<p>Additive manufacturing has enlarged the design space of variable stiffness continuous fiber-reinforced polymers by enabling increased freedom in the fibers’ geometric layout. Topology optimization can be used to fully harness such freedom in design of continuous fiber-reinforced polymer structures, but constraints are still needed to avoid manufacturing-induced defects like fiber buckling, gaps between fiber tows, or overlapping fiber tows. This paper introduces a topology optimization formulation for maximally-stiff structures composed of continuous fiber-reinforced polymers with constraints on structural volume and fiber path geometry. Density design variables define the structure’s topology and geometry, and fiber orientation design variables define the local fiber orientation. The fiber orientation design variables are defined at support points of radial basis functions so that differentiable functions describing the curl and divergence of the fiber orientation field can be used to control the local fiber curvature and growth of gaps or overlaps between fiber tows, respectively. The augmented Lagrangian method is used to handle the large number of local curl and divergence constraints. At present, this work is limited to a single, two-dimensional laminate. Several design examples illustrate how the curl and divergence constraints can be controlled to meet local fiber tow curvature restrictions and limit the growth of gaps and overlaps between fiber tows based on process-specific additive manufacturing constraints, and how the constraints influence the optimized topology, geometry, and fiber layout.</p>