# A Combined Electromagnetic and Mechanical Approach for EU-DEMO Toroidal Field Coils
## 5 Structural Calculation Methodology-Theromechanical Analysis  
The 3D structural model is shown in Figure 8. It is made of 3D 8-node (hexahedral) and 4-node (tetrahedral) linear element, with 4 degrees of freedom per node (three translations and the temperature). The structural mesh comprises 1,529,209 elements with 96% of 3D hexahedral elements and only 4% of 3D tetrahedral elements. Actually, as it is easily seen in Figure 8, beside the three orders of magnets (inherited from the electromagnetic  
Figure 7: (a–c) Lorentz force components and (d–f) moment components with respect to the machine central axis recorded as distributed loads along the TF axis curvilinear abscissa (the origin is on the equatorial plane, at the middle of the vertical inner leg). analysis); the model comprises the main structural elements with several details. As briefly mentioned above, there are two types of inter-coils structures, linking together the TF coils: the outer inter-coil structures (OISs) and the inner inter-coil structures (IISs). The outer inter-coil structures are organized in two orders, located in the curved outer part of the TF case, one above the equatorial plane and the other below. The main function of the OISs is to balance the out-of-plane forces acting on each D-shape coil. They are designed according to the double shear joint scheme and are composed of large-shaped plates rigidly connected to the TF case and bolted to each other on the other side by means of pairs of cover plates. Like ITER, DEMO also relies on the wedging effect to balance the radial forces acting on the inner leg of the TF coils. To prevent the possible detachment and to increase the wedging mechanism, the inner inter-coil structures are located at the ends of the straight leg of each TF coil, one at the top and the other at the bottom. They are of a box-type structure, bolted to each other on both sides in order to provide a very rigid connecting system. Finally, the CS module stack is enclosed inside a preload system capable to withstand the huge repulsion between the modules; the six PF coils are closed inside a dedicated support that counteracts the coil axial movements and allows the radial shrinking; the central solenoid is connected to the bottom end of the inner TF leg by means of a suitable cantilever connection, and the gravity support is modelled in detail. Each component is connected via mechanical contact elements that can reproduce both bonded connections for welded interfaces and friction interaction, where detachment or sliding conditions can occur. The contact interfaces implemented in the model are shown in Figure 9. As described, the machine can be divided into 16 sectors with 22.5-degree toroidal periodicity. The cyclic symmetry condition is defined enforcing a set of constraint equations for the corresponding nodes on the periodic boundaries. To avoid rigid body motion, the gravity support system is fully constrained at the bottom, modelling the fixing to the ground. Figure 8: The 3D structural model comprises a 22.5-degrees sector of the machine with the PF, CS, and TF coils, the inter-coil structures and the gravity support. All steel components, e.g., the TF case, the jacket of the CICC, the PF and CS support and the gravity support system, are made of AISI 316 LN. Different classes of AISI 316 LN are considered for the assessment, depending upon the mechanical performance required. The yield strength at 4K varies from 700 to 1000 MPa, except for the cable jacket and the TF case, for which a material with better performance (i.e., \"AISI 316 LN Class 1\") is needed, with a yield limit of 1000 MPa and an ultimate strength of 1470 MPa [13; 14]. Concerning the insulation components, a local Cartesian system of coordinates is used, where axis 1 is orthogonal to the lamination plane (LP), e.g., it goes through the thickness of the insulation; axis 2 follows the wrapping direction of the turn and lies on the LP, and axis 3 is perpendicular to the previous ones and lies on the LP.