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Next-generation particle accelerators require the development of high-field bending dipoles to enable precise beam control and enhance operational efficiency. $Nb_3Sn$ has emerged as a promising superconducting material, already proven in accelerator magnets like the MQXF quadrupoles for the high-luminosity upgrade of the LHC. In partnership with CERN, the INFN divisions in Genoa and Milan are leading the development of FalconD (Future Accelerator post-LHC Cosθ Optimized $Nb_3Sn$ dipole), a 12 T, $Nb_3Sn$ dipole model with a cosθ geometry. This project aims to push the boundaries of magnetic field strength and stability. This paper analyses the mechanical performance of the design after several modifications to the magnet's cross-section. The project's key challenge is its ‘bladder & key’ (B&K) mechanical structure, which must withstand intense Lorentz forces and will be implemented for the first time in a cosθ dipole. The study employs 2D and 3D finite element modelling (FEM) to evaluate the mechanical behaviour of the FalconD during each construction phase.
