### ASA 127th Meeting M.I.T. 1994 June 6-10

## 2aSA5. The theory of fuzzy structures---A statistical continuum mechanics
interpretation.

**J. J. McCoy
**

**
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*School of Eng., Catholic Univ. of America, Rm. 102, Pangborn Hall,
Washington, DC 20064
*

*
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The theory of fuzzy structures is demonstrated to follow from a
renormalization of a more fundamental continuum mechanics formulation. The
derivation accepts an explicitly statistical interpretation of the attached
fuzzy and the achieved renormalization applies for estimating the ensemble
averaged response of the master structure. An alternative interpretation of the
attached fuzzy acting on a much smaller length scale than that required for
describing the master structure response is briefly discussed. Several issues
are identified that suggest the theory cannot be rigorously justified as a
general mathematical framework. These issues relate to the uniqueness of
predictions, to the independence of the effective impedance operator that
reflects the presence of the fuzzy structure attachments to the master
structure, and to the well-posedness of the inverse problem for determining
this effective impedance from experiments of the response of the master
structure. The case of point-connected fuzzy structures is investigated in
detail and a distinction between an added inertia force and an added stiffness
is emphasized. The simplification of the renormalization required for the added
inertia forces is shown to reproduce a result of a statistical independence
assumption.