FE-FD model for magneto-elastic buckling of ferromagnetic plates

A cantilever beam-plate, of magnetically soft material, inserted with its middle surface normal to a uniform magnetic field will buckle when the magnetic field reaches a critical value. The system of differential equations derived in this study are based on the Moon-Pao's model. The basic difference lies in the abandonment of the assumption that the magnetic couple acting on an element of the plate is proportional to the rotation of the middle surface of the plate. This assumption is employed in previous studies and leads to linear differential equations that is similar to the buckling problem of compressed rods or plates. Consequently, the complexity of the problem is reduced considerably. The derivation in this paper shows that the magnetoelastic buckling problem of the beam-plate is nonlinear. The solution to the system of differential equations is derived by coupling a finite element model for the magnetic field and a finite difference model for the cantilever beam-plate. The critical magnetic field, derived in this study is about 20% smaller than the experimental one, while theoretical results from previous works are about 180% larger than the experimental ones.