A Proposed Algorithm to Compute the Stress-Strain Plastic Region and Displacement of a Deep-Lying Tunnel Considering Intermediate Stress and Strain-Softening Behavior

Past studies on deep-lying tunnels under the assumption of plane strain have generally neglected the influence of intermediate principal stress even though this affects the surrounding rocks in the plastic zone. This study proposes a finite difference method to compute the stress strain plastic region and displacement of a tunnel based on the Drucker–Prager (D–P) yield criterion and non-associated flow rule and considering the influences of intermediate principal stress and the strain-softening behavior of surrounding rock. The computed results were compared with those of other well-known solutions and the accuracy and validity of the method were confirmed through some examples. Parameter analysis was conducted to investigate the effects of intermediate principal stress on stress-strain, the plastic region, the ground response curve, and the dilatability of surrounding rock. The results showed that the plastic radius , the residual radius , and radial displacement of surrounding rock first decreased and then increased with increasing intermediate principal stress coefficient b from 0 to 1, with the minimums occurring at b = 0.75. On the contrary, the peak and rate of variation of the dilatancy coefficient first increased and then decreased with increasing b and the dilatancy coefficient gradually transitioned from nonlinear to linear variation. Meanwhile, the inhibition of the plastic radius and radial displacement gradually weakened with increasing support pressure, whereas the dilatancy coefficient of the tunnel opening gradually increased.

Computational Design of a Magnetic Mirror

A computer-aided design (CAD) has been carried out to investigate the properties of the magnetic electron mirror design. The work has been focused on suggesting a mathematical formula to represent the radial displacement. The function that has been taken into consideration was suggested to give rise to the mirror action. A numerical solution is carried out for solving the Paraxial-ray equation for determining the optical properties such as the focal length, the spherical and chromatic aberration coefficients and the excitation of the mirror. The pole shape of the mirror has been determined in two dimensions. In the present work, the profile of the mirror determined from the suggested trajectory is the single-pole types. The coefficients of the chromatic and spherical aberrations of the magnetic mirror are determined and normalized in terms of the focal length. The operational requirements are determining the choice of the mirror.

Decayless Kink Oscillations Excited by Random Driving: Motion in Transitional Layer

In this article we study the plasma motion in the transitional layer of a coronal loop randomly driven at one of its footpoints in the thin-tube and thin-boundary-layer (TTTB) approximation. We introduce the average of the square of a random function with respect to time. This average can be considered as the square of the oscillation amplitude of this quantity. Then we calculate the oscillation amplitudes of the radial and azimuthal plasma displacement as well as the perturbation of the magnetic pressure. We find that the amplitudes of the plasma radial displacement and the magnetic-pressure perturbation do not change across the transitional layer. The amplitude of the plasma radial displacement is of the same order as the driver amplitude. The amplitude of the magnetic-pressure perturbation is of the order of the driver amplitude times the ratio of the loop radius to the loop length squared. The amplitude of the plasma azimuthal displacement is of the order of the driver amplitude times $\text{Re}^{1/6}$ Re 1 / 6 , where Re is the Reynolds number. It has a peak at the position in the transitional layer where the local Alfvén frequency coincides with the fundamental frequency of the loop kink oscillation. The ratio of the amplitude near this position and far from it is of the order of $\ell$ ℓ , where $\ell$ ℓ is the ratio of thickness of the transitional layer to the loop radius. We calculate the dependence of the plasma azimuthal displacement on the radial distance in the transitional layer in a particular case where the density profile in this layer is linear.

Diffusion and flow across shape-perturbed plasmodesmata nanopores in plants

Plasmodesmata are slender nanochannels that link neighboring plant cells and enable the exchange of nutrients and signaling molecules. Recent experiments have demonstrated significant variability in the concentric pore shape. However, the impact of these geometric fluctuations on transport capacity is unknown. Here, we consider the effects on diffusion and advection of two ideal shape perturbations: a radial displacement of the entire central desmotubule and a harmonic variation in the cytoplasmic sleeve width along the length of the pore. We use Fick’s law and the lubrication approximation to determine the diffusive current and volumetric flow rate across the pore. Our results indicate that an off-center desmotubule always increases the pressure-driven flow rate. However, the diffusive current is only enhanced for particles comparable in size to the width of the channel. In contrast, harmonic variations in the cytoplasmic sleeve width along the length of the pore reduce both the diffusive current and the pressure-driven flow. The simple models presented here demonstrate that shape perturbations can significantly influence transport across plasmodesmata nanopores.

Numerical Simulation and Parameter Analysis of Electromagnetic Riveting Process for Ti-6Al-4V Titanium Rivet

Electromagnetic riveting process (EMR) is a high-speed impact connection technology with the advantages of fast loading speed, large impact force and stable rivet deformation. In this work, the axisymmetric sequential and loose electromagnetic-structural coupling simulation models were conducted to perform the electromagnetic riveting process of a Ti-6Al-4V titanium rivet, and the parameter analysis of the riveting setup was performed based on the sequential coupled simulation results. In addition, the single-objective optimization problem of punch displacement was conducted using the Hooke–Jeeves algorithm. Based on the adaptive remeshing technology adopted in air meshes, the deformation calculated in the structural field was well transferred to the electromagnetic field in the sequential coupled model. Thus, the sequential coupling simulation results presented higher accuracy on the punch speed and rivet deformation than the loose coupling numerical model. The maximum relative difference of electromagnetic force (EMF) on driver plate and radial displacement in the rivet shaft was 34.86% and 13.43%, respectively. The parameter analysis results showed that the outer diameter and the height of the driver plate had a significant first-order effect on the response of displacement, while the platform height, transition zone height, angle, and transition zone width of the amplifier presented a strong interaction effect. Using the obtained results on the optimal structural parameters, the punch speed was effectively improved from 6.13 to 8.12 m/s with a 32.46% increase. Furthermore, the displacement of the punch increasing from 3.38 to 3.81 mm would lead to an 80.55% increase in the maximum radial displacement of the rivet shaft. This indicated that the deformation of the rivet was efficiently improved by using the optimal rivet model.

The static response of axisymmetric conical shells exhibiting bistable behavior

Belleville springs are widely used in variety of mechanical systems. Recent advances in the field of multi-stable structures suggest that these conical axisymmetric washers may be extremely useful as bistable building-blocks for multi-stable architected metamaterials. In this paper, we examine the ability of existing analytical models to accurately predict the bistable behavior of Belleville springs, namely a non-monotonous force-displacement relation with two branches of positive stiffness separated by a branch of negative stiffness. By comparing to results of finite-element simulations, we find that current analytical models may suffer from significant inaccuracies associated with the assumption of rigid rotation. According to this assumption, adopted by all analytical models of Belleville springs, the cross-section of the spring rotates without bending, i.e. maintains zero curvature as the spring deforms. Motivated by this insight, we relax the rigid-rotation assumption and approximate the radial displacement field by a linear relation in terms of the distance from the spring axis. We find, based on extensive finite-element simulations, that the functional dependence of the radial displacement on the geometry of the springs is indifferent to the stage of deformation and can be expressed in terms of three geometrical parameters. These findings enable us to derive closed-form expressions that are simple and straight-forward to use, yet are significantly more accurate than existing analytical models.