Probabilistic crack trajectory analysis by a dimension reduction method

This paper proposes a novel analysis method of stochastic crack trajectory based on a dimension reduction approach. The developed method allows efficiently estimating the statistical moments, probability density function and cumulative distribution function of the crack trajectory for cracked elastic structures considering the randomness of the loads, material properties and crack geometries. First, the traditional dimension reduction method is extended to calculate the first four moments of the crack trajectory, in which the responses are eigenvectors rather than scalars. Then the probability density function and cumulative distribution function of the crack trajectory can be obtained using the maximum entropy principle constrained by the calculated moments. Finally, the simulation of the crack propagation paths is realized by using the scaled boundary finite element method. The proposed method is well validated by four numerical examples performed on varied cracked structures. It is demonstrated that this method outperforms the Monte Carlo simulation in terms of computational efficiency, and in the meanwhile, it has an acceptable computational accuracy.