A comparison of synthesis methods for cellular structures with application to additive manufacturing

Purpose - The purpose of this paper is to investigate design synthesis methods for designing lattice cellular structures to achieve desired stiffnesses. More generally, to find appropriate design problem formulations and solution algorithms for searching the large, complex design spaces associated w...

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Vydáno v:	Rapid prototyping journal Ročník 16; číslo 4; s. 275 - 283
Hlavní autoři:	Chu, Jane, Engelbrecht, Sarah, Graf, Gregory, Rosen, David W.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Bradford Emerald Group Publishing Limited 15.06.2010
Témata:	Additive manufacturing Algorithms Cellular manufacturing Cellular structure Composite materials Computer programming Decision making Deformation Design Design and development Design optimization Designers Formulations Hearing aids Manufacturing Manufacturing cells Manufacturing systems Mathematical analysis Mathematical models Optimization Polysulfone resins Programming and algorithm theory Rapid prototyping Structural systems Studies Synthesis Cellular manufacturing Design and development Structural systems Programming and algorithm theory Manufacturing systems
ISSN:	1355-2546, 1758-7670
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Abstract	Purpose - The purpose of this paper is to investigate design synthesis methods for designing lattice cellular structures to achieve desired stiffnesses. More generally, to find appropriate design problem formulations and solution algorithms for searching the large, complex design spaces associated with cellular structures.Design methodology approach - Two optimization algorithms were tested: particle swarm optimization (PSO) and Levenburg-Marquardt (LM), based on a least-squares minimization formulation. Two example problems of limited complexity, specifically a two-dimensional cantilever beam and a two-dimensional simply-supported plate, were investigated. Computational characteristics of the algorithms were reported for design problems with hundreds of variables. Constraints from additive manufacturing processes were incorporated to ensure that resulting designs are realizable.Findings - Both PSO and LM succeeded in searching the design spaces and finding good designs. LM is one to two orders of magnitude more efficient for this class of problems.Research limitations implications - Three-dimensional problems are not investigated in this paper.Practical implications - LM appears to be a viable algorithm for optimizing structures of complex geometry for minimum weight and desired stiffness.Originality value - The testing of design synthesis methods (problem formulations and algorithms) for lattice cellular structures, and the testing of PSO and LM algorithms, are of particular value.
AbstractList	Purpose - The purpose of this paper is to investigate design synthesis methods for designing lattice cellular structures to achieve desired stiffnesses. More generally, to find appropriate design problem formulations and solution algorithms for searching the large, complex design spaces associated with cellular structures.Design methodology approach - Two optimization algorithms were tested: particle swarm optimization (PSO) and Levenburg-Marquardt (LM), based on a least-squares minimization formulation. Two example problems of limited complexity, specifically a two-dimensional cantilever beam and a two-dimensional simply-supported plate, were investigated. Computational characteristics of the algorithms were reported for design problems with hundreds of variables. Constraints from additive manufacturing processes were incorporated to ensure that resulting designs are realizable.Findings - Both PSO and LM succeeded in searching the design spaces and finding good designs. LM is one to two orders of magnitude more efficient for this class of problems.Research limitations implications - Three-dimensional problems are not investigated in this paper.Practical implications - LM appears to be a viable algorithm for optimizing structures of complex geometry for minimum weight and desired stiffness.Originality value - The testing of design synthesis methods (problem formulations and algorithms) for lattice cellular structures, and the testing of PSO and LM algorithms, are of particular value. Purpose The purpose of this paper is to investigate design synthesis methods for designing lattice cellular structures to achieve desired stiffnesses. More generally, to find appropriate design problem formulations and solution algorithms for searching the large, complex design spaces associated with cellular structures. Designmethodologyapproach Two optimization algorithms were tested particle swarm optimization PSO and LevenburgMarquardt LM, based on a leastsquares minimization formulation. Two example problems of limited complexity, specifically a twodimensional cantilever beam and a twodimensional simplysupported plate, were investigated. Computational characteristics of the algorithms were reported for design problems with hundreds of variables. Constraints from additive manufacturing processes were incorporated to ensure that resulting designs are realizable. Findings Both PSO and LM succeeded in searching the design spaces and finding good designs. LM is one to two orders of magnitude more efficient for this class of problems. Research limitationsimplications Threedimensional problems are not investigated in this paper. Practical implications LM appears to be a viable algorithm for optimizing structures of complex geometry for minimum weight and desired stiffness. Originalityvalue The testing of design synthesis methods problem formulations and algorithms for lattice cellular structures, and the testing of PSO and LM algorithms, are of particular value. Purpose - The purpose of this paper is to investigate design synthesis methods for designing lattice cellular structures to achieve desired stiffnesses. More generally, to find appropriate design problem formulations and solution algorithms for searching the large, complex design spaces associated with cellular structures. Design/methodology/approach - Two optimization algorithms were tested: particle swarm optimization (PSO) and Levenburg-Marquardt (LM), based on a least-squares minimization formulation. Two example problems of limited complexity, specifically a two-dimensional cantilever beam and a two-dimensional simply-supported plate, were investigated. Computational characteristics of the algorithms were reported for design problems with hundreds of variables. Constraints from additive manufacturing processes were incorporated to ensure that resulting designs are realizable. Findings - Both PSO and LM succeeded in searching the design spaces and finding good designs. LM is one to two orders of magnitude more efficient for this class of problems. Research limitations/implications - Three-dimensional problems are not investigated in this paper. Practical implications - LM appears to be a viable algorithm for optimizing structures of complex geometry for minimum weight and desired stiffness. Originality/value - The testing of design synthesis methods (problem formulations and algorithms) for lattice cellular structures, and the testing of PSO and LM algorithms, are of particular value. [PUBLICATION ABSTRACT]
Author	Engelbrecht, Sarah Rosen, David W. Chu, Jane Graf, Gregory
Author_xml	– sequence: 1 givenname: Jane surname: Chu fullname: Chu, Jane organization: The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA – sequence: 2 givenname: Sarah surname: Engelbrecht fullname: Engelbrecht, Sarah organization: The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA – sequence: 3 givenname: Gregory surname: Graf fullname: Graf, Gregory organization: The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA – sequence: 4 givenname: David W. surname: Rosen fullname: Rosen, David W. organization: The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA
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SubjectTerms	Additive manufacturing Algorithms Cellular manufacturing Cellular structure Composite materials Computer programming Decision making Deformation Design Design and development Design optimization Designers Formulations Hearing aids Manufacturing Manufacturing cells Manufacturing systems Mathematical analysis Mathematical models Optimization Polysulfone resins Programming and algorithm theory Rapid prototyping Structural systems Studies Synthesis
Title	A comparison of synthesis methods for cellular structures with application to additive manufacturing
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