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

Authors:
Mariano Vázquez Espí;Jaime Cervera Bravo
Affiliations:
CIMNE--International Center for Numerical Methods in Engineering, Barcelona, España 08034;Departamento de Estructuras de Edificación, Universidad Politécnica de Madrid, Escuela Técnica Superior de Arquitectura, Madrid, España 28040
Venue:
Structural and Multidisciplinary Optimization
Year:
2011

Citing 2
Cited 4

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

Structural and Multidisciplinary Optimization
On symmetry and non-uniqueness in exact topology optimization

Structural and Multidisciplinary Optimization

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

Structural and Multidisciplinary Optimization
Comments on the Authors' Reply by T. Sokół and T. Lewiñski (2011) to a Discussion by Vazquez and Cervera (2011) on their Research Paper (Sokół and Lewiñski 2010)

Structural and Multidisciplinary Optimization
Exact truss topology optimization: allowance for support costs and different permissible stresses in tension and compression--extensions of a classical solution by Michell

Structural and Multidisciplinary Optimization
Near-optimal solutions for two point loads between two supports

Structural and Multidisciplinary Optimization

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Abstract

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 Sokół 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.