Analytical and numerical magnetostatic modeling of solid and hollow ferromagnetic structures with complex geometry

The accurate prediction of magnetic fields generated by ferromagnetic housings in large-scale engineered systems is essential for magnetic signature control and magnetic field management. This work aims to provide a general analytical framework for evaluating the static magnetic signature of complex ferromagnetic components by employing a formulation based on the magnetic scalar potential together with volume‑averaged magnetization and effective relative magnetic permeability. The proposed method models arbitrarily shaped housings through equivalent cylindrical bodies that preserve volume and characteristic dimensions, enabling rapid field evaluation in regimes where classical dipole approximations lose accuracy. The framework is applied to two representative structures, a rotating machinery housing and a thin-walled enclosure for energy conversion devices, and analytical predictions are benchmarked against finite element simulations, showing consistent trends and order‑of‑magnitude agreement. Material substitution effects are assessed, and the limiting case of near‑zero effective magnetic permeability is examined, providing a theoretical lower bound for magnetic signature reduction and illustrating an analogue of metamaterial-inspired behavior. Results indicate that decreasing both effective magnetic permeability and averaged magnetization yields substantial attenuation of the static magnetic signature, approaching two orders of magnitude in the limiting case. The proposed analytical model therefore offers a computationally efficient tool for magnetic field prediction and magnetic signature control in complex ferromagnetic housings.