Numerical simulation, constructal design, and systematic search applied to the geometrical evaluation of hat-stiffened plates under bending

Steel plates have wide structural applications in various engineering sectors due to their combination of lightness, efficiency, and high load-bearing capacity. When stiffeners are added to these structures, the deflections can be significantly minimized. In this study, hat-stiffened plates having box-girder stiffeners with a trapezoidal shape, positioned longitudinally along the plate, are considered to evaluate their influence on the maximum and central deflection of the structure. The analyses in this work are carried out using ANSYS Mechanical APDL software, employing a validated and verified computational model developed with the SHELL281 finite element. Starting from a reference plate without stiffeners, the Constructal Design method was applied, allowing to propose different geometric configurations for plates with longitudinal hat-stiffeners, keeping the total steel volume constant. All these cases were simulated numerically and their results were compared through a Systematic Search technique. Among these 100 different cases investigated, the geometric configuration with 1 hat-stiffener of 250 mm in height and 9.53 mm in thickness achieved the best performance, resulting in a reduction of approximately 86% in maximum and central deflections compared to the reference plate. This highlights its effectiveness in minimizing out-of-plane displacements.