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.     

Crystallographic analysis on small fatigue crack propagation behaviour of a nickel-based single crystal superalloy

In situ observations by scanning electron microscopy show that small fatigue cracks in a nickel-based single crystal superalloy are inclined to the loading direction and propagate in dominant crystallographic manners. In order to evaluate the driving forces for inclined crack propagation, three-dimensional anisotropic linear elastic finite-element analysis is conducted. The plastic zone size on the dominant slip plane has been calculated and proposed to correlate the fatigue crack growth. It is shown that this parameter takes into account both material anisotropy and octahedral fracture modes, and it can effectively characterize small crack propagation behaviour.     

An efficient uncertainty propagation method for parameterized probability boxes

In the response analysis of uncertain structural models with limited information, parameterized p-boxes are used to quantify the uncertain variables. In this study, a new technique is developed to compute the probability bounds of the structural response. Monotonicity analysis is performed on probability transformations of the random variables, revealing the relations between the interval distribution parameters and probability bounds of the structural response. Based on the monotonicity analysis, an algorithm for parameterized p-boxes is developed for computing the structural response. Three numerical examples are investigated to demonstrate the effectiveness of the proposed method.     

Integration of SPC and performance maintenance for supply chain system

In this paper, a supply chain system is viewed as a maintainable system, and the economic-statistical design of a likelihood ratio control chart with a maintenance application is considered for this system. The supply chain system is described by a three-state: normal state, warning state and failure state. A likelihood ratio control chart is used to monitor the system given that only categorical observations can be obtained. When the chart signals, a full inspection is performed to determine the actual system state (normal or warning), and preventive maintenance is immediately performed in the warning state. In addition, the supply chain system must be corrected upon failure (i.e. corrective maintenance), and should be maintained in a scheduled time (i.e. planned maintenance). A mathematical model is developed for the joint optimisation of the control chart parameters and planned maintenance time based on renewal theory. An example is presented to illustrate how to determine the optimal design parameters. We also investigate the effect of coefficients and statistical constraints on the decision variables and the expected cost.