The Application Of Galerkin Meshless Methods In Magnetoelastic Coupling Of Ferromagnetic Plates

With the development of modern technology, ferromagnetic structures are widelyused as main components in many electromagnetic apparatuses. As the ferromagneticstructures being in the magnetic field, they may bend even to lose stability caused bymagnetic force. Since it is related to the safety and effective operation of thesestructures and equipments, the studies on the characteristics of mechanics-magneticcoupling of the electromagnetic system is necessary. The meshless method based onfunction approaching approximations is one of the potential numerical methods andattracts more interest in recent years. Due to its independence from the meshes andreducing the difficulties caused by the mesh aberrance, the meshless method showseffective features in the problems associated with hypervelocity impact, dynamicrupture, coupling problem, and so on.In this thesis, the meshless method is employed in the magnetoelastic coupling analysis of a ferromagnetic plate for its advantage of good accuracy on the movable boundary and coupling effect. Based on the generalized magnetoelastic variational principle, we first establish the foundational equations of a ferromagnetic plate in applied magnetic field with Galerkin meshless method. Then a transformation method with virtual and actual magnetic potentials is used to treat with the connecting conditions on the interface of internal and external magnetic fields so that the magnetic field continuity and its derivative discontinuity can be satisfied. Finally, the magnetoelastic bending and buckling of a cantilevered ferromagnetic beam-plate are performed by means of the Galerkin meshless method with taking into account the mechanics-magnetic coupling, and the numerical results are compared with the experimental data and finite element results.