Abstract
Probabilistic failure risk assessment is becoming important in the field of airworthiness. In the fracture mechanics module of probabilistic failure risk assessment, it is important to efficiently and accurately calculate the stress intensity factors (SIFs). At present, the weight function method (WFM), especially the universal weight functions (UWFs) proposed by Glinka and Shen, has been adopted to calculate SIFs with high accuracy and computational efficiency. However, the concrete coefficients in the universal weight functions remain unknown, and the rules of the geometry parameters and these coefficients have not yet been summarized, which hinders their subsequent use. In this article, the specific type of embedded crack-central crack is under discussion, and the derivation of the UWF is introduced. The response surface method (RSM), as a means of database establishment, is used to construct the relations between the geometric parameters including the length and thickness of a three-dimensional finite plate and coefficients in the UWF. The errors of the SIF calculation between the UWF and finite element results are less than 2 MPa m within a certain range. For the evaluation of the boundary effect on central cracks, the difference between finite and infinite plates is discussed. In addition, considering the complexity of the general off-centre crack, an approximation method has been proposed to transform the off-centre crack to the central crack. The results show that the method can be applied with high precision in specific situations and stresses the necessity of follow-up research on general off-centre cracks.
Long-Time Behavior of a Reaction–Diffusion Model with Strong Allee Effect and Free Boundary: Effect of Protection Zone
