A hyperparameter-optimized Kriging surrogate model was developed for the structural collapse behavior framework presented in this paper. The assessment is conducted on a stiffened panel subject to axial load and lateral pressure, typical of the deck structure of a bulk carrier ship. This behavior is characterized using nonlinear finite element analysis to determine the collapse response. The surrogate model’s hyperparameters were optimized using a Genetic Algorithm to achieve the best performance, and the trained framework can predict ultimate strength. By following this approach, the problem can be reformulated as a multi-objective optimization task. This framework involves associating the Kriging surrogate model with a multi-objective evolutionary optimization algorithm based on Genetic Algorithms to balance the trade-off between the weight and ultimate strength of the stiffened panel. The results confirm the applicability of the Kriging surrogate framework to predict the ultimate strength and assess the collapse analysis of the stiffened panels, ensuring accuracy through GA-based hyperparameter optimization.

The size of ships has increased considerably in recent decades. This growth impacts the stress magnitude in the bottom hull plates, which constantly suffer from biaxial compression and lateral water pressure, potentially leading to buckling. Adding stiffeners is an effective alternative to increase mechanical buckling resistance if placed in a proper way. Several researchers have investigated the influence of stiffeners on plates under different loading conditions. However, the behavior under combined biaxial compression and lateral pressure has not yet been widely explored. This work aims to verify and validate a computational model to analyze the elastoplastic buckling of plates under biaxial compression and lateral pressure, applying it in a case study to define the ideal geometric configuration to increase ultimate buckling resistance, using the constructal design method and exhaustive search technique. In this study, a portion of the volume from a reference plate without stiffeners was converted into stiffeners to determine the optimal geometry for maximizing ultimate buckling resistance. The numerical model was verified and validated, and the case study identified the optimal plate configuration with five longitudinal and four transverse stiffeners, with a height-to-thickness ratio of 8.70, achieving a 284% increase in ultimate buckling resistance compared to the reference plate. These results highlight the importance of geometric evaluation in structural engineering problems.

RESUMO O objetivo desse estudo é avaliar a efetividade do tratamento termoquímico de carbonitretação empregado em engrenagens de motocicletas, para possível substituição de um aço médio carbono, por um aço de baixo carbono. Para isto foi determinada à composição química do material, analisado a microestrutura, verificado o perfil de microdureza e observando-se a conformidade dos ensaios. As engrenagens utilizadas no tratamento termoquímico foram produzidas com aço SAE 1015, as quais foram submetidas à austenitização na temperatura de 880 °C durante 6 horas, utilizando atmosfera controlada com potencial de carbono de 1% e reduzido volume de NH3, sendo posteriormente temperada em óleo e revenidas a uma temperatura de 180 °C durante um período de 1 hora. A microestrutura do núcleo apresentou ferrita, perlita e martensita de baixo carbono junto aos contornos de grão. Já na camada carbonitretada detectou-se nitretos de elevada dureza e martensita de alto carbono associada a pequeno volume de austenita retida. Através da técnica de difração de raios-x, confirmou-se a presença de austenita retida na superfície das amostras. A microdureza máxima atingida foi de 949 HV0,1 e a profundidade de camada carbonitretada de 0,8 mm. Conclui-se que a utilização de um aço baixo carbono e não ligado pode-se tornar uma rota de fabricação para engrenagens, quando submetidos ao tratamento termoquímico de carbonitretação. A presença de potencial de carbono muito elevado é elemento favorável para formação de austenita retida.

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.

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.

The buckling response of plates is governed by their geometric and material characteristics, loading conditions, and initial imperfections, while its numerical prediction is also influenced by modeling assumptions. Using finite element simulations in ANSYS Mechanical APDL, this study investigates the effects of shell reference surface position, through-thickness integration scheme, initial geometric imperfections, plate slenderness, aspect ratio, and loading condition (uniaxial or biaxial compression) on the elastic and elasto-plastic buckling behavior of plates. The shell reference surface position had a negligible influence on critical buckling loads but reduced ultimate loads by up to 57.72%. The evaluation of shell thickness integration schemes showed that three integration points are sufficient for elastic analyses and five for elasto-plastic simulations. Plate slenderness governed the development of post-buckling reserve, whereas aspect ratio became increasingly important under biaxial compression. Plates with lower slenderness exhibited ultimate loads up to 42.44% below the corresponding critical loads, while slender plates developed post-buckling reserves reaching 78.04%. The influence of biaxial compression was strongly dependent on plate aspect ratio, with ultimate load reductions reaching 84.78% compared to uniaxial compression. A strong interaction between aspect ratio and imperfection sensitivity was observed, with variations in ultimate load due to imperfection amplitude decreasing from 41.11% in plates with low aspect ratios to less than 5% in elongated plates. The results contribute to a better understanding of the interaction among modeling assumptions, plate geometry, initial imperfections, and buckling mechanisms under uniaxial and biaxial compression.