On a new class of separable models in topology and material optimization

Abstract: Separable models are used in specialized optimization solvers for structural optimization like the method of moving asymptotes (MMA) for many years. In this presentation, we derive a so called exact separable models using the Sherman-Morrison-Woodbury-Formula. In this context, exact means that the model matches an approximated function exactly, as long as the design of only one element is varied. In simple cases, there is a 1-to-1 correspondence to the MMA model. In more general situations, non-linear material parametrizations cause the exact separable model to be non-convex, non-smooth or even discontinuous. To cope with that, the sequential global programming (SGP) algorithm is used. In the first part of the talk the concepts of exact separable models and the SGP method are introduced and some theoretical results like a link to the calculus of topological derivatives and convergence properties are briefly discussed. In the second part, applications from various areas of material and topology optimization are used to demonstrate the accuracy and efficiency of the new approach.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)