Otimização baseada em confiabilidade de treliças planas

Abstract

Reliability Based Design Optimization (RBDO) allows the design of increasingly slender structures, with lower costs, without compromising its safety. Despite costs and safety being apparently opposing objectives in civil engineering, RDBO seeks to ensure both conditions simultaneously. For that, it is necessary to take into consideration, during the optimization process, not only the geometrical and mechanical restrictions, but also the failure probability that the optimized structure should have. This work presents a RDBO study, considering the buckling and yielding failure modes, in plane trusses formed by tubular bars, having the final structure volume as the objective function (to be minimized), and taking the tubular bars external diameter and thickness as variables to be optimized. The optimization was performed using genetic algorithm (GA) with the assistance of Matlab software. The model has linear constraints (geometric relations between diameter and thickness, to ensure local stability, according to NBR 8800) and nonlinear constraints (stress, displacement, slenderness ratio and reliability index). Isostatic trusses were used in a way to ensure closed-form expressions for the stresses and displacements, and the probabilistic constraint was considered by PMA (Performance Measure Approach) method, with the failure probability being previously defined. The main objective in this work is to verify whether the structures’ failure modes influence in the optimization results, when considered independently and simultaneously.