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

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

J. J. McCoy

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

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.