This article concerns the modeling and design of a slitted stator core for single-sided axial-flux permanent-magnet machine application. The stator core is specially designed to maximize the magnetic-flux density in the air gap and to minimize the eddy-current losses occurring at high rotational speeds. To reduce the effort needed for computing the motional eddy-current distribution in the presence of nonlinear material characteristics, a novel method is proposed. It combines the harmonic balance method, which is advantageous for simulating in the frequency domain the steady-state periodic response of a nonlinear system under harmonic excitation, together with a source description that introduces a complex magnetization that mimics the displacement of the permanent-magnet array. Following this method, time-domain distributions and losses can be reconstructed accurately with a low number of harmonics. A 3-D periodic model of the slotless axial-flux machine is built in the framework of isogeometric analysis (IGA) and a mixed formulation is employed, which relies on high-order Nédélec edge elements. The proposed model is embedded into a gradient-based optimization problem to determine the optimal shape of the slits in the stator core of the motor. This results in a novel cost-effective solution for improving the efficiency of axial-flux permanent-magnet machines.