Structural and Multidisciplinary Optimization

, Volume 51, Issue 6, pp 1247–1265 | Cite as

Discrete thickness optimization via piecewise constraint penalization



Structural engineers are often constrained by cost or manufacturing considerations to select member thicknesses from a discrete set of values. Conventional, gradient-free techniques to solve these discrete problems cannot handle large problem sizes, while discrete material optimization (DMO) techniques may encounter difficulties, especially for bending-dominated problems. To resolve these issues, we propose an efficient gradient-based technique to obtain engineering solutions to the discrete thickness selection problem. The proposed technique uses a series of constraints to enforce an effective stiffness-to-mass and strength-to-mass penalty on intermediate designs. In conjunction with these constraints, we apply an exact penalty function which drives the solution towards a discrete design. We utilize a continuation approach to obtain approximate solutions to the discrete thickness selection problem by solving a sequence of relaxed continuous problems with increasing penalization. We also show how this approach can be applied to combined discrete thickness selection and topology optimization design problems. To demonstrate the effectiveness of the proposed technique, we present both compliance and stress-constrained results for in-plane and bending-dominated problems.


Constraint penalization Discrete thickness Gradient-based optimization 



The author would like to thank the anonymous reviewers for their helpful recommendations that greatly improved the paper. The author gratefully acknowledges the financial support of the Georgia Institute of Technology.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Georgia Institute of TechnologySchool of Aerospace EngineeringAtlantaGeorgia

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