## 1 Introduction
The authors concluded that the position of the stiffeners significantly affects the ultimate strength, that considering local buckling as an initial imperfection provides more results of ultimate strength, and that the proposed design curves and empirical equations provide relatively high safety margins for reinforced plates concerning lateral pressure. [PERSON] et al. [11] developed a computational model using the finite element method (FEM) in the ANSYS software (Version 2023R1) to simulate elastoplastic buckling in plates under uniaxial, biaxial, lateral, and combined compressive loading for different plate models. The authors concluded that the computational model could be used for elastoplastic buckling analysis under combined loads, as it was verified and validated,achieving differences of 2.47% and 4.83% compared to analytical and numerical reference results, and a maximum error of 5.40% compared to experimental results. [PERSON] et al. [12] experimentally and numerically studied the ultimate strength and collapse modes of stiffened plates subjected to biaxial compression and lateral pressure. The authors considered scenarios of loadings with and without lateral pressure, concluding that lateral pressure can reduce the ultimate buckling strength. However, when the deformation of the plate occurred in the direction opposite to the application of the lateral pressure, the lateral pressure resulted in an increase on the ultimate strength due to the restrained displacements. [PERSON] et al. [13] applied the constructal design method and exhaustive search technique to investigate the influence of longitudinal and transverse stiffeners, and their height-to-thickness ratio in a plate on buckling subjected to uniaxial compression. The authors considered two unstiffened plates with volumes \(V_{T1}\) and \(V_{T2}\) as ultimate stress reference and converted part of volume from plates into stiffeners, investigating different configurations regarding the number of stiffeners and height-to-thickness ratio. For the \(V_{T2}\) plate, the improvement in ultimate buckling resistance was 88.50% with the plate configuration using two longitudinal stiffeners and two transverse stiffeners. The difference between the best and worst configuration was 481.24%. For the \(V_{T1}\) plate, converting part of the steel volume into stiffeners was ineffective, achieving only a 7.38% improvement in ultimate buckling stress, reinforcing the importance of the geometry influence research. [PERSON] et al. [14] also applied constructal design and exhaustive search to evaluate plates subjected to pure lateral load, ranging the number of longitudinal and transverse stiffeners. The authors concluded that plates with configuration using two longitudinal-five transverse stiffeners, and two longitudinal-six transverse stiffeners can efficiently reduce displacements and improve resistance in the proposed scenario. Improvement in displacements resulted in a 95.23% reduction compared to the reference plate, while bending resistance was increased by 44.98% compared to the reference plate. Just adding stiffeners to an unstiffened plate does not necessarily improve mechanical behavior. Despite some studies applying constructal design in different scenarios of plate and stiffener geometries subjected to different types of loadings, it remains a challenge to find studies that fully understand how the geometric configuration of stiffeners impacts the buckling resistance and displacements of plates subjected to combined loading, such as biaxial compression and lateral pressure. In this context and inspired by [PERSON] et al. [13], the main goals of the present study are: (i) to develop a computational model in ANSYS Mechanical APDL to numerically simulate the mechanical behavior of plates under elastoplastic buckling subjected to biaxial compressive loading combined with lateral pressure; and (ii) to apply the developed computational model together with the constructal design method and exhaustive search technique in a case study.