On the solution of the three forces problem and its application in optimal designing of a class of symmetric plane frameworks of least weight: Discussion on the Michell class concept

摘要

The details of the Theorem of Michell are examined. Some remarks are made about the quantity of structure and the Maxwell number of a framework and about the Michell optimality criterion. The two-loads bending problem is examined, comparing solutions derived from another one found by Sokó? and Lewiński (Struct Multidisc Optim 42:835-853, 2010) with others obtained from simulated annealing (SA) search. The collected data suggest that the Michell theorem is a sufficient test for a framework to be optimal, but maybe no necessary. As a consequence, there could exist problems for which the theorem is useless.