flow rule to model geometric and material non-linearities
respectively. Numerical and temporal integrations are carried out using Gauss quadrature and
the Newmark-P method respectively with Newton-Raphson iteration at each time step.
The analytical formulation used in conjunction with these numerical models takes
advantage of the overall accuracy of the deformed profile of the plates in calculating the in-plane
strain at each time step. For mode II failure, the total strain is calculated by estimating
the local bending and axial strain in the critical regions and avoiding the less accurate grid
dependent local strains. The total strain is then compared to a maximum allowable fracture
strain.
For the mode III failure of axisymmetric plates, equilibrium is used to calculate the
support reaction at the plate boundary at each time step. The calculated shear stress is then
compared to a maximum allowable shear stress to determine if shear failure has occurred. The
interaction between mode II and III failure is taken into account via an interaction
relationship. Once material separation has occurred, post failure analysis continues as the plate
translates freely through the air.
The results from the computer models for both the axisymmetric and square stiffened
and unstiffened plates are compared to experimental data available in the literature. The
numerical results show good comparison to the experimental results.
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