In order to assess the electrical response of the BC₃ nanosheets to megazol, computations according to the density functional theory (DFT) have been done. Pristine BC₃ is determined to have a notable trend towards the megazol molecules. For the most stable configuration, the adsorption energy is approximately −20.7 kcal/mol. Megazol adsorption makes a noticeable decrease in the gap of HOMO (highest occupied molecular orbital) -LUMO (lowest unoccupied molecular orbital) BC₃ nanosheets (from 1.45 to 0.75 V), thereby enhancing the electrical conductivity, which means the BC₃ can be a proper choice for megazol detection and electronic sensor applications. Additionally, megazol adsorption has affected the work function of BC₃, which remarkably shifts the current of field electron emission from its level, suggesting it for detecting megazol as a function-based sensor. Also, BC₃ has the benefit of a short recovery time of approximately 7.72 ms for megazol desorption. Graphical Abstract

The prediction of failure mechanisms in nonlinear elastic materials holds significant importance in engineering applications. In recent years, the phase-field model has emerged as an effective approach for addressing fracture problems. Compared with other discontinuous fracture methods, the phase-field method allows for the easy simulation of complex fracture paths, including crack initiation, propagation, coalescence, and branching phenomena, through a scalar field known as the phase field. This method offers distinct advantages in tackling complex fracture problems in nonlinear elastic materials and exhibits substantial potential in material design and manufacturing. The current research has indicated that the energy distribution method employed in phase-field approaches significantly influences the simulated results of material fracture, such as crack initiation load, crack propagation path, crack branching, and so forth. This impact is particularly pronounced when simulating the fracture of nonlinear materials under finite deformation. Therefore, this review outlines various strain energy decomposition methods proposed by researchers for phase-field models of fracture in tension–compression symmetric nonlinear elastic materials. Additionally, the energy decomposition model for tension–compression asymmetric nonlinear elastic materials is also presented. Moreover, the fracture behavior of hydrogels is investigated through the application of the phase-field model with energy decomposition. In addition to summarizing the research on these types of nonlinear elastic body fractures, this review presents numerical benchmark examples from relevant studies to assess and validate the accuracy and effectiveness of the methods presented.

Severe vibrations of the marine propulsion shaft can evidently affect the dynamical response of the propulsion system and degrade the performance of a ship. As the vibration forms couples which interact with each other, a better understanding of the coupled vibrations is essential for dynamic prediction to improve the efficiency and reliability of the marine propulsion system. Thus, an investigation of the lumped-mass method for coupled torsional-longitudinal vibrations of the shaft is proposed. First, a theoretical solution for the coupled ordinary differential equations demonstrates the accuracy of the proposed lumped-mass model. This model allows for the bifurcation diagram and the Poincare surface, and transient accelerations of the coupled vibrations are numerically calculated. Furthermore, the impact factors including various length-diameter ratios, coupling stiffness coefficients, and damping coefficients are respectively discussed. These impact factors are found to affect the coupled vibrations to different extents through the comparison of the transient accelerations. Finally, an accurate and applicative lumped-mass method for the coupled torsional-longitudinal vibrations of the marine propulsion shaft has been obtained. An optimal design and vibration reduction of the shaft, considering the above-mentioned impact factors, can be achieved.

This paper proposes a derivative-variance hybrid global sensitivity measure with optimal sampling method selection. The proposed sensitivity measure is as computationally efficient as the derivative-based global sensitivity measure, which also serves as the conservative estimation of the corresponding variance-based global sensitivity measure. Moreover, the optimal sampling method for the proposed sensitivity measure is studied. In search of the optimal sampling method, we investigated the performances of six widely used sampling methods, namely Monte Carlo sampling, Latin hypercube sampling, stratified sampling, Latinized stratified sampling, and quasi-Monte Carlo sampling using the Sobol and Halton sequences. In addition, the proposed sensitivity measure is validated through its application to a rural bridge.