Análise confiabilística em estruturas planas baseada no método dos elementos de contorno

Abstract

In Structural Engineering, one of the main objectives is to find robust solutions that ensure structural safety without compromising cost-effectiveness. To achieve this goal, one strategy involves accounting for the inherent uncertainties in design by considering the variability of design parameters rather than relying solely on characteristic values, such as those provided by semi-probabilistic approaches. This methodology enables the estimation of the failure probability of structural elements and systems, providing greater robustness in analysis and decision-making while reducing the risks associated with overly conservative and expensive designs or economical but unsafe and underperforming ones. This study presents the computational implementation and coupling of a mechanical model based on the Boundary Element Method (BEM) with a reliability model using Monte Carlo Simulation (MCS) and Latin Hypercube Sampling (LHS). All algorithms were implemented in Python. The random variables considered include mechanical parameters such as the modulus of elasticity, structural element dimensions, and applied loads. Examples analyzed include the Lamé problem, a tensioned plate with a central hole, and a simply supported beam, evaluating variables such as elasticity modulus, loads, and dimensions. The results demonstrated the validity of the proposed model, with LHS reducing computational cost without compromising accuracy, highlighting the effectiveness of the approach in estimating failure probabilities in structures.