Proposed Boundary Conditions Research Articles

Nonlinear consolidation finite element analysis of a layered soft soil foundation under multistage loading based on the continuous drainage boundary

To comprehensively consider the impacts of stratification, residual pore water pressure, soil nonlinearity, and boundary permeability on consolidation settlement of soft soil foundations for accurate prediction, a continuous drainage boundary condition is proposed in this study that reflects the residual pore pressure under multistage loading, and a nonlinear elastic constitutive model based on the double logarithmic model is adopted to account for the nonlinear consolidation behaviour of soils. A UMAT subroutine is developed based on the proposed boundary condition and nonlinear elastic constitutive model. Subsequently, the developed subroutine is compared with the built-in linear elastic soil constitutive model in ABAQUS and engineering examples. The application of continuous drainage boundaries in stratified foundations is analysed, as well as the influence of factors such as the loading rate and soil nonlinearity on consolidation settlement. The results indicate that, compared to the built-in model, the subroutine developed in this study can be employed to more accurately calculate the nonlinear consolidation of multilayered foundations under multistage loading. By adjusting the loading rate parameter αk, consolidation under different loading conditions can be predicted. Additionally, the proposed boundary condition simplifies the calculations for soft soil foundations with sand layers, providing a novel computational approach for the design of construction loading schemes and long-term settlement predictions in soft soil foundations.

Assessing the impact of aneurysm morphology on the risk of internal carotid artery aneurysm rupture: A statistical and computational analysis of endovascular coiling

Computational modeling and investigation have become increasingly useful in assessing the hemodynamic and structural factors that contribute to aneurysm rupture, particularly when conventional clinical tools are inadequate. To this end, we conduct a study of a realistic internal carotid artery (ICA) under various working conditions using computational fluid dynamics. We analyze nine specific real ICA geometries in terms of coiling porosity and blood hematocrit, using a response surface model to evaluate 25 runs across selected geometrical parameters and treatment factors. The computational domain is created using computed tomography data from an actual patient, and we apply proposed boundary conditions to solve three-dimensional transient Navier–Stokes equations. By analyzing these cases, we try to understand how the sac section area, mean radius of the parent vessel, hematocrit, and coiling porosity interact and affect the risk of ICA rupture. We conduct an extensive study of the effects of sac section area and mean radius of the parent vessel on blood hemodynamics, examining several factors and comparing them at the peak systolic time instant, including wall shear stress (WSS), oscillatory shear index (OSI), pressure distributions, and velocity. Our results show that a 12% increase in the mean radius of the parent vessel reduced the maximum OSI value by approximately 50%, while a 120% increase in the sac section area decreases WSS on the aneurysm wall by up to 300%. These findings demonstrate the potential of computational modeling to provide valuable insight into the complex factors that influence aneurysm rupture, especially in cases where traditional clinical tools may be insufficient.

Closed-Form Analytical Solutions for the Deflection of Elastic Beams in a Peridynamic Framework

Peridynamics is a continuum theory that operates with non-local deformation measures as well as long-range internal force/moment interactions. The resulting equations are of the integral type, in contrast to the classical theory, which deals with differential equations. The aim of this paper is to analyze peridynamic governing equations for elastic beams. To this end, the strain energy density is formulated as a function of the non-local curvature. By applying the Lagrange principle, the peridynamic equations of motion are derived. Examples of non-local boundary conditions, including simple support, clamped edge, roller clamped edge, and free edge, are presented by introducing the interaction domain. Novel closed-form analytical solutions to integral equations are presented for beams with various boundary conditions, including clamped—simply supported, clamped–clamped, simply supported–roller-clamped, and clamped–roller-clamped beams. Furthermore, different types of loadings, including uniformly distributed load, concentrated force, and concentrated moment, are considered. The results are validated by comparing the derived solutions against solutions to the classical Bernoulli–Euler beam theory. A very good agreement between the non-local and the classical theories is observed for the case of the small horizon sizes, which shows the capability of the derived equations of motion and proposed boundary conditions.

Peridynamic analysis of curved elastic beams

Peridynamics is an extended continuum theory which operates with non-local deformation measures as well as long range internal force/moment interactions. The aim of this paper is to present and to analyze peridynamic governing equations for elastic curved beams. To this end the strain energy density is formulated as a function of two non-local deformation measures including the axial deformation and curvature. Applying the Lagrangian formalism, peridynamic equations of motion are derived. To analyze curved beams of finite length peridynamic boundary conditions are required. Examples of boundary conditions including simple support and clamped edge are presented by introducing a fictitious domain. Solutions to PD equations of motion are presented for various problems including static analysis of simply supported and clamped arc beams as well as modal analysis of a slender ring and a simply supported arc beam. To validate peridynamic formulations, solutions for displacements, natural frequencies and vibration modes are compared with those by the classical beam theory. A very good agreement between the non-local and the classical theories is observed for the case of the small horizon sizes which shows the capability of the derived equations of motion and proposed boundary conditions.

Coupled THM formulation and wellbore analytical solution in naturally fractured media during injection/production

The heat extraction efficiency, storage, and safety of carbon dioxide (CO2) sequestration and methane (CH4) injection/post-production in naturally fractured formations have attracted significant interest. However, these studies require the examination of complex thermal-hydraulic-mechanical (THM) interacting processes, which include muti-discipline coupling and phase changes. Energy transfer mechanisms and thermally induced hydraulic and mechanical responses are critical for energy extraction efficiency , surface design optimization, and safety evaluation. The THM response in the wellbore, where fluids are injected and circulated, provides key information for design evaluation. A fully coupled formulation was developed based on a dual-porosity model to simulate the THM responses of a wellbore in naturally fractured aquifers under non-isothermal, two-phase fluid flow, and non-hydrostatic loading conditions. Local thermal non-equilibrium (LTNE) conditions are imposed for energy transportation between the fracture and matrix systems in the fissured porous solid skeleton. Different physical parameters reflecting various rock types and fracture characteristics are defined for the corresponding THM behavior models. Analytical solutions for the temperature perturbation and pressure changes in single-phase fluid flow in the vicinity of a wellbore in fissured media are developed to simulate the injection and production processes. Simulating a non-isothermal fluid circulation problem along a wellbore, an newly proposed mixed Type I (Dirichlet) and II (Neumann) boundary condition is imposed to study the heat exchange efficiency between wellbore fluid and the fissured NFM. The analytical solution has the advantages of being simple, explicitly possessing direct physical parameters, and serving as a tool for validating numerical solutions. The impacts of the newly proposed boundary condition on the near-well responses and THM results from the newly developed solution may be used to simulate the injectivity, storage capacity, reproduction, and design of supercritical carbon (scCO2) and CH4 are discussed.

Coseismic site response and slope instability using periodic boundary conditions in the material point method

This paper proposed the explicit generalized-α time scheme and periodic boundary conditions in the material point method (MPM) for the simulation of coseismic site response. The proposed boundary condition uses an intuitive particle-relocation algorithm ensuring material points always remain within the computational mesh. The explicit generalized-α time scheme was implemented in MPM to enable the damping of spurious high frequency oscillations. Firstly, the MPM was verified against finite element method (FEM). Secondly, ability of the MPM in capturing the analytical transfer function was investigated. Thirdly, a symmetric embankment was adopted to investigate the effects of ground motion arias intensity (Ia), geometry dimensions, and constitutive models. The results show that the larger the model size, the higher the crest runout and settlement for the same ground motion. When using a Mohr-Coulomb model, the crest runout increases with increasing Ia. However, if the strain-softening law is activated, the results are less influenced by the ground motion. Finally, the MPM results were compared with the Newmark sliding block solution. The simplified analysis herein highlights the capabilities of MPM to capture the full deformation process for earthquake engineering applications, the importance of geometry characterization, and the selection of appropriate constitutive models when simulating coseismic site response and subsequent large deformations.

Stable, entropy-pressure compatible subsonic Riemann boundary condition for embedded DG compressible flow simulations

One approach to reducing the computational cost of simulating transitional compressible boundary layer flow is to adopt a near body reduced domain with boundary conditions enforced to be compatible with a computationally cheaper three-dimensional RANS simulation. In such an approach it is desirable to enforce a consistent pressure distribution which is not typically the case when using the standard Riemann inflow boundary conditions. We therefore revisit the Riemann problem adopted in many DG based high fidelity formulations.Through analysis of the one-dimensional linearized Euler equations it is demonstrated that maintaining entropy compatibility with the RANS simulation is important for a stable solution. It is also necessary to maintain the invariant for the Riemann outflow boundary condition in a subsonic flow leaving one condition that can be imposed at the inflow boundary. Therefore the entropy-pressure enforcement is the only stable boundary condition to enforce a known pressure distribution. We further demonstrate that all the entropy compatible inflow Riemann boundary conditions are stable providing the invariant compatible Riemann outflow boundary condition is also respected.Although the entropy-pressure compatible Riemann inflow boundary condition is stable from the one-dimensional analysis, two-dimensional tests highlight divergence in the inviscid problem and neutrally stable wiggles in the velocity fields in viscous simulations around the stagnation point. A two-dimensional analysis about a non-uniform baseflow assumption provides insight into this stability issue (ill-posedness) and motivates the use of a mix of inflow boundary conditions in this region of the flow.As a validation we apply the proposed boundary conditions to a reduced domain of a wing section normal to the leading-edge of the CRM-NLF model taken out of a full three-dimensional RANS simulation at Mach 0.86 and a Reynolds number of 8.5 million. The results show that the entropy-pressure compatible Riemann inflow boundary condition leads to a good agreement in pressure distribution.

Structural response validation of composite cylindrical pressure vessels using FEA

Cylindrical pressure vessels constructed using filament winding technique are a good example of the advantages that fibre-reinforced composite materials offer over common structural materials on a specific/unit weight basis. The high specific properties of composite materials over metals can reduce the weight of pressure vessels with a high potential for applications in submarines and ROV/AUV. An innovative method for the optimisation of composite cylindrical structures is through simulation of the pressure vessel response using as parameterised finite element model. In this paper the effect of boundary conditions has been analysed for a cylindrical pressure vessel of carbon-epoxy composite material subjected to internal pressure. For the said study, a parametric Finite Element model using an 8 noded layered solid brick element has been created in the finite element analysis software ANSYS using its Parametric Design Language features. The elasticity solution for a single layer circular tube has also been presented in reference to the works of Herakovich and Pindera towards validation of the numerical model. Pressure vessel finite element models, with different boundary conditions have been used to study convergence in comparison to the exact solution. A comparison of the through thickness distribution of stresses from different finite element cylindrical models in ANSYS against the exact solution for a composite tube under internal pressure have been presented for the validation of the numerical model and proposed boundary conditions. It has been demonstrated that only one element in circumferential direction using displacement coupling conditions at the boundary is sufficient, which would significantly enhance the computational efficiency of a structural analysis and make these models computationally efficient even for a non-linear analysis with axi-symmetric loads for both static and dynamic cases.

Phase shift migration with absorbing boundary condition for full-matrix imaging heterogenous medium with high quality

Ultrasonic imaging with phased array has been widely employed for nondestructive testing in various fields. Phase shift migration (PSM) is a significant imaging method and shows great advantages for multilayer structures. However, the artifact reflections at the edges of the calculation region emerge in the wavefield reconstruction process, which greatly deteriorate the imaging quality of PSM. To overcome this problem, two absorbing boundary conditions for the wavefield extrapolation of PSM are proposed in this paper. The first absorbing boundary condition renders elements in the boundary regions lower weights in frequency-space domain. The second one follows a nonstationary phase shift scheme and filters the incident waves in the boundary regions in frequency-wavenumber domain. The implementing schemes of the absorbing boundary conditions for both homogenous and heterogenous medium are developed, and the full-matrix imaging method with absorbing boundary conditions is proposed. According to the simulation and experiment, the proposed boundary conditions have strong ability to suppress the background artifacts, and they can improve the signal-to-noise ratio (SNR) and resolution by 2 times when imaging heterogenous medium. Further experiments indicate that the boundary conditions are insensitive to the window functions, and a width of one-sixteenth the length of the scan line is recommended for the absorbing boundary conditions.

Study on seismic performance of suspended ceiling system with semi-free boundary condition

The failure of suspended ceiling system (SCS) has been one of the most widely reported seismic damage to non-structural components in buildings in recent years. In China, there are several types of SCSs applied in practice, among which the double-layer SCS with mineral wool boards is widely used in public buildings. It was found from the past earthquakes that the ceiling perimeter is one of the most vulnerable parts of SCS due to lack of reliable connection at the boundary. In this study a new semi-free boundary condition is proposed to improve the seismic performance of SCS. The full-scale shaking table tests on this type of SCS installed on a steel platform are conducted. The working mechanism, failure patterns, damage evolution, and earthquake responses including acceleration, displacement, and strain responses are studied. Experimental results verify that the proposed boundary condition is able to protect the ceiling perimeter from damage. The failure of SCS is mainly caused by the high vulnerability of grid connections. The pounding at the perimeter of SCS affects the seismic performance of the SCS harmfully. Effective seismic measures should be developed to reduce the impact between the ceiling and surroundings. A simplified numerical model for SCS with semi-free boundary condition is developed using OpenSEES. The calculated acceleration and displacement responses agree well with the test results. Moreover, seismic design recommendations for the type of SCS are provided.

Design and analysis of equal-channel angular pressing of Al6061: a comparative study

ABSTRACT Equal channel angular pressing (ECAP) technique can perform bulk deformation with nanostructured microstructures in materials. In this study, three-dimensional (3D) finite element simulation and experimentations were performed on Al-alloy. Both simulation and experimental studies were conducted under same boundary condition, i.e. with different processing temperature. The results from both computational and experimental studies were analysed and validated with comparing the effect obtained on microstructure of ECAPed Al-6061. FEM analysis was carried out to study the effect of processing temperature on stress and load. The simulation results show the effect of compression forces exerted over sample after first, second, third till sixth pass, respectively, at both room and elevated temperatures. Microstructural analysis was performed over ECAPed samples in order to get the insights of material behaviour under proposed boundary conditions. The result shows the stress decreases with the increase in process temperature due to ductile behaviour of Al6061. There is a difference in experimental and simulation study for room temperature and elevated temperature of 30.78% and 30.53%, respectively. Microstructural analysis is conducted to draw the relationship between the simulation and experimental results obtained before and after the equal channel angular pressing operation performed on Al 6061 billet.

Integrable boundaries for the q-Hahn process

Taking inspiration from the harmonic process with reservoirs introduced by Frassek, Giardinà and Kurchan in (2020 J. Stat. Phys. 180 135–71), we propose integrable boundary conditions for its trigonometric deformation, which is known as the q-Hahn process. Following the formalism established by Mangazeev and Lu in (2019 Nucl. Phys. B 945 114665) using the stochastic R-matrix, we argue that the proposed boundary conditions can be derived from a transfer matrix constructed in the framework of Sklyanin’s extension of the quantum inverse scattering method and consequently preserve the integrable structure of the model. The approach avoids the explicit construction of the K-matrix.

Appraising reconsolidation theory and its empirical validation.

Re-exposure to elements of prior experiences can create opportunities for inducing amnesia for those events. The dominant theoretical framework posits that such re-exposure can result in memory destabilization, making the memory representation temporarily sensitive to disruption while it awaits reconsolidation. If true, such a mechanism that allows for memories to be permanently changed could have important implications for the treatment of several forms of psychopathology. However, there have been contradictory findings and elusive occurrences of replication failures within the "reconsolidation" field. Considering its potential relevance for clinical applications, the fact that this "hot" research area is being dominated by a single mechanistic theory, and the presence of unexplainable contradictory findings, we believe that it is both useful and timely to critically evaluate the reconsolidation framework. We discuss potential issues that may arise from how reconsolidation interference has typically been deducted from behavioral observations, and provide a principled assessment of reconsolidation theory that illustrates that the theory and its proposed boundary conditions are vaguely defined, which has made it close to impossible to refute reconsolidation theory. We advocate for caution, encouraging researchers not to blindly assume that a reconsolidation process must underlie their findings, and pointing out the risks of doing so. Finally, we suggest concrete theoretical and methodological advances that can promote a fruitful translation of reminder-dependent amnesia into clinical treatment.

Steady-state thermal model based on new dedicated boundary conditions – application in the simulation of laser powder bed fusion process

Analytical and numerical methods have been widely used to predict the melt pool morphology and temperature distribution of thermomechanical processes involving a moving heat source, such as welding or additive manufacturing. Compared to analytical methods (based on the Rosenthal equation), the finite element method (FEM) provides more realistic results because it allows the consideration of more physical phenomena involved in the laser powder bed fusion (LPBF) process. However, its computation time is significantly longer than that of the analytical methods. In this context, this study proposes a new FE thermal model based on a steady-state simulation and analytically inspired boundary conditions to predict the melt pool morphology and temperature distribution. This proposed model possibly considers temperature-dependent material properties, Gaussian distribution of heat source, convective and radiative heat losses, powder-compact transition, enthalpy due to solid-liquid transition, and effect of heat convection in the melt pool, while allowing fast and accurate predictions of the melt pool size and steady-state temperature distribution. Single-track LPBF simulations were carried out for two most used materials (AlSi10Mg and Inconel 718). The melt pool sizes simulated by the proposed model are compared to those of a transient model and experimental results (melt pool morphology), and a relative error of less than 5% was observed for all the numerical and experimental validation tests. Furthermore, it is shown that the proposed boundary conditions allow accurate prediction of the steady temperature distribution, even with a short geometry in the source moving direction, which drastically reduces the computational cost and greatly facilitate the utilization of steady-state model.

Anisotropic slip boundary condition for three-dimensional lattice Boltzmann simulations of liquid microflows

To explore the anisotropic slip on hydrophobic surfaces, a new anisotropic slip boundary condition is proposed for three-dimensional simulations of liquid microflows using the lattice Boltzmann method with adjustable streamwise/spanwise slip length. The proposed boundary condition is derived based on the moment method, which is no longer limited to the assumption of the unidirectional steady flow. Numerical tests validated the effectiveness of the proposed method. Compared with the bounce-back and specular reflection scheme, the proposed method is more accurate and stable for capturing velocity profiles. The proposed method was applied to explore the effects of anisotropic slip on three-dimensional micro-lid-driven cavity flow. The numerical simulation results showed that the anisotropic slip has a greater influence on the flow than the pure streamwise/spanwise slip, and the streamwise slip plays a more important role in influencing the flow than the spanwise slip. The findings may hold significance for efficient development of microfluidic systems and micro-devices.

Evaluation of Nusselt Number for a Flow in a Parallel Plates Using Magnetohydrodynamics Second-Order Slip Model

Abstract This study is the examination of magnetohydrodinamics (MHD) flow and heat transfer between microparallel plates with constant wall heat flux using two different boundary condition coefficients, widely known in the literature, in a second-order slip flow and temperature jump boundary condition model. The stream of incompressible viscous liquid between rigid microtwin plates with electrical conductivity was assumed to be steady, laminar, hydrodynamically and thermally fully improved. The effects of dilution, viscous dissipation, and axial transmission, which are significant at the microscale, are also contained in the analysis. Momentum and energy equations are solved analytically under second-order slip velocity and temperature jump boundary conditions. Closed type answers for the temperature field and the fully developed Nusselt number are derived as a function of the magnetic parameter (MHD), Knudsen number and modified Brinkman number. Particular attention has been paid to the effects of the magnetic field on the second-order slip flow conditions. The use of the second-order boundary condition coefficients proposed in the study varies according to the proposed boundary conditions and tends to increase and decrease the heat transfer. Otherwise, MHD increases the heat transfer for both boundary conditions.

Multi-objective optimization of edge quality and surface integrity when wire electrical discharge machining of polycrystalline diamonds in cutting tool manufacture

This work presents an energy-saving approach to the single-pass wire electrical discharge machining (WEDM) of polycrystalline diamond with no degradation in edge geometry or surface integrity in cutting tool manufacture. The proposed boundary conditions and discharging wavelets enable the least number of pulse-off durations to effectively recover the electrical potential for the extended discharging action and the successively energy saving via a secondary MOSFET circuit. Secondly, the determined pulse-off durations could sufficiently improve the effectiveness of the Joule heat model which did not consider the extrinsic interference from the removed materials in the discharging gap. Full factorial design experiments were performed to validate the effects of the operating parameters on the material removal rate, surface roughness, cutting edge radius, and surface waviness in single-pass WEDM for the shaping of diamond cutting tools. Precision levels in the fitting of analytic models to experiment results were presented. Linear algebra was introduced to evaluate the selection of operating parameter combinations aimed at optimizing of observations with adjustable weightings. Thermal induced defects and alterations in the microstructures were reported and discussed. The proposed ready-to-use diamond cutting tools present a good balance between energy savings and appreciable outcomes.

When perspective-taking fails to inhibit customer aggression toward service employees

ABSTRACT The current research proposed boundary conditions for the inhibiting effect of perspective-taking on customer aggression toward service employees. In Study 1, we recruited participants (N = 241) from Prolific and conducted an online survey. The results showed that the inhibiting role of perspective-taking appeared among people with low perceived economic mobility (PEM) but disappeared among those with high PEM. In Study 2, we recruited people (N = 241) from MTurk and tested whether self-other referent priming influences the aforementioned effect by conducting an online experiment randomly assigning participants to either a self- or other-referent priming condition. The results revealed that perspective-taking inhibited customer aggression more among people with low (vs. high) PEM in the self-referent priming condition, but in the other-referent priming condition, the inhibiting effect appeared more among people with high (vs. low) PEM. The current research provides practical implications to help service firms to inhibit customer aggression.

Exact transparent boundary condition for the multidimensional Schrödinger equation in hyperrectangular computational domain.

In this paper an exact transparent boundary condition for the multidimensional Schrödinger equation in a hyperrectangular computational domain is proposed. It is derived as a generalization of exact transparent boundary conditions for two-dimensional (2D) and 3D equations reported before. An exact fully discrete (i.e., derived directly from the finite-difference scheme used) 1D transparent boundary condition is also proposed. Several numerical experiments using an improved unconditionally stable numerical implementation in the 3D space demonstrate propagation of Gaussian wave packets in free space and penetration of a particle through a 3D spherically asymmetrical barrier. The application of the multidimensional transparent boundary condition to the dynamics of the 2D system of two noninteracting particles is considered. The proposed boundary condition is simple, robust, and can be useful in the field of computational quantum mechanics, when an exact solution of the multidimensional Schrödinger equation (including multiparticle problems) is required.

A wall function approach in lattice Boltzmann method: algorithm and validation using turbulent channel flow

In the lattice Boltzmann method (LBM), the widely utilized wall boundary is the bounce-back (BB) boundary, corresponding to the no-slip boundary. The BB boundary prevents the LBM from capturing the accurate shear drag on the wall when addressing high Reynolds number flows using coarse-grid systems. This study proposed the ‘wall-function bounce (WFB)’ boundary, a general framework to incorporate wall functions into the LBM’s boundary condition, independent of specific information of discrete velocity schemes and collision functions. The WFB boundary calculates the appropriate shear drag on the wall using a wall function model, and thereafter just modifies partial diagonal distribution functions to reflect the shear drag. The Spalding’s law was utilized as the wall function in WFB. Simulations of turbulent channel flow at using the LBM-based large-eddy simulation were conducted to validate the effectiveness of the proposed boundary condition. The results indicate that the BB boundary underestimated the time-averaged velocity in the buffer layer at , and the averaged velocity in the entire domain at , when using coarse-grid systems. However, WFB obtained the proper shear drag on the wall and thus, compensated for the underestimation and agreed better with the experimental or direct numerical simulation data, especially at the 1st-layer grid. In addition, WFB improved the Reynolds normal stress in the near-wall region to some extent. The distributions of shear stress on the wall by WFB were analogous to those by the wall model function in the finite volume method.