Highlights• We implement an isogeometric BEM routine for fracture by use of dual boundary integral equations.• We propose a singular integration scheme to improve the quadrature accuracy for elements with high aspect ratios.• We investigate the approaches to compute stress intensity factors based on a NURBS representation of the crack surfaces.• We outline a geometric algorithm to propagate the crack based on the fatigue Paris law. AbstractWe present a novel numerical method to simulate crack growth in 3D, directly from the Computer-Aided Design (CAD) geometry of the component, without any mesh generation. The method is an isogeometric boundary element method (IGABEM) based on non-uniform rational B-splines (NURBS). NURBS basis functions are used for the domain and crack representation as well as to approximate the physical quantities involved in the simulations. A stable quadrature scheme for singular integration is proposed to enhance the robustness of the method in dealing with highly distorted elements. Convergence studies in the crack opening displacement is performed for a penny-shaped crack and an elliptical crack. Two approaches to extract stress intensity factors (SIFs): the contour M integral and the virtual crack closure integral are compared using dual integral equations. The results show remarkable accuracy in the computed SIFs, leading to smooth crack paths and reliable fatigue lives, without requiring the generation of any mesh from the CAD model of the component under consideration.

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We propose a method for simulating linear elastic crack growth through an isogeometric boundary element method directly from a CAD model and without any mesh generation. To capture the stress singularity around the crack tip, two methods are compared: (1) a graded knot insertion near crack tip; (2) partition of unity enrichment. A well-established CAD algorithm is adopted to generate smooth crack surfaces as the crack grows. The M integral and J k integral methods are used for the extraction of stress intensity factors (SIFs). The obtained SIFs and crack paths are compared with other numerical methods.

Weather radar echo is the data detected by the weather radar sensor and reflects the intensity of meteorological targets. Using the technique of radar echo extrapolation, which is the prediction of future echoes based on historical echo observations, the approaching short-term weather conditions can be forecasted, and warnings can be raised with regard to disastrous weather. Recently, deep learning based extrapolation methods have been proposed and show significant application potential. However, there are two limitations of existing extrapolation methods which should be considered. First, few methods have investigated the impact of the evolutionary process of weather systems on extrapolation accuracy. Second, current deep learning methods usually encounter the problem of blurry echo prediction as extrapolation goes deeper. In this paper, we aim to address the two problems by proposing a Multi-Level Correlation Long Short-Term Memory (MLC-LSTM) and integrate the adversarial training into our approach. The MLC-LSTM can exploit the spatiotemporal correlation between multi-level radar echoes and model their evolution, while the adversarial training can help the model extrapolate realistic and sharp echoes. To train and test our model, we build a real-life multi-level weather radar echoes dataset based on raw CINRAD/SA radar observations provided by the National Meteorological Information Center, China. Extrapolation experiments show that our model can accurately forecast the motion and evolution of an echo while keeping the predicted echo looking realistic and fine-grained. For quantitative evaluation on probability of detection (POD), false alarm rate (FAR), critical success index (CSI), and Heidke skill score (HSS) metrics, our model can reach average scores of 0.6538 POD, 0.2818 FAR, 0.5348 CSI, and 0.6298 HSS, respectively when extrapolating 15 echoes into the future, which outperforms the current state-of-the-art extrapolation methods. Both the qualitative and quantitative experimental results demonstrate the effectiveness of our model, suggesting that it can be effectively applied to operational weather forecasting practice.