The boundary conditions for simulations of a shake-table experiment on the seismic response of 3D slope

Boundary conditions can significantly affect a slope＇s behavior under strong earthquakes. To evaluate the importance of boundary conditions for finite element （FE） simulations of a shake-table experiment on the slope response, a validated three-dimensional （3D） nonlinear FE model is presented, and the numerical and experimental results are compared. For that purpose, the robust graphical user-interface ＂SlopeSAR＂, based on the open-source computational platform OpenSees, is employed, which simplifies the effort-intensive pre- and post-processing phases. The mesh resolution effect is also addressed. A parametric study is performed to evaluate the influence of boundary conditions on the FE model involving the boundary extent and three types of boundary conditions at the end faces. Generally, variations in the boundary extent produce inconsistent slope deformations. For the two end faces, fixing the y-direction displacement is not appropriate to simulate the shake-table experiment, in which the end walls are rigid and rough. In addition, the influence of the length of the 3D slope＇s top face and the width of the slope play an important role in the difference between two types of boundary conditions at the end faces （fixing the y-direction displacement and fixing the （y, z） direction displacement）. Overall, this study highlights that the assessment of a comparison between a simulation and an experimental result should be performed with due consideration to the effect of the boundary conditions.

Effect of grain boundary sliding on the toughness of ultrafine grain structure steel: A molecular dynamics simulation study

Molecular dynamics simulations are carried out to investigate the mechanisms of low-temperature impact toughness of the ultrafine grain structure steel. The simulation results suggest that the sliding of the {001 }/{ 110} type and { 110}/{ 111 } type grain boundary can improve the impact toughness. Then, the mechanism of grain boundary sliding is studied and it is found that the motion of dislocations along the grain boundary is the underlying cause of the grain boundary sliding. Finally, the sliding of the grain boundary is analyzed from the standpoint of the energy. We conclude that the measures which can increase the quantity of the {001}/{110} type and {110}/{ 111} type grain boundary and elongate the free gliding distance of dislocations along these grain boundaries will improve the low-temperature impact toughness of the ultrafine grain structure steel.

A Molecular Dynamics Simulation for Periodic Boundary Condition in the Bending Process of Ag／Ni Composite Interfaces

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An approach for simulating the air brake system of long freight trains based on fluid dynamics

Air brake systems are critical equipment for railway trains, which affects the running safety of the trains significantly. To study air braking characteristics of long freight trains, an approach for simulating air brake systems based on fuid dynamics theory was proposed. The structures and working mechanisms of locomotive and wagon air brakes are introduced, and mathematical models of the pipes, brake valves, reservoirs or chambers, cylinders, etc., are presented.Besides, the dynamic motions of parts in the main valve are considered. The simulation model of the whole air brake system is then formulated, and the solving method based on the finite-difference method is used. New efficient pipe boundary conditions without iterations are developed for brake pipes and branch pipes, which can achieve higher computational efficiency. The proposed approach for simulating the air brake system is validated by comparing with published measured data. Simulation results of different train formations indicate that models that consider the dynamic behavior of brake pipes are recommended for predicting the characteristics of long trains under service braking conditions.

Temperature effect on nanotwinned Ni under nanoindentation using molecular dynamic simulation

Temperature effect on atomic deformation of nanotwinned Ni (nt-Ni) under localized nanoindentation is investigated in comparison with nanocrystalline Ni (nc-Ni) through molecular simulation.The nt-Ni exhibits enhanced critical load and hardness compared to nc-Ni,where perfect,stair-rod and Shockley dislocations are activated at (111),(111) and (111) slip planes in nt-Ni compared to only SSockley dislocation nucleation at (111) and (111) slip planes of nc-Ni.The nt-Ni exhibits a less significant indentation size effect in comparison with nc-Ni due to the dislocation slips hindrance of the twin boundary.The atomic deformation associated with the indentation size effect is investigated during dislocation transmission.Different from the decreasing partial slips parallel to the indenter surface in nc-Ni with increasing temperature,the temperaturedependent atomic deformation of nt-Ni is closely related to the twin boundary:from the partial slips parallel to the twin boundary (~10 K),to increased confined layer slips and decreased twin migration(300 K–600 K),to decreased confined layer slips and increased dislocation interaction of dislocation pinning and dissociation (900 K–1200 K).Dislocation density and atomic structure types through quantitative analysis are implemented to further reveal the above-mentioned dislocation motion and atomic structure alteration.Our study is helpful for understanding the temperature-dependent plasticity of twin boundary in nanotwinned materials.

Application of inverse method to estimation of boundary conditions during investment casting simulation

Inverse method was used in single crystal superalloy DD6 processing simulation during solidification. Numerical modeling coupled with experiments has been used to estimate the interface heat transfer coefficient （IHTC） between the surface of slab casting and inner mold. Calculated temperature dependent values of IHTC were obtained from a numerical solution. The calculated temperatures agreed well with the measurement of cooling profile.

Dynamic stiffness method for free vibration of an axially moving beam with generalized boundary conditions

Axially moving beams are often discussed with several classic boundary conditions, such as simply-supported ends, fixed ends, and free ends. Here, axially moving beams with generalized boundary conditions are discussed for the first time. The beam is supported by torsional springs and vertical springs at both ends. By modifying the stiffness of the springs, generalized boundaries can replace those classical boundaries. Dynamic stiffness matrices are, respectively, established for axially moving Timoshenko beams and Euler-Bernoulli (EB) beams with generalized boundaries. In order to verify the applicability of the EB model, the natural frequencies of the axially moving Timoshenko beam and EB beam are compared. Furthermore, the effects of constrained spring stiffness on the vibration frequencies of the axially moving beam are studied. Interestingly, it can be found that the critical speed of the axially moving beam does not change with the vertical spring stiffness. In addition, both the moving speed and elastic boundaries make the Timoshenko beam theory more needed. The validity of the dynamic stiffness method is demonstrated by using numerical simulation.

Effect of twin boundary on nanoimprint process of bicrystal Al thin film studied by molecular dynamics simulation

The effects of a twin boundary（TB） on the mechanical properties of two types of bicrystal Al thin films during the nanoimprint process are investigated by using molecular dynamics simulations.The results indicate that for the TB direction parallel to the imprinting direction,the yield stress reaches the maximum for the initial dislocation nucleation when the mould directly imprints to the TB,and the yield stress first decreases with the increase of the marker interval and then increases.However,for the TB direction perpendicular to the imprinting direction,the effect of the TB location to the imprinting forces is very small,and the yield stress is greater than that with the TB direction parallel to the imprinting direction.The results also demonstrate that the direction of the slip dislocations and the deformation of the thin film caused by spring-back are different due to various positions and directions of the TB.

Solution of the Euler Equations with Approximate Boundary Conditions for Thin Airfoils

This paper presents an efficient numerical method for solving the Euler equations on rectilinear grids. Wall boundary conditions on the surface of an airfoil are implemented by using their first order expansions on the airfoil chord line, which is placed along a grid line. However, the method is not restricted to flows with small disturbances since there are no restrictions on the magnitude of the velocity or pressure perturbations. The mathematical formulation and the numerical implementation of the wall boundary conditions in a finite volume Euler code are described. Steady transonic flows are calculated about the NACA 0006, NACA 0012 and NACA 0015 airfoils, corresponding to thickness ratios of 6%, 12%, and 15%, respectively. The computed results, including surface pressure distributions, the lift coefficient, the wave drag coefficient, and the pitching moment coefficient, at angles of attack from 0° to 8° are compared with solutions at the same conditions by FLO52, a well established Euler code using body fitted curvilinear grids. Results demonstrate that the method yields acceptable accuracies even for the relatively thick NACA 0015 airfoil and at high angles of attack. This study establishes the potential of extending the method to computing unsteady fluid structure interaction problems, where the use of a stationary rectilinear grid offers substantial advantages in both computer time and human work since it would not require the generation of time dependent body fitted grids.

Numerical simulation of hydrodynamic characteristics during the diversion closure in a horizontal tunnel

Based on water inrush accident of 1841 working face of Desheng Coal Mine in Wu'an, Hebei province, China, an evaluation model of hydrodynamic characteristics of the project is set up and simulated using Matlab. It is assumed that the pipe flow would transform into seepage flow when the aggregates are plugged into the water inrush channel and the seepage flow would disappear along with grouting process. The simulation results show that the flow velocity will increase with an increase in height of aggregates accumulation body during the aggregates filling process; the maximum seepage velocity occurs on the top of plugging zone; and the water flow decreases with increasing plugging height of water inrush channel. Finally, the field construction results show that the water inrush channel can be plugged effectively by the compacted body prepared with aggregate and cement slurry.

MOLECULAR DYNAMICS SIMULATION OF ENTROPY AND SURFACE TENSION FOR GRAIN BOUNDARY OF α-Fe

The grain boundary is an interface and the surface tension is one of its important thermodynamic properties. In this paper, the surface tension of the Σ9 grain boundary for α-Fe at various temperatures and pressures is calculated by means of Computer Molecular Dynamics (CMD). The results agree satisfactorily with the experimental data. It. is shown that the contribution of entropy to surface tension of grain boundary can be ignored.

A note for the mechanism of high-frequency oscillation instability resulted from absorbing boundary conditions

In this paper the explanation of the mechanism of high-frequency oscillation instability resulted from absorbing boundary conditions is further improved. And we analytically prove the proposition that for one dimensional discrete model of elastic wave motion, the module of reflection factor will be greater than 1 in high frequency band when artificial wave velocity is greater than 1.5 times the ratio of discrete space step to discrete time step. Based on the proof, the frequency band in which instability occurs is discussed in detail, showing such high-frequency waves are meaningless for the numerical simulation of wave motion.

Exact Time Domain Solutions of 1-D Transient Dynamic Piezoelectric Problems with Nonlinear Damper Boundary Conditions

Novel exact solutions of one-dimensional transient dynamic piezoelectric problems for thickness polarized layers and disks, or length polarized rods, are obtained. The solutions are derived using a time-domain Green’s function method that leads to an exact analytical recursive procedure which is applicable for a wide variety of boundary conditions including nonlinear cases. A nonlinear damper boundary condition is considered in more detail. The corresponding nonlinear relationship between stresses and velocities at a current time moment is used in the recursive procedure. In addition to the exact recursive procedure that is effective for calculations, some new practically important explicit exact solutions are presented. Several examples of the time behavior of the output electric potential difference are given to illustrate the effectiveness of the proposed exact approach.

The Wave Equation Together with Matheu-Hill and Laguerre Form Dynamic Boundary Conditions

The present study illustrates a series method for the solutions of one dimensional wave equation together with non-classical dynamic boundary conditions. Matheu-Hill form, a differential equation with polynomial form and Laguerre differential equation form dynamic boundary conditions were taken into consideration. Series methods were given in order for the solutions of wave equation together with these dynamic boundary conditions along with semi-infinite axis of the spatial coordinate. Wave profiles were obtained by means of wave solutions of the wave equation given by d’Alembert.

The Response of a Shear Beam as 1D Medium to Seismic Excitations Dependent on the Boundary Conditions

We study response of a shear beam to seismic excitations at its base. The research is conducted using computer simulation of the wave propagation on a numerical model. The wave equation is solved using the method of finite differences （FD） where the spatial and temporal derivatives are approximated with FD. We used formulation of the wave equation via the particle velocities, strains, mid stresses. Integrating particle velocities in time, we obtained displacements at spatial points. The main goal in this research is to study phenomena occurring due to three different types of boundary conditions, Dirichlet, Neumann, and moving boundary when simple half-sine pulse propagates through 1D medium modeled as a shear beam.

Numerical Simulation of Viscous Flow Through Spherical Particle Assemblage with the Modified Cell Model

The cell model developed since 1950s is a useful tool forexploring the behavior of particle assemblages, but it demandsfurther careful development of the outer boundary conditions so thatinteraction in a particle swarm is better represented. In this paper,the cell model and its development were reviewed, and themodifications of outer cell boundary conditions were suggested. Atthe cell outer boundary, the restriction of uniform liquid flow wasremoved in our simulation conducted in the reference frame fixed withthe particle.

A Novel Approach for the Numerical Simulation of Fluid-Structure Interaction Problems in the Presence of Debris

A novel algorithm is proposed for the simulation of fluid-structure interaction problems.In particular,much attention is paid to natural phenomena such as debris flow.The fluid part(debris flow fluid)is simulated in the framework of the smoothed particle hydrodynamics(SPH)approach,while the solid part(downstream obstacles)is treated using the finite element method(FEM).Fluid-structure coupling is implemented through dynamic boundary conditions.In particular,the software“TensorFlow”and an algorithm based on Python are combined to conduct the required calculations.The simulation results show that the dynamics of viscous and non-viscous debris flows can be extremely different when there are obstacles in the downstream direction.The implemented SPH-FEM coupling method can simulate the fluid-structure coupling problem with a reasonable approximation.

CYCLIC HARDENING BEHAVIOR OF POLYCRYSTALS WITH PENETRABLE GRAIN BOUNDARIES:TWO-DIMENSIONAL DISCRETE DISLOCATION DYNAMICS SIMULATION

A two-dimensional discrete dislocation dynamics （DDD） technology by Giessen and Needleman （1995）, which has been extended by integrating a dislocation-grain boundary interaction model, is used to computationally analyze the micro-cyclic plastic response of polycrystals containing micron-sized grains, with special attentions to significant influence of dislocationpenetrable grain boundaries （GBs） on the micro-plastic cyclic responses of polycrystals and underlying dislocation mechanism. Toward this end, a typical polycrystalline rectangular specimen under simple tension-compression loading is considered. Results show that, with the increase of cycle accumulative strain, continual dislocation accumulation and enhanced dislocation-dislocation interactions induce the cyclic hardening behavior; however, when a dynamic balance among dislocation nucleation, penetration through GB and dislocation annihilation is approximately established, cyclic stress gradually tends to saturate. In addition, other factors, including the grain size, cyclic strain amplitude and its history, also have considerable influences on the cyclic hardening and saturation.

Effect of Pressure on Boundary Slip of Thin Film Lubrication Using Atomistic Simulation

Mechanical systems on all length scales may be subjected to nanoscale thin film lubrication(TFL). Molecular dynamics(MD) simulations were conducted to investigate the lubrication mechanism and boundary slip of squalane confined in nanogap at 293 K with two different film thicknesses and a wide range of pressures. The molecular distribution, density and velocity profiles of squalane were analyzed. The results show that the lubricant atoms tend to form layers parallel to the wall, but the lubricant molecules orient randomly throughout the film in the directions both parallel and perpendicular to the wall. Most squalane molecules appear twisted and folded, and extend to several atomic layers so that there are no slips between lubricant layers. The distances between the lubricant layers are irregular rather than broadening far away from the walls. The boundary slip at the interface of bcc Fe(001) and squalane only occurs at high pressure because of the strong nonbond interactions between lubricant atoms and wall atoms. The tendency of boundary slip is more obvious for films with thinner film thickness. According to the simulations, the relationship between the slip length and the pressure is given.

A Fast-Fractional Flow Reserve Simulation Method in A Patient with Coronary Stenosis Based on Resistance Boundary Conditions

Fractional flow reserve(FFR)is the gold standard to identify individual stenosis causing myocardial ischemia in catheter laboratory.The purpose of this study is to present a fast simulation method to estimate FFR value of a coronary artery,which can evaluate the performance of vascular stenosis,based on resistance boundary conditions.A patient-specific 3-dimensional(3D)model of the left coronary system with intermediate diameter stenosis was reconstructed based on the CTA images.The resistance boundary conditions used to simulate the coronary microcirculation were computed based on anatomical reconstruction of coronary 3D model.This study was performed by coupling the 3D coronary tree model with the lumped parameter model(0D model).The flow rate and pressure of coronary tree were calculated in twenty minutes.In addition,the effect of inlet pressure and myocardial mass on FFRss values has been investigated.The results showed that the effect of myocardial mass was greater than the effect of inlet pressure on FFRss.This FFRss simulation method can quickly and accurately assess the influence of coronary stenosis in aid clinical diagnosis.