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In the framework of continuum damage mechanics, a computational model for quasi-brittle crack modelling is proposed. The proposed model has significant mesh-objectivity and accuracy advantages over existing methods for modeling quasi-brittle crack. These stem from the combination of the local crack tracking algorithm, the new calculation of crack bandwidth and the non-local treatment regarding strain field. Resorting to the implementation of local crack tracking algorithm, it is desirable that the spurious dependence of conventional continuum damage mechanics-based model on mesh bias can be effectively addressed. The new estimation of the real-time crack bandwidth can be not only depending on the element size and pattern, but also on the physical crack path within each consolidate cracked element. Thus, the energy dissipation during crack propagation can be characterized in a more accurate, physically based manner. The non-local averaging regarding the strain field in the course of failure evolution is carried out within an elliptical domain, the configuration of which is related to finite element and crack trajectory obtained by the local crack track algorithm. With this combined technique, it is expected that a more accurate crack evolution course can be achieved numerically, which allows engineers to adopt relatively coarse unstructured discretizations without sacrificing solution accuracy. By numerical examples, the proposed model, empowered by the combined techniques, demonstrates significant improvements in the prediction of crack propagating of quasi-brittle materials. This model may provide engineers a more reliable tool in practical application of computational material failure.

Weights of honeycomb sandwich composite structures are strictly controlled in scenarios such as in contexts of aerospace engineering. However, such structures extensively studied in past investigations were partly or completely made of aluminum or other metallic materials. Sufficient research has not been reported for honeycomb sandwich composites made of lightweight non-metallic materials. This paper presents an investigation into the mechanical responses of the Nomex honeycomb sandwich structure in a three-point bending test. The mathematical relationship between the shear stress distribution in the skin and that in the Nomex honeycomb core under the bending load was deduced. By applying the commercial software ABAQUS/Explicit, numerical simulations were performed with a highly detailed finite element model (micromechanical level) and equivalent elastic parameters. By comparing the experimental and numerical results, the validity of the theoretical derivation was verified. The effects of the thickness of the skin and the direction of the core on the mechanical responses of the honeycomb sandwich structure were studied. The results showed two different failure patterns of the honeycomb sandwich structure in the three-point bending test, which has rarely been reported previously. The improving effect of the increase in the skin thickness on the ultimate bearing capacity was more remarkable when the honeycomb core had a higher shear rigidity. For the same core direction, the honeycomb sandwich structure with the thicker skin had a better crashworthiness. The skin shear force distribution coefficient decreased exponentially with the ratio of core height-to-skin thickness.

Considering the random and fuzzy nature of wind speed, this paper proposes a multiobjective random-fuzzy chance-constrained programming optimal power flow (OPF) for wind integrated power systems. The proposed method is based on random-fuzzy chance-constrained programming. The optimization model aims at minimizing generation cost, carbon dioxide (CO2) emission, and system functional power loss, and P-Q-V steady-state voltage stability is included in the constraints. Based on random-fuzzy chance-constrained programming, the corresponding solution process of the proposed multiobjective OPF is proposed, which is a hybrid of random-fuzzy simulation, non-dominated sorting genetic algorithm-II (NSGA-II), and fuzzy satisfaction-maximizing decision-making method. The proposed approach is simulated on the IEEE 30-bus system to provide an example of its application. The simulation results demonstrate that the proposed random-fuzzy chance-constrained programming OPF has higher security and more economy than dynamic stochastic optimal power flow (DSOPF) and dynamic fuzzy optimal power flow (DFOPF).

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