Shape optimization directly from CAD: An isogeometric boundary element approach using T-splines

We develop a T-spline isogeometric boundary element method (IGABEM) (Simpson et al., 2012; Scott et al., 2013; Simpson et al., 2014) to shape sensitivity analysis and gradient-based shape optimization in three dimensional linear elasticity. Contrary to finite element based isogeometric analysis (IGA) approaches, no parametrization of the volume is required. Hence, the iterative optimization algorithm can be implemented directly from CAD without any mesh generation or postprocessing step for returning the resulting structure to CAD designers. T-splines also guarantee a water-tight geometry without the manual geometrical-repair work as with non-uniform rational B-splines (NURBS). We demonstrate the worth of the method by analysing problems with and without analytical solutions, including engineering examples involving complex shapes. Additionally, we provide all the derivations of the required sensitivities and the details pertaining to the geometries examined in the benchmarking, to provide helpful reference problems for 3D shape optimization.