A non-deterministic fracture analysis tool by extending the scaled boundary finite element method

The existence of cracks can have a strong influence on the reliability of ageing infrastructures. However, the crack geometry is often difficult to measure accurately, leading to uncertainties. In order to consider these uncertainties in the safety assessment, the shape sensitivity of the stress intensity factors (SIFs) is integral.The primary goal of the current study is to develop an advanced numerical tool for the non-deterministic fracture analysis of cracked structures with uncertainties in the crack geometry, material properties and loading. Underpinning the approach is: (a) the extension of the scaled boundary finite element method (SBFEM) to evaluate the first-order shape sensitivity of the SIFs, (b) the application of reliability analysis techniques, including the Monte-Carlo simulation, to estimate the reliability of such structures.In the novel approach to shape sensitivity analysis, the finite element formulations are combined with the boundary element discretization. The original equations of the SBFEM are reformulated as functions of the scaling centre. The variation in crack geometry is modelled by arbitrarily shifting the scaling centre without remeshing. Shape sensitivity is then analyzed by direct differentiation.The approach is notably advantageous and innovative. The absence of remeshing allows a greater sensitivity data to be acquired more efficiently, which accounts for a greater degree of uncertainty in the crack geometry. No mesh perturbation or complex velocity field is necessary. In addition to square-root singularities in homogeneous cracked structures, complex stress singularities occurring at bi-material interfaces and multi-material corners are studied for the first time in the sensitivity analysis. The sensitivity of the SIFs with respect to the crack angle, as well as the crack size, is developed herein. The hybrid random-interval moment method is coupled with the shape sensitivity analysis. Uncertainties are modelled as random and interval variables simultaneously, of which the crack geometry are modelled as the interval variables. Several numerical examples are demonstrated to verify each step of the research developments.Ultimately, the developed numerical tool will provide engineers with a more efficient and greater quantitative analysis to assess the safety of cracked structures subjected to uncertainties