Structural Reliability of the Cessna 172 Main Spar with Multiple Variable Parameters: A Monte Carlo-Based Analysis

Resumo

This paper aims to analyze the structural reliability of the main spar of a Cessna 172 Skyhawk aircraft in order to evaluate its operational safety under varying conditions. A probabilistic reliability analysis is carried out using the Monte Carlo Method, considering multiple correlated random variables. The study incorporates geometric properties, material characteristics, and dynamic excitations ranging from 0 to 200 Hz. The spar is modeled as a cantilever beam with an I-shaped cross-section, made of 2024-T3 aluminum alloy. A computational routine developed in MATLAB simulates the structural response of the spar under harmonic excitations, accounting for dynamic amplification and applying the Von Mises failure criterion. Initial results were obtained by performing frequency band simulations in progressive intervals. These indicated high structural reliability outside the natural frequencies, but also revealed vulnerability to resonance when excitation frequencies align with the system's natural modes, leading to an increased probability of failure in those ranges. Subsequently, simulations were conducted over a single, broad frequency band encompassing all possible excitation frequencies relevant to the operational conditions of the aircraft. These simulations yielded excellent results, with a low failure probability of approximately 0.8% and a high reliability index (β). The study highlights how resonance-induced amplification can significantly influence reliability outcomes and demonstrates the effectiveness of the Monte Carlo Method in capturing uncertainties and confirming the structural reliability of this critical aircraft component.