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Isogeometric shape optimization of shells using semi-analytical sensitivity analysis and sensitivity weighting. (English) Zbl 1296.74082
Summary: We present isogeometric shape optimization for shell structures applying sensitivity weighting and semi-analytical analysis. We use a rotation-free shell formulation and all involved geometry models, i.e., initial design, analysis model, optimization model, and final design use the same geometric basis, in particular NURBS. A sensitivity weighting scheme is presented which eliminates certain effects of the chosen discretization on the design update. A multilevel design approach is applied such that the design space can be chosen independently from the analysis space. The use of semi-analytical sensitivities allows having different polynomial degrees for design and analysis model. Different numerical examples are performed which confirm the applicability of the proposed method. Furthermore, a shape optimization example with an exact solution is presented which can serve as general benchmark for shape optimization methods.

MSC:
74P15 Topological methods for optimization problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74K25 Shells
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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