Numerical and Geometric Analysis of Side-Wall Inclination Angle Effects on Longitudinal Hat-Stiffeners in Steel Plates

Thin steel plates with stiffeners are widely employed in several branches of engineering, combining mechanical strength with low weight and serving as both structural and cladding components. However, the influence of the side-wall inclination angle of hat-stiffeners on the stiffness distribution and deflection patterns of steel plates remains insufficiently explored. This study conducts computational modeling to evaluate the deflection of thin steel plates reinforced with hat-stiffeners. The plates were considered simply supported and subjected to a uniformly distributed load. The Constructal Design method and the exhaustive search technique were employed, allowing for geometric evaluation and optimization. A fraction corresponding to 30% of the plate volume was removed and redistributed to generate longitudinal hat-stiffener geometries by varying its side-wall angle and thickness. The smaller base of the hat-stiffeners was imposed as a geometric constraint and therefore kept fixed. The results indicate a nonlinear trend between the side-wall angle, the moment of inertia, and the resulting deflection, leading to a new geometrical pattern that connects the angular inclination to the overall stiffness behavior of the plate. Angles between 105° and 130° provided the best performance, reducing the maximum deflection by 93.72% compared with the reference plate and improving it by around 7.5% relative to previous studies. These findings illustrate how geometric configuration can enhance performance in line with Constructal Design principles.