Simple Boundary Conditions Research Articles

Study via the finite element method of the behavior of deck joints in a bridge composed of precast concrete segments

AbstractThere is a demand for research to better understand the structural performance of segmental bridge joints. In this context, the main objective of this work is to present a 3D numerical modeling using the Finite Element Method (FEM) to physically simulate the behavior of concrete joints in a segmental concrete bridge. The analysis was conducted using the design of a real bridge, and the structure studied was the main span of the New Guaíba Bridge, located in Porto Alegre, RS, Brazil. The modeling was implemented using ANSYS software, version 21.2. The simulation considers a complete model of the span to provide a more realistic determination of the joint openings and the stress distributions in the elements. It is crucial to emphasize that the results obtained from the model do not reproduce the observed behavior of the studied bridge. The analysis considered only one span with simplified boundary conditions and higher loads than those typically adopted in usual design procedures.

The catastrophic break‐up of the ureilite parent body: Modeling constraints on the debris size

AbstractThe ureilite parent body (UPB) was, in all likelihood, completely broken apart when hit by another object early in its history and reassembled into daughter bodies. We here present a study tailored to constrain the dimensions of the impact debris produced in the catastrophic disruption. Using a customized Python code to simulate the thermal evolution of the UPB fragments, we compared the FeO profiles modeled for different depths within those fragments with those measured across the reduction rims in olivines of 12 different ureilites (n = 37). Our profile data were fitted to the theoretical cooling profiles determined with a transient thermal model. The results are coherent and consistent with earlier studies and, despite using simplified boundary conditions (fragments described as ideal spheres and maximum radiation), our data provide valuable context on possible cooling pathways of the UPB debris. In detail, we found that the average depths within the given fragments from which our samples of ureilites originated were limited to 0.3–0.4 ± 0.1 m, with only few exceptions (e.g., one highly reduced sample lacked suitable reduction profiles suggesting either a depth of origin of >2 m or shielding of this fragment from rapid cooling, e.g., due to hovering in the center of a relatively dense cloud of debris). In addition, we calculated that the cooling from 1473 to 1100 K of the average fragment at the depth of our samples took no more than 3–4 days, suggesting that the reassembly of the ureilite daughter bodies could have been a very fast process.

Research on precise and standardized numerical simulation strategy for vehicle aerodynamics

PurposeThe purpose of this study is to propose a precise and standardized strategy for numerically simulating vehicle aerodynamics.Design/methodology/approachError sources in computational fluid dynamics were analyzed. Additionally, controllable experiential and discretization errors, which significantly influence the calculated results, are expounded upon. Considering the airflow mechanism around a vehicle, the computational efficiency and accuracy of each solution strategy were compared and analyzed through numerous computational cases. Finally, the most suitable numerical strategy, including the turbulence model, simplified vehicle model, calculation domain, boundary conditions, grids and discretization scheme, was identified. Two simplified vehicle models were introduced, and relevant wind tunnel tests were performed to validate the selected strategy.FindingsErrors in vehicle computational aerodynamics mainly stem from the unreasonable simplification of the vehicle model, calculation domain, definite solution conditions, grid strategy and discretization schemes. Using the proposed standardized numerical strategy, the simulated steady and transient aerodynamic characteristics agreed well with the experimental results.Originality/valueBuilding upon the modified Low-Reynolds Number k-e model and Scale Adaptive Simulation model, to the best of the authors’ knowledge, a precise and standardized numerical simulation strategy for vehicle aerodynamics is proposed for the first time, which can be integrated into vehicle research and design.

A two-direction cross-iteration solution for in-plane vibrations of thin-walled composite plates with a simplified explicit vibration mechanical model

For the fine and high reliability design of advanced precision engineering structures, this work presents an analytically cross-iteration method for in-plane vibrations analysis of thin-walled composite plates, the single-layer and laminated structures both involved. The governing equations and corresponding boundary conditions are derived adopting Rayleigh’s principle, in which the governing partial differential equations are transferred into ordinary differential equations. The most important advantage of this method lies in the fact that the explicit eigenvalue equations and mode functions are obtained with only a series of four-by-four matrices by simplifying boundary conditions in the two-direction cross-iteration procedures. Accuracy of the present method is verified by comparison with the previous studies and the finite element method in natural characteristics solutions, and convergence analysis on the single-layer orthotropic plates and composite laminates reveals the high efficiency and stability. Finally, the effects of boundary conditions, ply orientation angles, stacking sequences, aspect ratios and stiffness ratios on the in-plane natural characteristics are investigated. The extensive results presented in this work for the first time can be taken as the benchmarks data compared with other methods.

Accelerate the numerical convergence of incompressible flows: Novel preconditioned characteristic boundary conditions

For the first time, the locally power-law preconditioning method (LPLPM) is used to formulate the preconditioned characteristic boundary conditions (CBCs). Then, it is implemented to solve the numerical modeling of unsteady and steady flows from viscous to turbulent regimes. The compatibility equations and Riemann invariants are mathematically derived and then utilized to the incompressible flow solvers as suitable boundary conditions. This method discretizes time derivative and governing equations' space terms by applying the four-stage, fourth-order Runge–Kutta method, and a finite volume, respectively. The preconditioning matrix in the LPLPM is automatically derived by local velocity sensors through a power-law formulation. The baseline k−ω is applied as an appropriate turbulence model. Several test cases are conducted around airfoils of Office National d'Etudes et de Recherches Aerospatiales, NACA0012 (National Advisory Committee for Aeronautics), and S809 at varied angles of attack of 0–20 and Reynolds numbers of 500 to 5.25 × 106 to examine the effectiveness and accuracy of the LPLPM employing preconditioned CBCs. A sensitivity analysis is also performed to examine how numerical parameters affect the simulation. The results show that using preconditioned CBCs in conjunction with LPLPM at the artificial boundary is precise, reliable, and computationally efficient in simulating viscous/turbulent flows. Furthermore, it is also concluded that the present approach considerably improves the convergence speed contrasted to the simplified boundary conditions.

Asymptotic boundary condition for numerical modeling of wave packets in a supersonic boundary layer

Within the framework of linear stability theory, a simple non-stationary boundary condition is developed to simulate the far-field asymptotic behavior of linear wave packets propagating in a compressible boundary layer. This condition allows us to skip the linear stage of instability evolution in direct numerical simulations (DNS) of laminar-turbulent transition. It is also suggested to perform numerical simulations of the linear stage without recalculating the Jacobi matrix in the Newton iteration procedure. Robustness and efficiency of the both approaches are evaluated by computations of the first-mode wave packet propagating in the boundary layer on a flat plate at freestream Mach number 2. DNS of the nonlinear stage show that the wave packet quickly breaks down into a turbulent spot, if its hump amplitude is umax′≥0.1U∞. This confirms an amplitude nature of the transition onset criterion. The spectral analysis indicates that the breakdown mechanism differs from the oblique, fundamental or subharmonic resonance and requires additional studies.

An analytical transient coal permeability model: Sorption non-equilibrium index-based swelling switch

Long-term permeability experiments have indicated that sorption-induced swelling can switch from internal to bulk depending on the evolutive sorption status. However, this sorption swelling switch mechanism has not been considered in current analytical permeability models. This study introduces a normalized sorption non-equilibrium index (SNEI) to characterize the sorption status, quantify the dynamical variations of matrix swelling accumulation and internal swelling partition, and formulate the sorption swelling switch model. The incorporation of this index into the extended total effective stress concept leads to an analytical transient coal permeability model. Model results show that the sorption swelling switch itself results in the permeability switch under stress-constrained conditions, while the confined bulk swelling suppresses the permeability recovery to the continuous reduction under displacement-constrained conditions. Model verifications show that current experimental observations correspond to the early stages of the transient process, and they could be extended to the whole process with these models. This study demonstrates the importance of the sorption swelling switch in determining permeability evolution using simple boundary conditions. It provides new insights into experimentally revealing the sorption swelling switch in the future, and underscores the requirement of a rigorous model for complex coupled processes in large-scale coal seams.

Topanga: A kinetic ion plasma code for large-scale ionospheric simulations on magnetohydrodynamic timescales

Topanga is a kinetic ion code developed for simulating large-scale plasma phenomena in the Earth's ionosphere on magnetohydrodynamic timescales. It is a domain-decomposed parallel code that runs on high-performance computing platforms. Features of Topanga include spherical geometry for simplified boundary conditions and computational efficiency; a hybrid plasma model with inertia-less fluid electrons, kinetic ions, and an electric field specified via an Ohm's law; a Maxwell-FDTD (finite difference time domain) plasma model which retains the displacement current in Maxwell's equations and models electron currents in the ionosphere with a tensor conductivity; sponge-layer boundary conditions for absorption of electromagnetic and plasma waves incident on the domain boundaries; and a novel mixed-implicit algorithm for evolving the EM fields inside the Maxwell-FDTD region that is stable over many orders of magnitude in the electron–ion collision frequency. We verify the numerical methods used in Topanga on a pair of test problems. The first test involves modeling a three-dimensional collisionless shock using the hybrid set of equations. The second test involves modeling a spherical TEM mode in vacuum using the Maxwell-FDTD set of equations. Finally, we demonstrate how using the combined set of hybrid and Maxwell-FDTD equations to model the Starfish Prime high-altitude nuclear test recovers a “missing” EM signal on the ground that is not present when using only the hybrid set of equations. The magnitude of this signal in the simulation containing the Maxwell-FDTD region agrees well with the E3a portion of the magnetohydrodynamic electromagnetic pulse from Starfish Prime.

Semi-analytical dynamic modeling and fluid-structure interaction analysis of L-shaped pipeline

The traditional semi-analytic modeling is mainly aimed at the straight pipeline with simple boundary conditions. In contrast, the actual aero-engine pipeline needs to consider the effects of complex configuration, boundary and multiple clamps, so proposing an improved semi-analytic method to model an arbitrary fluid-conveying L-shaped pipeline is challenging. Based on the Hamiltonian principle, the differential equations of the L-shaped pipeline are derived. Then, the modal shape functions are determined under the conditions that the elastic support points and the joints of the straight pipeline and the curved pipeline meet the deformation coordination requirements. The proposed semi-analytical model is verified by comparing the natural frequencies and mode shapes obtained from the finite element method using ANSYS and experiment; the error of each order natural frequency is less than 5 %. In addition, the model is verified under various working conditions: different center angle and boundary conditions (clamp position and pipeline end constraints). The effects of the fluid velocity and pressure on the natural characteristics of the L-shaped pipeline are also analyzed. The results show that under the critical pressure of 60.51 MPa and the critical velocity of 247 m/s, the natural frequency decreases with the increase of fluid velocity and pressure. The proposed method can provide theoretical support for efficient and accurate modeling of complex spatial pipeline systems.

Temperature and shear-rate effects in two pure clays: Possible implications for clay landslides

Temperature fluctuations in landslide shear zones can originate from heat exchanges with deeper layers as well as with the atmosphere through the landslide body. Shallow landslides (depth <10 m) are especially subject to seasonal temperature oscillations and rapid climatic changes. Various hydro-mechanical properties of clayey soils are sensitive to changes in temperature. Few studies suggested that the residual shear strength may vary significantly even in temperature ranges typical of shallow layers in temperate and warm regions. Here, we verified the response of two pure clays (Ca-bentonite, kaolin) to shearing at temperatures up to ∼55 °C under various normal stresses (50–150 kPa) and shear rates (0.018–44.5 mm/min) by equipping a ring-shear device with a temperature-control system. Then, we performed experiments on an ideal slope to quantify the extent to which ground temperature can condition the stability of clay slopes, across the seasons and under prolonged warming. Considering the largest effects evaluated experimentally (change in residual shear strength by ±1.5 %/°C), we determined changes in global factor of safety by ∼20 % for rotational slides ∼6 m deep, solely attributable to seasonal heating-cooling. Warming of 5 °C over decades would change the stability condition by an additional ±7 %. Although these results were obtained under simplified geometry and boundary conditions, without considering changes in triggers, preconditions, and effects of other thermo-hydro-mechanical couplings, they provide an upper bound to the role of the temperature-dependence of the residual shear strength on the factor of safety. We argue that this role should not be neglected in slope stability and landslide hazard assessments in clay-rich soils, thus warranting in-depth experimental analyses and advanced modelling.

Density-Based Topological Optimization of 3D-Printed Casts for Fracture Treatment with Freefem Software

Abstract 3D printed plastic casts can be used for healing bone fractures. The main requirements for these cases are: they should be light, require little printing time, have good mechanical properties, and ensure proper skin ventilation. We present a density-based topology optimization algorithm for obtaining optimal cast shapes that fulfil these requirements. The algorithm uses a linear stress model and simplified boundary conditions to model the contact problems. The cast shapes were optimized against the influence of several sharp corners. The parametric studies showed that the mass of optimized casts was reduced by 20 %–25 % in comparison with original industrial casts, and the printing time is reduced by 1.4–1.7 h for the largest cast. A major model drawback is the use of 3D numerical volume to model the density distribution. The density distribution should be homogenized across the cast layer. The overhang problem should also be addressed. We also suggest that the cast producers collect more experimental data on the cast breakages for a better calibration of the numerical model.

Experimental and numerical investigation to elucidate the fluid flow through packed beds with structured particle packings

The present paper presents an experimental and numerical investigation of the dispersion of the gaseous jet flow and co-flow for the simple unit cell (SUC) and body-centred cubic (BCC) configuration of particles in packed beds. The experimental setup is built in such a way that suitable and simplified boundary conditions are imposed for the corresponding numerical framework, so the simulations can be done under very similar conditions as the experiments. Accordingly, a porous plate is used for the co-flow to achieve the uniform velocity and the fully developed flow is ensured for the jet flow. The SUC and BCC particle beds consist of 3D-printed spheres, and the non-isotropy near the walls is mostly eliminated by placing half-spheres at the channel walls. The flow velocities are analysed directly at the exit of the particle bed for both beds over 36 pores for the SUC configuration and 60 pores for the BCC configuration, for particle Reynolds numbers of 200, 300, and 400. Stereo particle image velocimetry is experimentally arranged in such a way that the velocities over the entire region at the exit of the packed bed are obtained instantaneously. The numerical method consists of a state-of-the-art immersed boundary method with adaptive mesh refinement. The paper presents the pore jet structure and velocity field exiting from each pore for the SUC and BCC packed particle beds. The numerical and experimental studies show a good agreement for the SUC configuration for all flow velocities. For the BCC configuration, some differences can be observed in the pore jet flow structure between the simulations and the experiments, but the general flow velocity distribution shows a good overall agreement. The axial velocity is generally higher for the pores located near the centre of the packed bed than for the pores near the wall. In addition, the axial velocities are observed to increase near the peripheral pores of the packed bed. This behaviour is predominant for the BCC configuration as compared to the SUC configuration. The velocities near the peripheral pores can become even higher than those at the central pores for the BCC configuration. It is shown that both the experiments as well as the simulations can be used to study the complex fluid structures inside a packed bed reactor.

Analytical model for organic contaminant transport in a cut-off wall and aquifer dual-domain system considering barrier arrangements

This paper presents an analytical study of organic contaminants transport in a cut-off wall and aquifer dual-domain system, considering the effects of the inlet boundary conditions and cut-off structural arrangements. The comprehensive sensitivity analysis of parameters focusing on the breakthrough time, attenuation time and cumulative concentration are presented using the Monte Carlo simulation and Sobol global method. The simplified constant inlet boundary condition can lead to an excessively conservative prediction of the contaminant breakthrough compared to the ‘finite mass’ and ‘decaying source’ boundary conditions. The cut-off wall hydraulic performance can be enhanced by reducing the contaminant's head loss, shape factor, half-life and cut-off wall hydraulic conductivity while increasing the retardation factor. The contaminant's half-life can largely influence the maximum contaminant concentration, attenuation time and breakthrough time. For example, the maximum contaminant concentrations for T1/2 = 1.4 years and T1/2 = 100 years are 13 and 123 times greater than that for T1/2 = 0.1 year, respectively. The influence of the variation of shape factor on the breakthrough curve should be taken into consideration. Altering the structural arrangement of the cut-off wall to accommodate a smaller shape factor increases the contaminant breakthrough time. The proposed solution allows the analysis of a cut-off wall and aquifer system with different inlet boundary conditions and structural arrangements of the cut-off wall.

Frictional boundary condition for lattice Boltzmann modelling of dense granular flows

Hydrodynamic approaches that treat granular materials as a continuum via the homogenization of discrete flow properties have become viable options for efficient predictions of bulk flow behaviours. However, simplified boundary conditions in computational fluid dynamics are often adopted, which have difficulty in describing the complex stick–slip phenomenon at the boundaries. This paper extends the lattice Boltzmann method for granular flow simulations by incorporating a novel frictional boundary condition. The wall slip velocity is first calculated based on the shear rate limited by the Coulomb friction, followed by the reconstruction of unknown density distribution functions through a modified bounce-back scheme. Validation is performed against a unique plane Couette flow configuration, and the analytical solutions for the flow velocity profile and the wall slip velocity, as functions of the friction coefficient, are reproduced by the numerical model. The transition between no-slip and partial-slip regimes is captured well, but the convergence rate drops from second order to first order when slip occurs. The rheological parameters and the basal friction coefficient are calibrated further against the discrete element simulation of a square granular column collapsing over a horizontal bottom plane. It is found that the calibrated continuum model can predict other granular column collapses with different initial aspect ratios and slope inclination angles, including the basal slip and the complex internal flow structures, without any further adjustments to the model parameters. This highlights the generalization ability of the numerical model, which has a wide range of application in granular flow predictions and controls.

Effects of the Seal Wire on the Nonlinear Dynamics of the Aircraft Engine Turbine Blades

Abstract Complicated systems made of multiple components are known to be difficult to model, considering their solutions can change dramatically even with the slightest variations in conditions. Aircraft engines contain such complicated systems, and some components in aircraft engines' turbines can cause significant changes in the system's overall response. Hence, this study is focused on investigating the behavior of a turbine blade of an aircraft engine and the effects of the contact between the blade and the seal wire on the dynamics of the blade-disk system. The investigation is performed via various numerical simulations in time and frequency domains. One sector of the bladed disk is modeled using the finite element method with the lock plate and the seal wire imposing cyclic symmetry boundary conditions in the static, modal, and frequency domain forced response analyses. In time domain analyses, the cyclic symmetry is replaced with simplified displacement restricting boundary conditions. The time domain analysis contains steady-state forced responses of the system. The results show that contact with the seal wire is not a major source of nonlinearity and damping. The contacts with the lock plate contribute more to the vibration damping than the seal wire. However, compared to the contacts at the root of the blade, both components remain less significant with regard to frictional damping and nonlinearity.

Investigating hygrothermal bending behavior of FG nanobeams via local/nonlocal stress gradient theory of elasticity with general boundary conditions

The bending response of functionally graded (FG) nanobeams under hygrothermal loading was investigated to emphasize the different scenarios that arise when using simplified and original boundary conditions. The governing equations were derived by using the principle of virtual work on the basis of the local/nonlocal stress gradient theory of elasticity. A Wolfram language code in Mathematica was written by the authors to develop a numerical investigation for different values of the material gradient index, the gradient length parameter, the nonlocal parameter, and considering two distinct types of thermal loading, that is, uniform temperature rise and heat conduction across the thickness of FG nanobeam cross-section.

Анализ процессов теплообмена на поверхности надземного трубопровода с теплоизоляцией

Purpose: Transport infrastructure facilities include a variety of water supply systems. In the conditions of negative ambient temperatures, there is a risk of freezing and destruction of water pipelines. In mathematical modeling of the operation of aboveground pipelines, the correct description of the heat exchange process between the outer wall of the pipeline and the surrounding atmosphere is of great importance. The boundary condition corresponding to this process traditionally includes a heat transfer coefficient depending on a number of unpredictable parameters (wind speed and direction, atmospheric pressure, air humidity). The purpose of this work is to carry out a comparative analysis of the role of free and forced convective heat exchange and to justify the possibility of setting a boundary condition that depends only on the outside air temperature. Methods: To solve this problem, the work uses numerical analysis of similarity criteria for the heat exchange process under conditions typical for the operation of an above-ground pipeline with thermal insulation. The justification of the boundary condition on the external surface of the pipeline is based on the law of energy conservation. Results: The values of the parameters of the problem are determined, in which free or forced convective heat exchange prevails. It has been shown that forced convection prevails in conditions typical for the operation of above-ground water pipelines. Under these conditions, the difference between the temperature of the external surface of the insulated pipeline and the surrounding atmosphere is small. It has been shown that in this case, it is advisable to use the equality of atmospheric air temperatures and pipeline surface temperatures as a boundary condition. Practical significance: Understanding the mechanisms of heat exchange makes it possible to create an adequate model of the operation of pipelines in conditions of negative temperatures. Setting a more accurate and simple boundary condition on the surface of the pipeline simplifies the task of mathematical modeling. The results obtained in this article can be used in mathematical modeling of any pipelines with thermal insulation.

Finite Difference Method for Solving the Two-Dimensional Laplace Equation in Curvilinear Coordinates

Abstract This paper presents a numerical method for solving the two-dimensional Laplace equation in curvilinear coordinates using a finite difference scheme. Laplace equation is a differential equation used to describe various physical phenomena studied within different branches of engineering. The two-dimensional Laplace equation has analytic solutions only for simple shaped domains and simple boundary conditions (first and second kind). Even so, the results are usually complicated to interpret and use. The present paper proposes a method to solve the equation for domains bounded by complex inner and outer curves. The boundary curves are defined by a set of points from which the equations of curves are approximated by using Fourier series. The domain is generated by blending the two curves using a blending function. The results are a set of continuous parametric equations which are defining the domain in angle and radius variables. Following a method presented in the literature, the Laplace equation is transformed from Cartesian coordinates to curvilinear coordinates, as the Fourier series is easily differentiable. Next, the new Laplace equation is approximated using the finite difference method and a MATLAB code is developed to solve the system of linear equations using successive over-relaxation method (SOR). The presented method is used to simulate steady two-dimensional heat conduction in a polygonal shape domain, with uniform and non-uniform Dirichlet boundary conditions. Results are analyzed in order to determine the model’s precision, speed and convergence criteria.

A complex solution on the dynamic response of sandwich graphene‐reinforced aluminum‐based composite beams with copper face sheets under two moving constant loads on an elastic foundation

AbstractAn analytical solution was used to investigate the elastic response of a sandwich beam with a graphene‐reinforced aluminum‐based composite (GRAC) on an elastic foundation using copper as the face layer of the functionally graded composite beam and a simply supported boundary condition. Mantari's higher‐order shear deformation theory was utilized to derive the equations, which were solved in Laplace space and then converted into space–time using Laplace inversion. The exact response of the GRAC sandwich beam was obtained by considering the displacement at the mid‐span of the sandwich beam. Two moving loads with different speed ratios were applied at a single point, and the effect of various parameters, including the spring constant, the speed ratio, the percentage of graphene, the moving load speed, and the distribution pattern, was investigated. This study aimed to eliminate any overlap and improve the accuracy of the results. The exact solving method presented has not been reported in other articles so far. Additionally, due to the difficulty of solving mathematical equations, this method is only applicable to simple boundary conditions.

Dynamic characteristics of cracked simply supported bidirectional functionally graded Rayleigh beam

This paper investigates the dynamic behavior of cracked Rayleigh beams constructed from bidirectional functionally graded (BDFG) materials under simple boundary conditions. A torsional massless spring is employed to model the beam's open crack type. The vibration equations are obtained using Hamilton's principle. The graded beam material properties are varied throughout the thickness based on the power-law distribution and in the longitudinal direction using the exponential material distribution. To solve the dynamic equations, Galerkin's approach is employed. The paper evaluates the impacts of the axial index, gradient property index, beam modulus ratio, and crack parameters on the natural frequencies of the FG beam. The results indicate that the dimensionless natural frequencies of intact graded beams decrease with increased gradient index k. In contrast, they increase with a rise in the modulus ratio. Additionally, the results demonstrate that an increase in the crack depth ratio decreases dimensionless natural frequencies.