Developments in Mitchell Theory,
CENTRE EXPERIMENTAL DE RECHERCHES ET D'ETUDES DU BATIMENT ET DE TRAVAUX PUBLICS PARIS (FRANCE)
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The design of trusses of minimum volume is considered, subject to the conditions that members are included in some feasible region and safely carry a given system of loads to a rigid foundation. Michell Theory then relates upon virtual feasible displacements. Three theorems about feasible displacements are given in the present paper 1 There exists at least one extremal feasible displacement, which makes the work of external loads a maximum upon the class of all feasible displacements 2 Should an optimal truss exist or not, the minimum volume for trusses, V min, and the maximum feasible work, W max, satisfy W max V min and 3 The computation of only one extremal displacement allows all optimum frames to be synthetized by a converse application of Michell Criterion. Specially, there is no optimum frame at all when the Criterion is inapplicable.