This work presents various improvements made to the Unsteady Vortex Lattice Method (UVLM) integrated into the open-source, nonlinear aeroelastic simulation environment SHARPy. The UVLM is extended by non-lifting body effects, polar corrections, and a new wake discretization scheme. The theory behind these enhancements is discussed and successfully verified. Finally, some of these enhancements are employed on a flexible aircraft demonstrator model. The results indicate an influence of the fuselage on the aeroelastic behavior of the wing, which becomes increasingly important for larger wing deformations and fuselage diameters. The polar corrections provide valuable refinements to the aerodynamic forces and moments, and the new wake discretization scheme significantly speeds up the simulations.