## 2 Methodology
### Research Methodology  
All devised frame models were studied under identical conditions of stress and quasi-identical meshing, that allows their comparative analysis in relation to the constructive solution of reference. For each frame model, the study included the state of stress, the state of deformation, the estimated stiffness, and the required volume of material. The discretisation of the 3D-models was achieved by tetrahedral elements [20; 25], Figure 9. In the model frame used for reference, 55,912 nodes and 29,743 elements were obtained. In the studied models with ribbed lateral walls, depending on their geometrical complexity and the difference in volume, the number of nodes and elements is greater, in general, by up to 10% [20], the common values being \(\approx\)61,000 nodes and \(\approx\)32,500 elements. Greater values can be found in models with more dense ribbing, spaced at 50 mm (\(\approx\)63,000 nodes and \(\approx\)33,500 elements), while the maximum values pertain to the models with intersected ribs (\(\approx\)67,000 nodes and \(\approx\)36,000 elements). The extremes correspond to frame B-PAI25_g18 (55,520 nodes and 29,567 elements), without ribs and with a small lateral wall thickness, and to frame B-PAI25_g20_e75_a45 + \(\beta\)135 (68,290 nodes and 36,557 elements), with tilted intersected ribs. All models were loaded realistically, in static conditions, by a uniformly distributed force acting upon both the table working surface and the superior part of the main shaft bearing bores [20; 25] (Figure 10). The force was considered equal to the nominal force \(\mathrm{F_{N}}=250\) kN, the maximum admissible force. The constraints of the frame reflect its connection to the press base by means of four bolts. Figure 9: Discretized model of PAI 25 press, the reference constructive solution. The finite element analysis of the reference model, the B-PAI25_g20 frame, revealed three areas of high stress in the frame body, Figure 11:  
1. the inferior area of connection of the front pillars to the frame table (elongation stress);
2. the superior area of connection of the front pillars to the superior part of the frame; (elongation stress);
3. the area of the main shaft bearing bore (crushing stress). Figure 11: Stress state in the reference constructive solution (frame code B0). Figure 10: Force load and constraints in the reference constructive solution. Figure 16: Stress state in curved rib frame B-PAI25_g20_var_curv (frame code B47). Figure 14: Stress state in frame B-PAI25_g20_e75_\(\alpha\)130 (frame code B36). Figure 15: Stress state in frame B-PAI25_g20_e75_\(\alpha\)30 + \(\beta\)120 (frame code B44). Table 2 features the maximum stress values in the critical areas A, B and C for several frame groups, with various wall thicknesses, with lateral walls ribbed with left tilted, right tilted, intersected, and curved ribs. Table 2 also includes the deviations of the maximum stress values in the critical areas A, B and C of the studied models in relation to the corresponding values of the reference model, expressed as a percentage and determined with relations:  
\[\Delta(\sigma_{A})_{i}=((\sigma_{A})_{i}-(\sigma_{A})_{0})/(\sigma_{A})_{0};\ \Delta( \sigma_{B})_{i}=((\sigma_{B})_{i}-(\sigma_{B})_{0})/(\sigma_{B})_{0};\ \Delta(\sigma_{C})_{i}=((\sigma_{C})_{i}-(\sigma_{C})_{0})/(\sigma_{C})_{0}\]  
The critical areas A and B are the most intensively strained and require the focus of any study on the distribution and the evolution of stress in C-frames of the considered type. In a critical area C stress is transmitted indirectly from the main shaft of the press by means of a bronze sleeve. Consequently, the magnitude and variation of stress (in the present study depending on the lateral wall thickness and ribbing modality) in the critical areas A and B represent priority evaluation criteria. The magnitude and variation of stress in the critical area C being a criterion of lesser significance. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.