Advancements in the Mechanical Structure Design of FalconD: The INFN-CERN Collaboration for the Nb$_{3}$Sn 12 T Cos-Theta Dipole Within the High-Field Magnets R&D Program

The FalconD project (Future Accelerator post-LHC Optimized Nb$_{3}$Sn Dipole), conducted by INFN Genoa and Milan in collaboration with CERN, is dedicated to the development of a 1.5 m long, 12 T Nb$_{3}$Sn dipole. Nb$_{3}$Sn has already proven its effectiveness in accelerator magnets, and its application to bending dipoles is a key step toward future high-field accelerator technologies. A major challenge of the design is the mechanical structure, which must withstand the substantial Lorentz forces generated by the high magnetic field. To address this, the innovative bladder and key (B$\text{&}$K) concept is adopted, applied here for the first time to a cos-theta dipole. This contribution presents a 2D finite element mechanical analysis of the FalconD, focusing on stress distribution and gap evolution during the main assembly and operational stages, with the aim of validating the design approach.