**Tung Le-Duc 1,\* and Gerard Meunier <sup>2</sup>**


Received: 11 May 2020; Accepted: 19 June 2020; Published: 22 June 2020

**Abstract:** The aim of this article is to present a hybrid integral formulation for modelling structures made by conductors and thin electromagnetic shell models. Based on the principle of shell elements, the proposed method provides a solution to various problems without meshing the air regions, and at the same time helps to take care of the skin effect. By integrating the system of circuit equations, the method presented in this paper can also model the conductor structures. In addition, the equations describing the interaction between the conductors and the thin shell are also developed. Finally, the formulation is validated via an axisymmetric finite element method and the obtained results are compared with those implemented from another shell formulation.

**Keywords:** electromagnetic modelling; integral formulation; skin effect; thin shell approach; mutual inductance; finite element method; partial element equivalent circuit method
