SC Seminar: Rozan I. Rosandi

Rozan I. Rosandi, Differential-Algebraic Systems Group, TU Kaiserslautern

A Riemannian Framework for the Isogeometric Shape Optimization of Thin Shells


Structural optimization is concerned with finding an optimal design for a structure under mechanical load. In this talk, we consider thin elastic shell structures based on the linearized Koiter model, whose shape can be described by a surface embedded in Euclidean space. We regard the set of all embeddings of the surface as an infinite-dimensional Riemannian manifold and perform optimization in this setting using the Riemannian shape gradient. Non-uniform rational B-splines (NURBS) are employed to parameterize the surface and solve the underlying equations that govern the mechanical behavior of the shell via isogeometric analysis (IGA). By representing NURBS patches as B-spline patches in projective space, NURBS weights can also be incorporated into the optimization routine. We discuss the practical implementation of the method and demonstrate our approach on the compliance minimization of a half-cylindrical shell under static load and fixed area constraint.

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