Natural Structural Shapes of Shallow Arches

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Abstract
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.

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