The research project addresses the multiphysical simulation and shape optimization of electrical machines based on Isogeometric Analysis (IGA) in three dimensions. Isogeometric analysis is based on the use of B-splines and nonuniform rational B-splines (NURBS) for both geometry representation and solution space instead of non-smoothly interconnected polynomials. These bases allow for the direct and approximation-free use of geometry data of computer-aided design (CAD), and therefore a simplified implementation of freeform optimization. In IGA, the solutions are also given in terms of splines, such that neither interpolation nor remeshing are necessary when considering the interaction between electromagnetic, thermal and mechanical phenomena and Noise-Vibration-Harshness calculations. Furthermore, for smooth solutions IGA has a higher accuracy per degree of freedom. This is especially relevant in the air gap of an electric machine, where the smoothness of the solution can be exploited. High numerical efficiency when considering rotation of the machine will be achieved by the use of mortaring, , e.g. by harmonic stator-rotor coupling.