Isogeometric shape optimization of shells using semi-analytical sensitivity analysis and sensitivity weighting

• DOI: 10.1016/j.cma.2014.02.001
• Publication Date: 2014-02-08T12:31:49Z
• Authors: J. Kiendl; R. Schmidt; R. Wüchner; K.-U. Bletzinger
• Keywords: Isogeometric analysis; Shape Optimization; Basis (linear algebra); Benchmark (surveying); Optimal design

Abstract 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.