## 4 Conclusions  
Through the verification and validation of a numerical model capable of performing elastoplastic analyses of unstiffened and stiffened plates under combined loading, consisting of biaxial compression and lateral pressure, it was possible to apply the constructal  
Figure 27: Displacements and von Mises stress distribution of best and worst plate configurations on \(\left(\sigma_{uN}\right)_{mm}\): (a) P(5;4) displacements, (b) P(5;4) stress distribution, (c) P(2;5) displacements, and (d) P(2;5) stress distribution. design and exhaustive search to understand insights into the elastoplastic buckling behavior. The computational model was verified and validated, respectively, achieving a difference of 3.64% compared to another numerical model and a maximum error of 1.57% compared to the experimental reference. Thereafter, by converting part of the reference plate volume into stiffener volume, all proposed geometric configurations increased \(\sigma_{uN}\). The geometry that showed the maximized normalized ultimate buckling stress was P(5;4), with \((\sigma_{uN})_{mmm}\)= 3.84, \((h_{s}/t_{s})_{ooq}\)= 8.70, \((N_{ts})_{oo}\) =4, and \((N_{ts})_{o}=5\), representing a 284% improvement compared to \(\sigma_{uR}\) of the unstiffened plate adopted as the reference. In addition, the optimized stiffened plate geometry was 262% superior to the worst stiffened plate geometry P(5;3), with \(\sigma_{uN}\) = 1.22 and \(h_{s}/t_{s}\)= 0.57. Several relevant conclusions were drawn from this work. The mesh element size and the number of sub-steps in the load application slightly affect the ultimate strength, displacements, and stress distribution of the plates. The application of lateral pressure opposite to the displacement due to biaxial compression can increase buckling resistance by helping to prevent displacements or decrease buckling resistance adding displacements. Converting part of the plate volume into stiffeners can increase the ultimate buckling strength, but it is necessary to determine a better geometric configuration to achieve the best results. The \(N_{ls},N_{ls},\) and \(h_{s}/t_{s}\) ratio directly affects the displacements caused by lateral pressure and biaxial compression. Very high \(h_{s}/t_{s}\) values tend to improve the moment of inertia, prevent out-of-plane displacement of the stiffeners, concentrate stresses on the plate, and favor the occurrence of local plate collapse. Conversely, very low \(h_{s}/t_{s}\) values tend to cause the stiffeners to displace out of the plane, resulting in the global collapse of the plate and stiffeners. Therefore, the choice of the \(N_{ls}\) and \(N_{ls}\), as well as their respective \(h_{s}/t_{s}\), should be made to increase the stiffness of the plate-stiffener system, ensuring that both components work together. This behavior will improve the displacement and stress distribution between the plate and stiffeners, leading to higher plate ultimate strength and reduced displacements. For future work, it is suggested to apply the developed methodology to investigate the mechanical behavior of various stiffener types, explore different plate a/b aspect ratios, and analyze the effects of cyclic loading, welding, and corrosion, together with combined loadings and how the design can improve the ultimate buckling stress in these conditions. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app15063354/s1](https://www.mdpi.com/article/10.3390/app15063354/s1)]([https://www.mdpi.com/article/10.3390/app15063354/s1](https://www.mdpi.com/article/10.3390/app15063354/s1)), Table S1: Constructal design application; Table S2: Exhaustive search application; Figure S1: Influence of \(N_{ls}\), \(N_{ls}\), and \(t_{s}\) over \(h_{s}\) for each plate configuration; Figure S2: Influence of \(N_{ls}\) and \(N_{ls}\) over maximum \(h_{s}/t_{s}\) values for each plate configuration. Conceptualization, R.L.V., T.d.S., J.P.S.L. and L.A.I. ; methodology, R.L.V., E.D.d.S., L.A.O.R., T.d.S., J.P.S.L. and L.A.I. ; software, R.L.V. and G.R.B.