scholarly journals Accretion and ablation in deformable solids with an Eulerian description: examples using the method of characteristics

2021 ◽  
pp. 108128652110545
Author(s):  
S Kiana Naghibzadeh ◽  
Noel Walkington ◽  
Kaushik Dayal
Keyword(s):  
Method Of Characteristics ◽  
Deformation Gradient ◽  
Closed Form Solution ◽  
Biological Tissues ◽  
Explicit Construction ◽  
Form Solution ◽  
The Body ◽  
Reference Configuration ◽  
The Method Of Characteristics ◽  
Wide Range

Accretion and ablation, i.e., the addition and removal of mass at the surface, are important in a wide range of physical processes, including solidification, growth of biological tissues, environmental processes, and additive manufacturing. The description of accretion requires the addition of new continuum particles to the body, and is therefore challenging for standard continuum formulations for solids that require a reference configuration. Recent work has proposed an Eulerian approach to this problem, enabling side-stepping of the issue of constructing the reference configuration. However, this raises the complementary challenge of determining the stress response of the solid, which typically requires the deformation gradient that is not immediately available in the Eulerian formulation. To resolve this, the approach introduced the elastic deformation as an additional kinematic descriptor of the added material, and its evolution has been shown to be governed by a transport equation. In this work, the method of characteristics is applied to solve concrete simplified problems motivated by biomechanics and manufacturing. Specifically, (1) for a problem with both ablation and accretion in a fixed domain and (2) for a problem with a time-varying domain, the closed-form solution is obtained in the Eulerian framework using the method of characteristics without explicit construction of the reference configuration.

Seismic passive earth pressure coefficients using the method of characteristics

2002 ◽  
Vol 39 (2) ◽  
pp. 463-471 ◽  
Author(s):  
Jyant Kumar ◽  
Sridhar Chitikela
Keyword(s):  
Method Of Characteristics ◽  
Closed Form Solution ◽  
Earth Pressure ◽  
Retaining Walls ◽  
Form Solution ◽  
Unit Weight ◽  
Passive Earth Pressure ◽  
Pressure Coefficients ◽  
The Method Of Characteristics ◽  
Earth Pressures

The method of characteristics was used to generate passive earth pressure coefficients for an inclined wall retaining cohesionless backfill material in the presence of pseudostatic horizontal earthquake body forces. The variation of the passive earth pressure coefficients Kpq and Kpγ with changes in horizontal earthquake acceleration coefficient due to the components of soil unit weight and surcharge pressure, respectively, has been obtained; a closed-form solution for Kpq is also provided. The passive earth resistance has been found to decrease sharply with an increase in the magnitude of horizontal earthquake acceleration. The computed passive earth pressure coefficients were found to be the lowest when compared to all of the previous solutions available in the literature.Key words: earth pressures, earthquakes, method of characteristics, retaining walls, sands.

The attachment length in orificed hollow cathodes

2021 ◽  
Author(s):  
Christopher Wordingham ◽  
Pierre-Yves Taunay ◽  
Edgar Choueiri
Keyword(s):  
Electron Temperature ◽  
Plasma Density ◽  
Hollow Cathode ◽  
Computational Models ◽  
Closed Form Solution ◽  
Form Solution ◽  
Decay Length ◽  
Plasma Density Profile ◽  
Wide Range ◽  
Approximate Boundary Condition

Abstract A first-principles approach to obtain the attachment length within a hollow cathode with a constrictive orifice, and its scaling with internal cathode pressure, is developed. This parameter, defined herein as the plasma density decay length scale upstream of (away from) the cathode orifice, is critical because it controls the utilization of the hollow cathode insert and influences cathode life. A two-dimensional framework is developed from the ambipolar diffusion equation for the insert-region plasma. A closed-form solution for the plasma density is obtained using standard partial differential equation techniques by applying an approximate boundary condition at the cathode orifice plane. This approach also yields the attachment length and electron temperature without reliance on measured plasma property data or complex computational models. The predicted plasma density profile is validated against measurements from the NSTAR discharge cathode, and calculated electron temperatures and attachment lengths agree with published values. Nondimensionalization of the governing equations reveals that the solution depends almost exclusively on the neutral pressure-diameter product in the insert plasma region. Evaluation of analytical results over a wide range of input parameters yields scaling relations for the variation of the attachment length and electron temperature with the pressure-diameter product. For the range of orifice-to-insert diameter ratio studied, the influence of orifice size is shown to be small except through its effect on insert pressure, and the attachment length is shown to be proportional to the insert inner radius, suggesting high-pressure cathodes should be constructed with larger-diameter inserts.

On the solution near the critical frequency for an oscillating and translating body in or near a free surface

1993 ◽  
Vol 254 ◽  
pp. 251-266 ◽  
Author(s):  
Yuming Liu ◽  
Dick K. P. Yue
Keyword(s):  
Free Surface ◽  
Closed Form Solution ◽  
Geometric Interpretation ◽  
Form Solution ◽  
The Body ◽  
Geometric Condition ◽  
Sufficient Condition ◽  
Gravitational Acceleration ◽  
Submerged Body ◽  
Necessary And Sufficient

We consider a floating or submerged body in deep water translating parallel to the undisturbed free surface with a steady velocity U while undergoing small oscillations at frequency ω. It is known that for a single source, the solution becomes singular at the resonant frequency given by τ ≡ Uω/g=¼, where g is the gravitational acceleration. In this paper, we show that for a general body, a finite solution exists as τ → ¼ if and only if a certain geometric condition (which depends only on the frequency ω but not on U) is satisfied. For a submerged body, a necessary and sufficient condition is that the body must have non-zero volume. For a surface-piercing body, a sufficient condition is derived which has a geometric interpretation similar to that of John (1950). As an illustration, we provide an analytic (closed-form) solution for the case of a submerged circular cylinder oscillating near τ = ¼. Finally, we identify the underlying difficulties of existing approximate theories and numerical computations near τ = ¼, and offer a simple remedy for the latter.

scholarly journals A Stochastic Analysis of Hard Disk Drives

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Field Cady ◽  
Yi Zhuang ◽  
Mor Harchol-Balter
Keyword(s):  
Stochastic Analysis ◽  
Hard Disk Drives ◽  
Closed Form Solution ◽  
Hard Disk ◽  
Form Solution ◽  
Access Time ◽  
Analytical Technique ◽  
Wide Range ◽  
Average Access Time ◽  
Memory Request

We provide a stochastic analysis of hard disk performance, including a closed form solution for the average access time of a memory request. The model we use covers a wide range of types and applications of disks, and in particular it captures modern innovations like zone bit recording. The derivation is based on an analytical technique we call “shuffling”, which greatly simplifies the analysis relative to previous work and provides a simple, easy-to-use formula for the average access time. Our analysis can predict performance of single disks for a wide range of disk types and workloads. Furthermore, it can predict the performance benefits of several optimizations, including short stroking and mirroring, which are common in disk arrays.

scholarly journals On 3D Anticrack Problem of Thermoelectroelasticity

2018 ◽  
Vol 12 (2) ◽  
pp. 109-114 ◽  
Author(s):  
Andrzej Kaczyński
Keyword(s):  
Arbitrary Shape ◽  
Closed Form Solution ◽  
Transversely Isotropic ◽  
Static Problem ◽  
Form Solution ◽  
Boundary Integral ◽  
The Body ◽  
Circular Rigid Inclusion ◽  
Stress Discontinuity ◽  
Suitable Potential

Abstract A solution is presented for the static problem of thermoelectroelasticity involving a transversely isotropic space with a heat-insulated rigid sheet-like inclusion (anticrack) located in the isotropy plane. It is assumed that far from this defect the body is in a uniform heat flow perpendicular to the inclusion plane. Besides, considered is the case where the electric potential on the anticrack faces is equal to zero. Accurate results are obtained by constructing suitable potential solutions and reducing the thermoelectromechanical problem to its thermomechanical counterpart. The governing boundary integral equation for a planar anticrack of arbitrary shape is obtained in terms of a normal stress discontinuity. As an illustration, a closed-form solution is given and discussed for a circular rigid inclusion.

A Ternary Solution for Independent Acoustic Impedance and Speed of Sound Matching to Biological Tissues

1982 ◽  
Vol 4 (2) ◽  
pp. 163-170 ◽  
Author(s):  
Jonathan Ophir ◽  
Paul Jaeger
Keyword(s):  
Speed Of Sound ◽  
Acoustic Impedance ◽  
Soft Tissues ◽  
Sound Propagation ◽  
Biological Tissues ◽  
Liquid System ◽  
The Body ◽  
Acoustic Parameters ◽  
Wide Range

In applications requiring a liquid which is acoustically well matched to biological tissues, it is often difficult to find a material which is matched well in terms of both the acoustic impedance and speed of sound propagation in it; changing one parameter invariably affects the other. A three component liquid system is described, which allows independent adjustment of these two acoustic parameters over a wide range. This range encompasses the soft tissues of the body. Results of parameter measurements are presented in the form which allows simple determination of the mixture required to match any combination of acoustic impedance and speed of sound propagation over a given range.

A Hybrid Reactive Multiphasic Mixture with a Compressible Fluid Solvent

2021 ◽  
Author(s):  
Jay J. Shim ◽  
Gerard A. Ateshian
Keyword(s):  
Fluid Dynamics ◽  
Lagrange Multiplier ◽  
Deformation Gradient ◽  
Fluid Pressure ◽  
Volumetric Strain ◽  
Mixture Theory ◽  
Biological Tissues ◽  
Solid Matrix ◽  
State Function ◽  
Wide Range

Abstract Mixture theory is a general framework that has been used to model mixtures of solid, fluid, and solute constituents, leading to significant advances in modeling the mechanics of biological tissues and cells. Though versatile and applicable to a wide range of problems in biomechanics and biophysics, standard multiphasic mixture frameworks incorporate neither dynamics of viscous fluids nor fluid compressibility, both of which facilitate the finite element implementation of computational fluid dynamics solvers. This study formulates governing equations for reactive multiphasic mixtures where the interstitial fluid has a solvent which is viscous and compressible. This hybrid reactive multiphasic framework uses state variables that include the deformation gradient of the porous solid matrix, the volumetric strain and rate of deformation of the solvent, the solute concentrations, and the relative velocities between the various constituents. Unlike standard formulations which employ a Lagrange multiplier to model fluid pressure, this framework requires the formulation of a function of state for the pressure, which depends on solvent volumetric strain and solute concentrations. Under isothermal conditions the formulation shows that the solvent volumetric strain remains continuous across interfaces between hybrid multiphasic domains. Apart from the Lagrange multiplier-state function distinction for the fluid pressure, and the ability to accommodate viscous fluid dynamics, this hybrid multiphasic framework remains fully consistent with standard multiphasic formulations previously employed in biomechanics. With these additional features, the hybrid multiphasic mixture theory makes it possible to address a wider range of problems that are important in biomechanics and mechanobiology.

Analysis and Synthesis of Dynamic Response of a Flexibly Coupled Rotor Assembly

1997 ◽  
Author(s):  
Valdas Chaika
Keyword(s):  
Equations Of Motion ◽  
Excitation Frequency ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Response ◽  
Wide Range ◽  
Analysis And Synthesis ◽  
Coupling Parameters ◽  
Elastic Couplings ◽  
Rotor Assembly

Abstract Torsional vibration of two flexibly coupled reciprocating machines is investigated. The rotors of the machines are connected by elastic couplings of several types. The system is excited by a harmonic torque. The excitation frequency is proportional to the rotational speed which varies within a wide range. The motion of the system is described by nonlinear ordinary differential equations. These are linearized for the specific case of the rotor assembly design. Applying impedance functions, a closed-form solution of the equations of motion is derived. Three different cases of the system response are analyzed in the frequency domain. The passive vibration control of the rotor assembly using the centrifugal coupling is investigated. An analytical synthesis technique of the coupling parameters is devised.

Exact Analytical Hyperbolic Temperature Profile in a Three-Dimensional Media Under Pulse Surface Heat Flux

2015 ◽  
Vol 32 (3) ◽  
pp. 339-347 ◽  
Author(s):  
M. R. Talaee ◽  
V. Sarafrazi ◽  
S. Bakhshandeh
Keyword(s):  
Heat Flux ◽  
Numerical Solutions ◽  
Rectangular Cross Section ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Biological Tissues ◽  
Form Solution ◽  
Hyperbolic Heat Conduction ◽  
Duhamel Integral

AbstractIn this paper three-dimensional hyperbolic heat conduction equation in a cubic media with rectangular cross-section under a pulsed heat flux on the upper side has been solved analytically using the method of separation of variables and the Duhamel integral. The closed form solution of both Fourier and non-Fourier profiles are introduced with both modes of steady and pulsed fluxes. The results show the considerable difference between the Fourier and Non-Fourier temperature profiles. Then the answer procedure is used for modeling of interaction of a cubical tissue under a short laser pulse heating. The effects of pulse duration and laser intensity are studied analytically. Furthermore the results can be applied as a verification branch for other numerical solutions or laser treatments of biological tissues.

A novel method for defining the Greyhound talocrural joint axis of rotation for hinged transarticular external skeletal fixation

2013 ◽  
Vol 26 (04) ◽  
pp. 298-303 ◽  
Author(s):  
N. R. Hadley ◽  
A. M. Wallace ◽  
G. R. Colborne
Keyword(s):  
Articular Surface ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
The Body ◽  
Transverse Axis ◽  
Talocrural Joint ◽  
Distal Articular Surface ◽  
Intertarsal Joint ◽  
Centre Of Rotation

SummaryIn order to apply hinged transarticular external skeletal fixation for stabilization of the injured canine tarsal joint, knowledge of the three-dimensional (3D) location and orientation of the transverse axis is necessary. This method of immobilization may be used as a primary or adjunctive method of stabilisation for a large number of traumatic conditions. Using pin-mounted markers in the cadaveric Greyhound crus and talus, a closed-form solution of absolute orientation was used to identify, on radiographs, the lateral and medial locations of the transverse axis by tracking the 3D excursions of the markers during flexion and extension. A line was drawn across the dorsal aspect of the calcaneus from the most dorsal point on the distal articular surface (proximal intertarsal joint: PIJ) to the most dorsal point on its proximal articulation with the body of the talus, and the location of the centre of rotation was expressed in terms of the length of that line. In seven Greyhound tarsal joints, the medial end of the axis was located 73 ± 10% proximal to the PIJ and 11 ± 7% dorsal to the line. The lateral end was 73 ± 9% proximal to the PIJ and -2 ± 3% plantar to the line.

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