Problem formulations are presented for the evaluation of upper and
lower bounds on the effect of progressive structural degradation.
For the purposes of this study, degradation effect is measured by
an increase in global structural compliance (flexibility). Thus
the stated bounds are given simply by the maximum and minimum
values, respectively, of the increase in compliance corresponding
to a specified global interval of degradation. Solutions to these
optimization problems identify the particular patterns of local
degradation associated with the respective 'worst case' and 'least
degrading' interpretations. Several formulations for extremal
'loss of stiffness', each with one or another form of model for
local degradation, are compared and evaluated. An isoperimetric
constraint controls the degree of loss in overall structural
stiffness. Results obtained sequentially for a set of specified,
increasing values for the bound in this constraint track the
evolution of local degradation. While the full exposition of the
paper is written specifically for trussed structures, analogues
for the more useful formulations are described as well for the
treatment of continuum systems. Implementation of methods for
computational solution are described in detail, and computational
results are given for the bound solutions corresponding to
evolution from a starting structure through to its fully degraded
form.

Number of pages | 34 |
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Publication status | Published - 1997 |
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