**1. Introduction**

Some documented studies to interpret the cause of aircraft accidents [1, 2]. One of the classical cases is the accidents with the Comet aircraft and Boeing 737–200 [2]. Regarding the Comet accident, the reports concluded fatigue failure as the main reason for the disintegration of the pressurized cabin. This study also reported that although designed for the operating conditions, its structure was unable to prevent the crack propagation, particularly unstable cracks that after reaching the critical length would continue to propagate until complete rupture of the structure.

As for the Boeing 737 Aloha Airlines, it stabilized at 7,000 meters altitude as planned, and a loud bang suddenly followed by the disintegration of the roof leaving a gap of six meters in the fuselage in flight, but it was still possible to land the aircraft with a damaged structure as shown in **Figure 1**. In this case, the investigations indicated that fatigue crack initiation in several areas (multiple damage site - MSD) greatly reduced the strength of the structure causing it to collapse.

Designers are always looking for fast and reliable simulation methods that produce accurate results to avoid damage processes and, consequently, the occurrence of accidents. Automation is then seen as a key point to evaluate several scenarios for parametric studies resulting in design optimization [3]. Thus, numerical methods as

**Figure 1.**

*Boeing 737–200 fuselage fatigue failure. NTSB. Aircraft Accident Report NTSB/AAR-89/03, Aloha Airlines, Flight 243, Boeing 737–200, N73711; Near Maui, Hawaii; April 28, 1988.*

domain methods (Finite Element Method – FEM, Extended Finite Element Method – XFEM, Generalized Finite Element Method - GFEM), contour methods (Boundary Element Method – BEM, Dual Boundary Element Method – DBEM, Radial Integration Method - RIM) and mesh-free methods appear as an alternative for solving fracture problems. The DBEM shows further advantages simplifying the modeling of the crack area, direct SIF calculation, run times reduced, and accurate simulation of crack growth [4–6]. The need for discretization only of the solid contour allows, using the DBEM, the analysis of thousands of probabilistic and reliability simulations, such as flaws, initial defects, fatigue behavior prediction, multiple local damages, among others [7–11].

The literature analyzes the damage tolerance (number of cycles) based on the crack size. This chapter presents an innovative method for damage tolerance based on probabilistic global–local analysis. In this context, the method can find a relationship between the number of fatigue cycles and the respective compliance in local elements considering the statistical nature of the input parameters.
