Reliability analysis of fatigue crack growth in shallow shell structures using the Dual Boundary Element Method

Abstract

This work presents a novel methodology for fatigue life reliability analysis using a newly developed Dual Boundary Element Method-based Implicit Differentiation Method (DBEM-IDM) in shallow shell structures. The proposed DBEM formulations evaluate stress intensity factors and fatigue life sensitivities in shallow shells considering geometrical variables and curvature. The IDM formulations, obtained through direct differentiation of the shallow shell DBEM formulations, uses the First-Order Reliability Method (FORM) to assess the reliability index and probability of failure of shallow shell structures with multiple cracks. Two numerical examples were simulated to illustrate the effectiveness of the proposed methodology. The first example examines a shallow shell with a centre hole and cracks subjected to various loads. The critical crack length required to ensure structural reliability and inspectability is determined. Fatigue reliability assessment is performed for the same example, employing limit state functions expressed in terms of fatigue life. FORM results are compared with the results of Monte Carlo Simulations (MCS), and provided a maximum difference of 3.67%. Parametric analyses are conducted to identify significant variables that affect reliability, and it was found that precise determination of design parameters is necessary to reduce the probability of failure, particularly for the Paris law constants. The second example, featuring more complex geometry, involved assessing fatigue reliability in a cylindrical shallow shell structure with multiple cracks. The results of this example indicate a 3.49% maximum difference between FORM and MCS. The results exhibit a low error compared to the MCS, and the inherent efficiency of the IDM-based FORM underscores its suitability for addressing uncertainty in reliability analysis.