The investigation in this thesis addresses the challenges posed by the stochastic characteristics of
design parameters under complex loading conditions. The focus is on the reliability and fatigue life
analysis of engineering structures. The thesis introduces innovative formulations utilizing the Dual
Boundary Element Method (DBEM) to accurately evaluate key parameters, aiming to enhance
the modelling accuracy of the reliability index and fatigue life for intricate structures.
Specifically, the study is concerned with fatigue life reliability analysis within shallow shell struc tures, presenting a novel methodology for assessing design sensitivities. The development of the
Boundary Element Method-based Implicit Differentiation Method (BEM-IDM) enables the appli cation of the First Order Reliability Method (FORM) to evaluate structural reliability. Expanding
on this, a methodology for fatigue life reliability analysis using DBEM-IDM is introduced. This
approach demonstrates superior efficiency in evaluating fatigue life sensitivities compared to the
Finite Difference Method and Monte Carlo Simulations, resulting in significant reductions in CPU
time.
Another related topic investigated involves the statistical inference of the Equivalent Initial Flaw
Size Distribution (EIFSD) for both 2D anisotropic and isotropic shell structures. The assessment
of EIFSD for the initial size of cracks and its impact on the remaining useful life of structures un der fatigue loading is demonstrated. The Dual Boundary Element Method (DBEM) formulation is
shown as a highly efficient computational tool, with Bayesian updating refining EIFSD estimates
using simulated inspection data. The efficiency of the method is further improved through surro gate modelling, demonstrating its effectiveness in estimating fatigue life with significant agreement
compared to actual fatigue life.