Constructal design and numerical simulation applied to geometric evaluation of stiffened steel plates subjected to elasto-plastic buckling under biaxial compressive loading

Abstract

Widely employed in diverse engineering applications, stiffened steel plates are often subjected to biaxial compressive loads. Under these conditions, buckling may occur, initially within the elastic range but potentially progressing into the elasto-plastic domain, which can lead to permanent deformations or structural collapse. To increase the ultimate buckling stress of plates, the implementation of longitudinal and transverse stiffeners is effective; however, this complexity makes analytical stress calculations challenging. As a result, numerical methods like the Finite Element Method (FEM) are attractive alternatives. In this study, the Constructal Design method and the Exhaustive Search technique were employed and associated with the FEM to optimize the geometric configuration of stiffened plates. A steel plate without stiffeners was considered, and 30% of its volume was redistributed into stiffeners, creating multiple configuration scenarios. The objective was to investigate how different arrangements and geometries of stiffeners affect the ultimate buckling stress under biaxial compressive loading. Among the configurations evaluated, the optimal design featured four longitudinal and two transverse stiffeners, with a height-to-thickness ratio of 4.80. This configuration significantly improved the performance, achieving an ultimate buckling stress 472% higher than the unstiffened reference plate. In contrast, the worst stiffened configuration led to a 57% reduction in performance, showing that not all stiffening strategies are beneficial. These results demonstrate that geometric optimization of stiffeners can significantly enhance the structural performance of steel plates under biaxial compression, even without increasing material usage. The approach also revealed that intermediate slenderness values lead to better stress distribution and delayed local buckling. Therefore, the methodology adopted in this work provides a practical and effective tool for the design of more efficient stiffened plates.