A moment-based stochastic edge-based smoothed finite element method for electromagnetic forming process

In this paper, a novel stochastic method named as the moment-based stochastic edge-based finite element method (MSES-FEM) is proposed to deal with the uncertain electromagnetic problems. First, electromagnetic and mechanical field are formulated by smoothed Galerkin Weak Form under edge-based smoothed finite element method (ES-FEM) scheme. The moment analysis is then applied to obtain the first four moments of the responses and to observe the effects of each random variable on electromagnetic field responses. The maximum entropy theory is employed to calculate the probability density functions (PDFs) of the responses. A quasi-static electromagnetic problem and a practical electromagnetic forming problem (EMF) are performed. The proposed method successfully solves stochastic electromagnetic forming analysis under the uncertain parameters. Numerical results obtained by the proposed MSES-FEM are quite satisfactory with the ones by the Monte Carlo simulation (MCS).