Discrete thickness optimization via piecewise constraint penalization
- 38k Downloads
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.
KeywordsConstraint 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.
- Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. SpringerGoogle Scholar
- Kennedy GJ, Martins JRRA (2010) Parallel solution methods for aerostructural analysis and design optimization. In: Proceedings of the 13th AIAA/ISSMO multidisciplinary analysis optimization conference, Fort Worth. AIAA 2010–9308Google Scholar
- Kennedy GJ, Martins J RRA (2013) A laminate parametrization technique for discrete ply-angle problems with manufacturing constraints. Struct Multidiscip Optim:1–15. doi:10.1007/s00158-013-0906-9. ISSN 1615-147X
- Kreisselmeier G, Steinhauser R (1979) Systematic control design by optimizing a vector performance index. In: International federation of active controls symposium on computer-aided design of control systems. Zurich, SwitzerlandGoogle Scholar
- Nocedal J, Wright SJ (2006) Numerical Optimization. Springer series in operations research and financial engineering. SpringerGoogle Scholar
- Stegmann J, Lund E (2005) Discrete material optimization of general composite shell structures. Int J Numer Methods Eng:2009–2027. doi:10.1002/nme.1259. ISSN 1097-0207