Abstract
Design of composite laminated lay-ups are formulated as discrete multi-material selection problems. The design problem can be modeled as a non-convex mixed-integer optimization problem. Such problems are in general only solvable to global optimality for small to moderate sized problems. To attack larger problem instances we formulate convex and non-convex continuous relaxations which can be solved using gradient based optimization algorithms. The convex relaxation yields a lower bound on the attainable performance. The optimal solution to the convex relaxation is used as a starting guess in a continuation approach where the convex relaxation is changed to a non-convex relaxation by introduction of a quadratic penalty constraint whereby intermediate-valued designs are prevented. The minimum compliance, mass constrained multiple load case problem is formulated and solved for a number of examples which numerically confirm the sought properties of the new scheme in terms of convergence to a discrete solution.
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Notes
Carbon fiber reinforced polymer.
Glass fiber reinforced polymer.
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Acknowledgements
The authors wish to thank José Pedro Albergaria Amaral Blasques and Eduardo Muñoz, Technical University of Denmark, for fruitful discussions and ideas for challenging benchmark examples. This research is part of the “Multi-material design optimization of composite structures”-project sponsored by the Danish Research Council for Technology and Production Sciences (FTP), Grant no. 274-06-0443, this support is gratefully acknowledged.
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Hvejsel, C.F., Lund, E. & Stolpe, M. Optimization strategies for discrete multi-material stiffness optimization. Struct Multidisc Optim 44, 149–163 (2011). https://doi.org/10.1007/s00158-011-0648-5
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DOI: https://doi.org/10.1007/s00158-011-0648-5