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

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.

Citation

Chu, J., Engelbrecht, S., Graf, G. and Rosen, D.W. (2010), "A comparison of synthesis methods for cellular structures with application to additive manufacturing", Rapid Prototyping Journal, Vol. 16 No. 4, pp. 275-283. https://doi.org/10.1108/13552541011049298