Numerical Study of Constructal Design Applied to Perforated Thin Plates Under Elasto-Plastic Buckling Due to Combined Loading

Thin plates are widely used and can be subjected to combined loads that trigger elasto-plastic buckling. Often, these plates are perforated, which significantly changes their mechanical response. This study investigates six perforation geometries (elliptical, longitudinal hexagonal, transverse hexagonal, longitudinal oblong, transverse oblong, and rectangular) and their influence on the ultimate buckling stress of perforated plates under biaxial compression and lateral pressure. Three plates with a distinct width b and length a ratio (b/a) and five unperforated plate volume and perforation volume ratios (ϕ) are analyzed using finite element analysis in ANSYS®, combined with Constructal Design, Exhaustive Search, and the Technique for Order Preference by Similarity to an Ideal (TOPSIS). Perforation geometry is shown to be a decisive parameter: elliptical perforations are the most efficient, limiting strength loss in rectangular plates with b/a = 1/3 and ϕ = 0.025 to about 6%, while oblong perforations cause reductions of up to 14%. In square plates (b/a = 1), elliptical perforations preserve more than 98% of the original strength for ϕ ≤ 0.05 and over 90% at ϕ = 0.20. TOPSIS results highlight configurations that balance small reductions in ultimate buckling stress with up to 23% lower maximum deflection, providing practical design guidelines.