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 element (FE) field solutions is proposed, based on the principle of virtual work. 111 this method, a force is derived for each nodc by direct differentiation of the stored magnctic energy or co-energy or the finite clcmcnts surrounding the node with respect to tlic virtual displaccmcnt while keeping the magnetic potential conslant. The force distribution around the node is then obtained by spreading the ‘nodal’ forcc over an appropriate ‘touching’ area or volume of the clcmcnts surrounding the node. This method can be easily implemcnled in 2D and 3D FE field calculation programs. Numerical cvaluation for both linear and nonlinear ficld problems in two dimensions and (by implication from an axisymmctric treatment) in three dimensions shows that the results computed by the proposed heuristic method are in good agreement with analytical solutions and experiincntal results.