Technical Brief

On the Pareto Optimality of Ashby's Selection Method for Beams Under Bending

[+] Author and Article Information
Giorgio Previati

Department of Mechanical Engineering,
Politecnico di Milano,
Milan 20156, Italy
e-mail: giorgio.previati@polimi.it

Gianpiero Mastinu

Department of Mechanical Engineering,
Politecnico di Milano,
Milan 20156, Italy
e-mail: gianpiero.mastinu@polimi.it

Massimiliano Gobbi

Department of Mechanical Engineering,
Politecnico di Milano,
Milan 20156, Italy
e-mail: massimiliano.gobbi@polimi.it

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 7, 2016; final manuscript received October 15, 2017; published online November 9, 2017. Assoc. Editor: James K. Guest.

J. Mech. Des 140(1), 014501 (Nov 09, 2017) (4 pages) Paper No: MD-16-1424; doi: 10.1115/1.4038296 History: Received June 07, 2016; Revised October 15, 2017

The paper deals with the problem of choosing the material and the cross section of a beam subjected to bending under structural safety, elastic stability, and available room constraints. An extension of the theory proposed by Ashby is presented. The Pareto-optimal set for the multi-objective problem of stiffness maximization and mass minimization under elastic stability, structural safety, and available room constraints for a beam under bending is derived analytically. The Pareto-optimal set is compared with the solution of the Ashby's selection method.

Copyright © 2017 by ASME
Topics: Design , Shapes , Stiffness
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Ashby, M. , 2011, Materials Selection in Mechanical Design, 4th ed., Butterworth-Heinemann, Oxford, UK.
Hudson, C. W. , Carruthers, J. J. , and Robinson, A. M. , 2010, “ Multiple Objective Optimisation of Composite Sandwich Structures for Rail Vehicle Floor Panels,” Compos. Struct., 92(9), pp. 2077–2082. [CrossRef]
Ashby, M. , 2000, “ Multi-Objective Optimization in Material Design and Selection,” Acta Mater., 48(1), pp. 359–369. [CrossRef]
Sirisalee, P. , Ashby, M. , Parks, G. , and Clarkson, P. , 2004, “ Multi-Criteria Material Selection in Engineering Design,” Adv. Eng. Mater., 6(1–2), pp. 84–92. [CrossRef]
Yuan, C. Y. , and Dornfeld, D. A. , 2010, “ A Schematic Method for Sustainable Material Selection of Toxic Chemicals in Design and Manufacturing,” ASME J. Mech. Des., 132(9), p. 091014. [CrossRef]
Fitch, P. E. , and Cooper, J. S. , 2004, “ Life Cycle Energy Analysis as a Method for Material Selection,” ASME J. Mech. Des., 126(5), pp. 798–804. [CrossRef]
Mattson, C. A. , Lofthouse, V. , and Bhamra, T. , 2015, “ Exploring Decision Tradeoffs in Sustainable Design,” ASME Paper No. DETC2015-47295.
Jahan, A. , Ismail, M. , Sapuan, S. , and Mustapha, F. , 2010, “ Material Screening and Choosing Methods—A Review,” Mater. Des., 31(2), pp. 696–705. [CrossRef]
Papalambros, P. , and Wilde, D. , 2000, Principles of Optimal Design. Modeling and Computation, Cambridge University Press, Cambridge, UK. [CrossRef]
Miettinen, K. , 1999, Nonlinear Multi-Objective Optimization, Kluwer Academic Publishers, Boston, MA.
Banichukl, N. V. , 1990, Introduction to Optimization of Structures, Springer-Verlag, New York. [CrossRef]
Mastinu, G. , Gobbi, M. , and Miano, C. , 2006, Optimal Design of Complex Mechanical Systems, Springer-Verlag, Berlin.
Gobbi, M. , Previati, G. , Ballo, F. , and Mastinu, G. , 2017, “ Bending of Beams of Arbitrary Cross Sections—Optimal Design by Analytical Formulae,” Struct. Multidiscip. Optim., 55(3), pp. 827–838. [CrossRef]
Gobbi, M. , Levi, F. , Mastinu, G. , and Previati, G. , 2015, “ On the Analytical Derivation of the Pareto-Optimal Set With an Application to Structural Design,” Struct. Multidiscip. Optim., 51(3), pp. 645–657. [CrossRef]
Levi, F. , and Gobbi, M. , 2006, “ An Application of Analytical Multi-Objective Optimization to Truss Structures,” AIAA Paper No. 2006-6975.


Grahic Jump Location
Fig. 1

Pareto-optimal in the objective functions domain for a beam under bending. Left: rectangular section of structural steel. Middle: different sections of structural steel. Right: different sections and different materials (thinner lines represent the region where the solution jumps between different sections). Section numbers refer to Table 2. Applied moment 1000 Nm, the available room is a square with 0.15 m side.



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