## 5 Numerical Modelling for Form-Finding of TEL-Gridshells
### Residual Stresses  
The applied method allows the elements of the structure to be deformed elastically until the target geometry is reached (_Stage 4_) and, consequently, it also makes it possible to obtain the internal stresses at each point of the structure due to the deformation process. Furthermore, after the relaxation phase (_Stage 5_), it allows estimating the final shape of the structure and the final stresses in both members and joints. For the sake of clarity of the results, the self-weight of the structure is not taken into account in this section. To analyse bending stresses due to curving in the target geometry (_Stage 4_) as well as changes in shape and residual stresses after the relaxation process (_Stage 5_) including slip at the joints, the results obtained for the structure in both stages are compared (model A). The stiffness values assigned to the springs are the same as in the previous section (see Table 5). Figure 14: Simulation of the construction process of the TEL-gridshell lab prototype: (**a**) and (**b**) grid bending; (**c**) and (**d**) bending of transverse laths. Table 9 shows the displacement values in model A at control points C and D-E (see Section 3.6), the maximum values obtained for N, M\({}_{y}\), M\({}_{z}\) and M\({}_{t}\) of the longitudinal grid members, and N and M\({}_{y}\) in the transverse laths (M\({}_{z}\) and M\({}_{t}\) are null). Results are shown before and after relaxation (_Stages 4_ and _5_). As can be seen from the above results, the maximum moments M\({}_{y}\), M\({}_{z}\) and M\({}_{t}\) of the main grid are almost identical for _Stages 4_ and \(5\). This is because, in general, the movements produced after relaxation of the structure are actually very small and similar in both cases. When the inner links are deactivated, the grid moves slightly until it reaches a new equilibrium position. Movements occur mainly in the area where the structure has the lowest stiffness, which, as discussed in the previous section, corresponds to the central area of the longitudinal lateral edges. The maximum displacements occur at control points D and E, which have practically identical moduli as they are symmetrical, and the model does not consider imperfections. These points were displaced by 18.4 mm. This displacement is not negligible, so again there is a need to increase the stiffness of the structure in this area. Figure 15 shows the residual bending moment after the relaxation process. The longitudinal laths show high curving moments in the two axes of inertia. This is because their longitudinal axes are not geodesic curves of the structure surface. The maximum weak axis bending moment (M\({}_{y}\)) of the longitudinal laths occurs in the area of the central transverse lath and has a value of 0.164 kNm, which produces a maximum bending stress of 26.24 N/mm\({}^{2}\). On the other hand, the strong axis bending moments (M\({}_{z}\)) of the main laths are maximum in the vicinity of the other two transverse laths, with a maximum value of 0.308 kNm and a stress of 20.53 N/mm\({}^{2}\), being zero in the area near the central transverse lath. The maximum value of the stress produced by both bending moments in the longitudinal laths is 33.97 N/mm\({}^{2}\) and is located in the section of maximum M\({}_{z}\). The longitudinal laths also exhibit normal stresses due to axial forces, but these are very low compared to those caused by bending. Specifically, the normal stress corresponding to the maximum axial force (1.984 kN compression) is only 1.32 N/mm\({}^{2}\) and is located in a different section from the maximum combined bending section, which happens to be the maximum combined normal stress section. The shear stresses produced by the construction process are moderate and do not require special attention during the design process. The maximum torsional moment is 0.032 kNm, producing a maximum shear stress of only 1.39 N/mm\({}^{2}\). The maximum stresses due to shear forces (V\({}_{y}\) and V\({}_{z}\)) are practically negligible, not exceeding 0.2 N/mm\({}^{2}\).