Sliding Boundary Conditions Research Articles

Establishing Standardization Guidelines For Finite-Element Optomechanical Simulations of Refractive Laser Surgeries: An Application to Photorefractive Keratectomy.

Computational models can help clinicians plan surgeries by accounting for factors such as mechanical imbalances or testing different surgical techniques beforehand. Different levels of modeling complexity are found in the literature, and it is still not clear what aspects should be included to obtain accurate results in finite-element (FE) corneal models. This work presents a methodology to narrow down minimal requirements of modeling features to report clinical data for a refractive intervention such as PRK. A pipeline to create FE models of a refractive surgery is presented: It tests different geometries, boundary conditions, loading, and mesh size on the optomechanical simulation output. The mechanical model for the corneal tissue accounts for the collagen fiber distribution in human corneas. Both mechanical and optical outcome are analyzed for the different models. Finally, the methodology is applied to five patient-specific models to ensure accuracy. To simulate the postsurgical corneal optomechanics, our results suggest that the most precise outcome is obtained with patient-specific models with a 100 µm mesh size, sliding boundary condition at the limbus, and intraocular pressure enforced as a distributed load. A methodology for laser surgery simulation has been developed that is able to reproduce the optical target of the laser intervention while also analyzing the mechanical outcome. The lack of standardization in modeling refractive interventions leads to different simulation strategies, making difficult to compare them against other publications. This work establishes the standardization guidelines to be followed when performing optomechanical simulations of refractive interventions.

The Spectral Decomposition of the Continuous and Discrete Linear Elasticity Operators with Sliding Boundary Conditions

The Spectral Decomposition of the Continuous and Discrete Linear Elasticity Operators with Sliding Boundary Conditions

Natural angular frequencies and eigenmodes of orthotropic rectangular parallelepiped with sliding boundary conditions for all faces

Natural angular frequencies and eigenmodes of orthotropic rectangular parallelepiped with sliding boundary conditions for all faces

On Powell-Eyring hybridity nanofluidic flow based Carboxy-Methyl-Cellulose (CMC) with solar thermal radiation: A quadratic regression estimation

Examining the thorough double-hybrid nanofluid mode Yamada-Ota and Xue provide a detailed description of the Powell-Eyring fluid model (PEFM) with the grouping of the base streaming Carboxy-Methyl-Cellulose (CMC) and doubly changed Carbon nanotubes CNTs (Single-walled carbon nanotubes (SWCNT), Multi-walled carbon nanotubes (MWCNT)). The coordinate systems are considered normal vectors, which are all regarded to be components of the spinning cone system in which this fluid is thought to movement. The PEFM move and thermal characteristics are governed by the sliding boundary conditions, the porous medium, and buoyancy. Similarity transformations are employed to derive a set of ordinary differential equations (ODEs) indicated by the accurate initial requirement. These ODEs are after that numerically solved using a particular technique called the Galerkin finite element method (GFEM). In addition to the thermal dispersion, this investigation consumes likewise shaped graphical consequences for the velocity in different 2D-directions. Along with the dimensionless Nusselt number, the outcomes of the skin friction constants are tabulated under the influence of pertinent regulating factors. According to the findings, radiation increases the current field while the Darcy-Forchheimer limitation increases the movement of the 2D-axis. The frictional coefficient is additionally increased together with the x- and y-components by the buoyancy ratio parameter. Additionally, by controlling elements approximating radioactivity, absorbency, and sliding boundary conditions, the dimensionless Nusselt number is reduced (velocity and temperature). Furthermore, regarding the frictional factor Cfx, after testing with 100 combinations of Powell-Eyring-II parameter (β2) and speed slippage constrain (γ1) in between the 20% and 110%, it was noted that those constrains tends to resist frictional factor.

On non-axisymmetrical buckling modes ofcircular plates under normal pressure

The paper presents the results of a study of the bifurcation of axisymmetric equilibrium forms of round plates under various conditions for fixing the outer edge. It is shown that for the case of sliding edge, the analytical, asymptotic and finite element approaches give close results. When the edge of the plate is hinged, the buckling to a non-axisymmetric state occurs at a much higher load and with the formation of a smaller number of waves than for a sliding boundary conditions. Difficulties in obtaining a numerical solution based on the analytical approach are apparently associated with the need for a more accurate description of the stress-strain subcritical state of the plate.

Causes of altered ventricular mechanics in hypertrophic cardiomyopathy: an in-silico study

BackgroundHypertrophic cardiomyopathy (HCM) is typically caused by mutations in sarcomeric genes leading to cardiomyocyte disarray, replacement fibrosis, impaired contractility, and elevated filling pressures. These varying tissue properties are associated with certain strain patterns that may allow to establish a diagnosis by means of non-invasive imaging without the necessity of harmful myocardial biopsies or contrast agent application. With a numerical study, we aim to answer: how the variability in each of these mechanisms contributes to altered mechanics of the left ventricle (LV) and if the deformation obtained in in-silico experiments is comparable to values reported from clinical measurements.MethodsWe conducted an in-silico sensitivity study on physiological and pathological mechanisms potentially underlying the clinical HCM phenotype. The deformation of the four-chamber heart models was simulated using a finite-element mechanical solver with a sliding boundary condition to mimic the tissue surrounding the heart. Furthermore, a closed-loop circulatory model delivered the pressure values acting on the endocardium. Deformation measures and mechanical behavior of the heart models were evaluated globally and regionally.ResultsHypertrophy of the LV affected the course of strain, strain rate, and wall thickening—the root-mean-squared difference of the wall thickening between control (mean thickness 10 mm) and hypertrophic geometries (17 mm) was >10%. A reduction of active force development by 40% led to less overall deformation: maximal radial strain reduced from 26 to 21%. A fivefold increase in tissue stiffness caused a more homogeneous distribution of the strain values among 17 heart segments. Fiber disarray led to minor changes in the circumferential and radial strain. A combination of pathological mechanisms led to reduced and slower deformation of the LV and halved the longitudinal shortening of the LA.ConclusionsThis study uses a computer model to determine the changes in LV deformation caused by pathological mechanisms that are presumed to underlay HCM. This knowledge can complement imaging-derived information to obtain a more accurate diagnosis of HCM.

Approximate Formulation of the Rigid Body Motions of an Elastic Rectangle Under Sliding Boundary Conditions

Abstract Low-frequency analysis of in-plane motion of an elastic rectangle subject to end loadings together with sliding boundary conditions is considered. A perturbation scheme is employed to analyze the dynamic response of the elastic rectangle revealing nonhomogeneous boundary-value problems for harmonic and biharmonic equations corresponding to leading and next order expansions, respectively. The solution of the biharmonic equation obtained by the separation of variables, a consequence of sliding boundary conditions, gives an asymptotic correction to the rigid body motion of the rectangle. The derived explicit approximate formulae are tested for different kinds of end loadings together with numerical examples demonstrating the comparison against the exact solutions.

Local 𝐶^{1,𝛽}-regularity at the boundary of two dimensional sliding almost minimal sets in ℝ³

In this paper, we will give a C 1 , β C^{1,\beta } -regularity result on the boundary for two dimensional sliding almost minimal sets in R 3 \mathbb {R}^3 . This effect may apply to the regularity of the soap films at the boundary, and may also lead to the existence of a solution to the Plateau problem with sliding boundary conditions proposed by Guy David in the case that the boundary is a 2-dimensional smooth submanifold.

Slip-bias extension test: A characterization tool for understanding and modeling the effect of clamping conditions in forming of woven fabrics

It has been well recognized that intra-ply shear and inter-ply slippage are the principal mechanisms allowing the woven fabrics to conform to doubly-curved geometries. The implication of boundary conditions on the forming response of this class of reinforcements is complex in nature, and time-consuming simulations are often needed during process optimization. This study aims to better understand the influence of sliding boundary conditions during forming process of woven fabrics, via a new well-controlled 2D characterization test (termed Slip-bias Extension test). Thereby, a modified shear stress formulation has been developed for the sake of faster 3D simulations, while accounting for the effect of frictional interactions between the fabric and blank holder at different shear angles, normal pressures, and under asymmetric gripping conditions. A key advantage of the new equivalent formulation is that the frictional contact between the ply and the tool at various shear angles and normal pressures does not need to be explicitly modeled in the simulations. The overall applicability of the proposed test and modeling framework is validated against a hemispherical forming of a plain carbon woven fabric. Results suggested an improved modeling accuracy under different forming configurations while reducing the run time by 20%.

An implicit boundary finite element method with extension to frictional sliding boundary conditions and elasto-plastic analyses

Implicit boundary methods, which enrich the interpolation structure with implicit weight functions, are straightforward methods for the enforcement of Dirichlet boundary conditions. In this article, we follow the implicit boundary method that uses approximate step functions (the step boundary method) developed by Kumar et al. and provide modifications that have several advantages. Roller boundary conditions have wide practical applications in engineering, however, the step boundary method for roller boundary conditions with inclinations has yet to be fully formulated through to the final linear system of equations. Thus we provide a complete derivation that leads to simplified stiffness matrices compared to the original approach, which can be implemented directly in fictitious domain finite element analysis. The approach is then extended, we believe for the first time, to the nonlinear cases of frictional boundary conditions and elasto-plastic material behaviour. The proposed formulation and procedures are validated on a number of example problems that test different aspects of the method.

Rectification of chiral active particles driven by transversal temperature difference

Rectification of chiral active particles driven by transversal temperature difference is investigated in a two-dimensional periodic channel. Chiral active particles can be rectified by transversal temperature difference. Transport behaviors are qualitatively different for different wall boundary conditions. For the sliding boundary condition, the direction of transport completely depends on the chirality of particles. The average velocity is a peaked function of angular velocity or temperature difference. The average velocity increases linearly with the self-propulsion speed, while it decreases monotonically with the increase in the packing fraction. For randomized boundary condition, the transport behaviors become complex. When self-propulsion speed is small, in contrast with the sliding boundary condition, particles move in the opposite direction. However, for large self-propulsion speed, current reversals can occur by continuously changing the system parameters (angular velocity, temperature difference, packing fraction, and width of the channel).

Diffusion of active particles in a complex environment: Role of surface scattering.

Experiments have shown that self-propelled particles can slide along the surface of a circular obstacle without becoming trapped over long times. Using simulations and theory, we study the impact of boundary conditions on the diffusive transport of active particles in an obstacle lattice. We find that particle dynamics with sliding boundary conditions result in large diffusivities even at high obstacle density, unlike classical specular reflection. These dynamics are very well described by a model based on run-and-tumble particles with microscopically derived reorientation functions arising from obstacle-induced tumbles. This model, however, fails to describe fine structure in the diffusivity at high obstacle density predicted by simulations for pusherlike collisions. Using a simple deterministic model, we show that this structure results from particles being guided by the lattice. Our results thus show how nonclassical surface scattering introduces a dependence on the lattice geometry at high densities. We discuss implications for the study of bacteria in complex environments.

Local Regularity Properties of Almost and Quasiminimal sets with a Sliding Boundary Condition

We study the boundary regularity of almost minimal and quasiminimal sets that satisfy sliding boundary conditions. The competitors of a set E are defined as F = φ1(E), where {φt} is a one parameter family of continuous mappings defined on E, and that preserve a given collection of boundary pieces. We generalize known interior regularity results, and in particular we show that the quasiminimal sets are locally Ahlfors-regular, rectifiable, and some times uniformly rectifiable, that our classes are stable under limits, and that for almost minimal sets the density of Hausdorff measure in balls centered on the boundary is almost nondecreasing. AMS classification. 49K99, 49Q20.

A circular inclusion with inhomogeneous sliding imperfect interface in harmonic materials

In the following study we rigorously analyze the problem of a circular inclusion with inhomogeneous imperfect sliding interface in finite deformation of harmonic materials. The work begins by defining the inhomogeneous sliding boundary conditions characterized by two interface parameters corresponding to the normal and tangential coordinate directions (with respect to the interface boundary curve), respectively. Then, through the process of analytic continuation the problem is eventually reduced to the determination of a single analytic function given by an ordinary differential equation with variable coefficients. A specific example is selected to illustrate the method. The effects of the circumferential variation of the interface parameter on the mean stress at the interface and the average mean stress in the inclusion are discussed.

Full-Annulus Simulation of Nonsynchronous Blade Vibration Excitation of an Axial Compressor

A high speed 1–1/2 axial compressor stage is simulated in this paper using an unsteady Reynolds-averaged Navier–Stokes (URANS) solver for a full-annulus configuration to capture its nonsynchronous vibration (NSV) flow excitation with rigid blades. A third-order weighted essentially nonoscillatory scheme for the inviscid flux and a second-order central differencing for the viscous terms are used to resolve nonlinear unsteady fluid flows. A fully conservative rotor/stator sliding boundary condition (BC) is employed with multiple-processor capability for rotor/stator sliding interface that accurately captures unsteady wake propagation between the rotor and stator blades while conserving fluxes across the rotor/stator interfaces. The predicted dominant frequencies using the blade tip response signals are not harmonic to the engine order, which is the NSV excitation. The simulation is based on a rotor blade with a 1.1% tip-chord clearance. Comparison with the previous 1/7 annulus simulations show that the time-shifted phase-lag BCs used in the 1/7 annulus are accurate. For most of the blades, the NSV excitation frequency is 6.2% lower than the measurement in the rig test, although some blades displayed slightly different NSV excitation frequencies. The simulation confirms that the NSV is a full annulus phenomenon. The instability of the circumferential traveling vortices in the vicinity of the rotor tip due to the strong interaction of incoming flow is the main cause of the NSV excitation. This instability is present in all blades of the rotor annulus. For circumferentially averaged parameters like total pressure ratio, NSV is observed to have an effect on the radial profile, particularly at radial locations above 70% span. A design with a lower loading of the upper blade span and a higher loading of the midblade spans is recommended to mitigate or remove NSV.

Strain Growth in a Finite-Length Cylindrical Shell Under Internal Pressure Pulse

Strain growth is a phenomenon observed in the elastic response of containment vessels subjected to internal blast loading. The local dynamic response of a containment vessel may become larger in a later stage than its response in the earlier stage. In order to understand the possible mechanisms of the strain growth phenomenon in a cylindrical vessel, dynamic elastic responses of a finite-length cylindrical shell with different boundary conditions subjected to internal pressure pulse are studied by finite-element simulation using LS-DYNA. It is found that the strain growth in a finite-length cylindrical shell with sliding–sliding boundary conditions is caused by nonlinear modal coupling. Strain growth in a finite-length cylindrical shell with free–free or simply supported boundary conditions is primarily caused by the linear modal superposition, possibly enhanced by the nonlinear modal coupling. The understanding of these strain growth mechanisms can guide the design of cylindrical containment vessels.

Evaluation of adaptive carbon fibre-reinforced door beams

An expandable, carbon fibre reinforced polymer (CFRP) door beam was designed, built and experimentally evaluated to improve side impact performance and reduce mass in passenger vehicles. Pressurisation and expansion of the beam was achieved using gas generator technology. The impact performance of the beam was evaluated by means of a sub system test method, mimicking vehicle-to-pole side impact. The sub system test method comprised a 3-point, bending load case, with a spring loaded sliding boundary condition at one end of the beam, while the other end was rigidly fixed. The beam was impacted by a 60 kg cylindrical impactor at 6 m/s. For the expanded and pressurised beam peak deflection was 193 mm. For the folded unpressurised beam peak deflection was 216 mm. To achieve the same impact performance with the expandable CFRP beam, as with a state of the art aluminium door beam, mass reductions seem plausible.

High-speed deformation of a high-strength coated thin plate

The punch with cone-shaped working part impact into aluminum alloy thin-walled structures is mathematical modelled applying thermo-mechanical coupling of the physical processes during their deformation. The nonlinear physical properties contain a nonlinear stress-strain rate dependence of temperature. To solve the contact problem the sliding boundary conditions (friction) on moving bodies introduced. Numerical simulation of impact process performed using the finite element method and the independent Lagrange-Euler approach for two variants of the thin-walled box structure. The solution of the dynamic viscous plastic contact problem allowed to determine and to design the stress-strain fields in the thin-walled box section. For comparison, the deformation process of the similar aluminum construction with an additional rib considered when the punch with the conical working part impact. Analysis of stress-strain state for two various types of structural geometries demonstrated that mounting the additional medial rib into its design let redistribute the stress fields and significantly reduce the plastic deformation area during the impact because of four fold increasing in its contact stiffness. Such modification of the structure rigidity may improve the strength properties of the entire composite security device applying changes only to its part.

Numerical ill-conditioning in evaluation of the dynamic response of structures with mode superposition method

Dynamic response of structures can be determined by mode superposition method which uses mode shape functions and modal coordinate functions. If the structure can be modelled with a uniform Euler–Bernoulli beam and a combination of clamped, free, pinned or sliding boundary conditions, analytical expressions for mode shape functions and modal coordinate functions are used. If analytical expressions for higher-order mode shapes or analytical expressions for the modal coordinate functions at high value of time are numerically evaluated, errors occur since the programming language cannot recognise the resulting value as a number, due to ill-conditioned analytical expressions. An analytical expression is ill-conditioned if small errors in the data may produce large errors in the solution. In this paper, we present a procedure for the exact numerical evaluation of analytical expressions for modal coordinates at high value of time while existing modified analytical expressions are used for exact calculation of higher-order mode shapes of the Euler–Bernoulli beam. The proposed procedure can be applied in the design of structure elements whose response is calculated with mode superposition method, e.g. for designing of metal frames for sawing machines in woodworking industry.

Three-dimensional quasi-conformal transformation optics through numerical optimization.

In this paper we demonstrate the possibility to achieve 3-dimensional quasi-conformal transformation optics through parametrization and numerical optimization without using sliding boundary conditions. The proposed technique, which uses a quasi-Newton method, is validated in two cylindrical waveguide bends as design examples. Our results indicate an arbitrarily small average anisotropy can be achieved in 3D transformation optics as the number of degrees of freedom provided by the parametrization was increased. The waveguide simulations confirm modal preservation when the residual anisotropy is neglected.