Time-variant reliability problems commonly occur in practical engineering due to the deterioration in material properties, external disturbance and other uncertain factors. Considering the non-probabilistic method can effectively deal with the uncertainties in reliability analysis. Based on the stress–strength interference method and interval method, a time-variant stress–strength interference interval model is established by considering the stress and strength as time-variant intervals. And then, the stress and strength intervals are converted into the normalized intervals to define the non-probabilistic time-variant reliability index [Formula: see text] according to the different relationships between the limit state function and the normalized intervals. The structural state at any time can be described by the non-probabilistic time-variant reliability index [Formula: see text]. In addition, a strength power exponential degradation model is given as an example to clearly verify the non-probabilistic time-variant method, and the analysis results are compared with the interval method, the uniform distribution stress–strength interference method and the normal distribution stress–strength interference method, which confirm that the non-probabilistic time-variant method is feasible and valid to analyze the structural time-variant reliability without the probability density functions of the parameters.

A massive explosion of a liquid-propellant rocket in the course of an accident can lead to a truly catastrophic event, which would threaten the safety of personnel and facilities around the launch site. In order to study the propagation of near-ground shock wave and quantify the enhancement effect on the overpressure, models with different grounds have been established based on an explicit nonlinear dynamic ANSYS/LS-DYNA 970 program. Results show that the existence of the ground will change the propagation law and conform to the reflection law of the shock wave. Rigid ground absorbs no energy and reflects all of it, while concrete ground absorbs and reflects some of the energy, respectively. Ground may influence the pressure-time curve of the shock wave. When the gauge is close to the explosive, the pressure-time curve presents a bimodal feature, while when the gauge reaches a certain distance to the explosive, it presents a single-peak feature. For gauges at different heights, different grounds may have different effects on the peak overpressure. For gauges of height not greater than 4 m, the impact on the shock wave is obvious when the radial to the explosive is small. On the contrary, as for the gauges of height greater than 4 m, the impact on the shock wave is obvious when the radial to the explosive is big. Ground has the enhancement effect on peak overpressure, but different grounds have different ways. For rigid ground, the peak overpressure factor is about 2. However, for the concrete and soil ground, peak overpressure factor is from 1.43 to 2.1.

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Setting up an expansion chamber in the local tunnel can accelerate the attenuation speed of the shock wave, which is of great importance for safety protection of the tunnel staff. Under the same simplified conditions, the reliability of the numerical model was verified according to the theoretical formula calculation results. The simulation results of the long straight tunnel and the tunnel with expansion chamber were compared. Results show that the overpressure in the tunnel with expansion chamber is lower than that in the long straight tunnel at the same distance. Then, the length-width ratio was changed. Taking both the protection performance and construction cost into consideration, it is concluded that expansion chamber with the length-width ratio of 2.5 is relatively appropriate. The study can offer effective reference for structure design of the underground tunnel.

To study the hydrodynamic ram effect caused by the debris hypervelocity impact on the satellite tank, a numerical simulation of the spherical debris impacting the satellite tank at the velocity of 7000 m/s was carried out based on ANSYS/LS-DYNA software. The attenuation law of debris velocity, the propagation process of the shock wave and the deformation of the tank walls were investigated. The influences of the liquid-filling ratio, the magnitude, and direction of angular velocity on the hydrodynamic ram effect were analyzed. Results show that the debris velocity decreased rapidly and the residual velocity was 263 m/s when the debris passed through the tank. The shock wave was hemispherical, and the pressure of shock wave was the smallest at the element with an angle of 90° to the impact line. The maximum diameter of the front perforation was larger than that of the back perforation and the bulge height on the front wall was smaller than that on the back wall. With the decrease of the liquid-filling ratio, the diameter of the perforations and bulge height decreased. When the debris impacted the satellite tank with the angular velocity in the x direction, the debris trajectory did not deflect. When the debris impacted the satellite tank with the angular velocities in the y and z direction, the debris trajectory deflected to the negative direction of the z axis and y axis, respectively. The magnitude of the angular velocity affects the residual velocity of debris and the diameter of perforations.