Virtual work approach to the computation of magnetic force distribution from finite element field solutions

A method for the computation of magnetic force distribution from finite clement (FE) field solutions is proposed, based on the principle of virtual work. In this method, a force is derived for each node by direct differentiation of the stored magnetic energy or co-energy of the finite elements surrounding the node with respect to the virtual displacement while keeping the magnetic potential constant. The force distribution around the node is then obtained by spreading the 'nodal' force over an appropriate 'touching' area or volume of the elements surrounding the node. This method can be easily implemented in 2D and 3D FE field calculation programs. Numerical evaluation for both linear and nonlinear field problems in two dimensions and (by implication from an axisymmetric treatment) in three dimensions shows that the results computed by the proposed heuristic method are in good agreement with analytical solutions and experimental results.