Developments in Mitchell Theory,
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1981
- Accession Number
- ADP000045
Entities
People
- Jean-marie Lagache