Natural Structural Shapes of Shallow Arches

[+] Author and Article Information
W. Stadler

Technische Universität München, Lehrstuhl und Institut B für Mechanik, Arcisshasse 21, D-8000 München 21, Germany

J. Appl. Mech 44(2), 291-298 (Jun 01, 1977) (8 pages) doi:10.1115/1.3424040 History: Received August 01, 1976; Revised January 01, 1977; Online July 12, 2010


This paper serves as a further illustration of the concept of natural structural shapes, a concept in optimal structural design. Natural shapes occur as solutions of a multicriteria control problem with criteria “mass” and “stored energy” of the deformed structure. The corresponding optimality concept is that of Pareto-optimality. This general approach is applied to the calculation of optimal initial shapes of uniform shallow arches. The resultant problem is a so-called unbounded problem in multicriteria control theory; there are no state constraints. The solution consists of a family of optimal shapes. The subsequent specification of additional constraints such as the maximum allowable deflection, stress, mass, and the like, then yields a particular member of the family. The solutions to the minimum weight and the minimum of the maximum deflection problem appear as limiting cases.

Copyright © 1977 by ASME
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