University of Birmingham > Talks@bham > Optimisation and Numerical Analysis Seminars > Topology optimization of discrete structures by semidefinite programming

Topology optimization of discrete structures by semidefinite programming

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  • UserMarek Tyburec (Czech Technical University, Prague)
  • ClockWednesday 16 October 2019, 12:00-13:00
  • HouseStrathcona, SR5.

If you have a question about this talk, please contact Sergey Sergeev.

This contribution investigates applications of semidefinite programming (SDP) techniques to two problems of structural topology optimization. We consider first the problem of designing optimum truss reinforcement of a thin-walled composite laminate to withstand manufacturing and operational loads and to suppress elastic wall instabilities. For this problem, the instabilities can be described using free-vibration eigenmodes, allowing thus for a convex SDP representation. To accelerate the solution of these types of problems, we utilize the static condensation/(generalized) Schur complement lemma, which additionally provides us with an upper bound on the maximum admissible fundamental eigenfrequency, and a lower bound on the minimum admissible compliance of the manufacturing load case. Finally, we manufacture the composite beam prototype with a 3D-printed internal structure, perform experimental validation, and conclude that the structural response agrees well with the model predictions. As the second problem, we consider the topology optimization of frame structures. In this case, the SDP formulation is no longer convex in general. However, because the SDP constraints are polynomial matrix inequalities, we adopt the moment-sums-of-squares hierarchy for their solution. It turns out that each relaxation of this hierarchy generates both lower and upper bounds on the optimal design, which provides us not only with a measure of the solution quality but also an inexpensive sufficient condition of global optimality. For all the tested problems, finite convergence was observed.

This talk is part of the Optimisation and Numerical Analysis Seminars series.

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