Abstract
In this article, we present the Free Material Optimization (FMO) problem for plates and shells based on Naghdi’s shell model. In FMO – a branch of structural optimization – we search for the ultimately best material properties in a given design domain loaded by a set of given forces. The optimization variable is the full material tensor at each point of the design domain. We give a basic formulation of the problem and prove existence of an optimal solution. Lagrange duality theory allows to identify the basic problem as the dual of an infinite-dimensional convex nonlinear semidefinite program. After discretization by the finite element method the latter problem can be solved using a nonlinear SDP code. The article is concluded by a few numerical studies.
This work has been supported by the European Commission within the Sixth Framework Programme 2002 – 2006 (FP-6 STREP 30717 PLATO-N).
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Gaile, S., Leugering, G., Stingl, M. (2009). Free Material Optimization for Plates and Shells. In: Korytowski, A., Malanowski, K., Mitkowski, W., Szymkat, M. (eds) System Modeling and Optimization. CSMO 2007. IFIP Advances in Information and Communication Technology, vol 312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04802-9_12
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DOI: https://doi.org/10.1007/978-3-642-04802-9_12
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