Optimal design of a class of symmetric plane frameworks of least weight

Abstract

The aim of the paper is to place the recent results on the Michell-like problem of transmitting two vertical forces to two fixed hinge supports in the context of C. Maxwell's result and to provide answers to the remarks by Vázquez Espí and Cervera Bravo (Struct Multidisc Optim, 2011) published in their Discussion Paper: 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.

Topology optimization in structural mechanics

“…The problem related to Fig. 1 but with one roller has been solved in Sokół and Lewiński [55,56] and Sokół and Rozvany [54]. New Michell's structures for different permissible stresses in tension and compression with taking into account the cost of supports have been put forward recently by Rozvany and Sokół [57].…”

New analytical benchmarks for topology optimization and their implications. Part I: bi-symmetric trusses with two point loads between supports

“…Various cases of truss topology problems with two symmetrical loads between two supports (pin or roller) and for different domains (full or half-plane) were recently reviewed briefly by Sokół and Lewiński (2011b).…”