scholarly journals Bending of Rectangular Plates With Finite Deflections

1965 ◽  
Vol 32 (4) ◽  
pp. 821-825 ◽  
Author(s):  
Frances Bauer ◽  
Louis Bauer ◽  
William Becker ◽  
Edward L. Reiss
Keyword(s):  
Aspect Ratio ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Normal Pressure ◽  
Rectangular Plates ◽  
Membrane Stress ◽  
Wide Range ◽  
Loading Parameter ◽  
Range Of Values ◽  
Membrane Displacement

A previously developed iterative procedure is applied to obtain numerical solutions of the von Ka´rma´n equations for rectangular plates subjected to a uniform normal pressure. On the simply supported boundary, it is assumed that the normal membrane stress and the tangential membrane displacement vanish. Solutions are obtained for a wide range of values of the loading parameter and the aspect ratio. Boundary layers develop both as the loading parameter and the aspect ratio increase. The stresses and deflections are examined and compared with an “asymptotic” solution which can be valid only in the interiors of long plates. A comparison is also made with previously obtained approximate solutions.

Free Molecule Flow Through a Vacuum Seal

1970 ◽  
Vol 92 (3) ◽  
pp. 405-410
Author(s):  
H. S. Yu ◽  
E. M. Sparrow
Keyword(s):  
Mass Flow ◽  
Numerical Solutions ◽  
Rarefied Gas ◽  
Coupled System ◽  
Mass Fluxes ◽  
Wide Range ◽  
Flow Through ◽  
Molecule Flow ◽  
Range Of Values

An analysis is made of the rate of the mass flow through a vacuum seal separating two rarefied gas environments. The determination of the mass throughflow characteristics involves the formulation and solution of a coupled system of six integral equations. The formulation is performed using the methods of kinetic theory. Numerical solutions are carried out for a wide range of values of the seal geometrical parameter. Mass flow results evaluated from these solutions are presented graphically. In addition, representative distributions of the mass fluxes at the participating surfaces are given.

Analytical approximate solutions for two-dimensional viscous flow through expanding or contracting gaps with permeable walls

Open Physics ◽  
2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Saeed Dinarvand ◽  
Mohammad Rashidi ◽  
Ahmad Doosthoseini
Keyword(s):  
Viscous Flow ◽  
Numerical Solutions ◽  
Biological Fluids ◽  
Approximate Solutions ◽  
Normal Pressure ◽  
Rectangular Domain ◽  
Permeable Walls ◽  
Homotopy Analysis ◽  
Flow Through ◽  
Expanding Or Contracting Walls

AbstractIn this paper, the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions is solved analytically by using the homotopy analysis method (HAM). Graphical results are presented to investigate the influence of the nondimensional wall dilation rate α and permeation Reynolds number Re on the velocity, normal pressure distribution and wall shear stress. The obtained solutions, in comparison with the numerical solutions, demonstrate remarkable accuracy. The present problem for slowly expanding or contracting walls with weak permeability is a simple model for the transport of biological fluids through contracting or expanding vessels.

Evaluation of Stress Intensity Factor Interactions Between Adjacent Flaws With Large Aspect Ratios

2015 ◽  
Author(s):  
Kisaburo Azuma ◽  
Yinsheng Li ◽  
Kunio Hasegawa
Keyword(s):  
Stress Intensity ◽  
Aspect Ratio ◽  
Large Aspect Ratio ◽  
Finite Element Analyses ◽  
Intensity Factors ◽  
Membrane Stress ◽  
Combination Rules ◽  
Aspect Ratios ◽  
Wide Range ◽  
Factor Interactions

Multiple flaws detected during in-service inspections are evaluated in accordance with the flaw combination rules provided in the ASME B&PV Code Section XI. The rules treat adjacent two flaws as a single combined flaw if the distance between the two flaws is equal to or less than half of the flaw depth. That is, the combination rules are consisted of flaw depth basis. However, its applicability has not been clarified systematically to the flaws with large aspect ratio, the depth of which are greater than half its length. Interactions of stress intensity factors for multiple flaws under membrane stress were investigated using finite element analyses. The numerical results suggest that the flaw combination rules might be better to use flaw length basis, instead of flaw depth, over a wide range of the aspect ratio.

The Accuracy of Short Bearing Theory for Newtonian Lubricants

1986 ◽  
Vol 108 (1) ◽  
pp. 73-79 ◽  
Author(s):  
R. H. Buckholz ◽  
B. Hwang
Keyword(s):  
Aspect Ratio ◽  
Journal Bearing ◽  
Numerical Solutions ◽  
Load Capacity ◽  
Perturbation Expansion ◽  
Approximate Solutions ◽  
Matched Asymptotic Expansion ◽  
Eccentricity Ratio ◽  
Regular Perturbation ◽  
Slider Bearings

The accuracy of the short bearing approximation is analyzed in this discussion. The results apply to Newtonian lubricants, and they can also be extended to non-Newtonian power-law lubricants. Reynolds’ lubrication equation is first solved by applying a regular perturbation expansion in pressure to the π film journal bearing; after this, a matched asymptotic expansion is applied to linear slider bearings. Approximate solutions are then compared with numerical solutions, to estimate the accuracy of the short bearing approximation. Finally, the accuracy of fluid film pressures predicted via short bearing theory is shown to depend upon three factors: the bearing aspect ratio, eccentricity ratio, and the partial-arc extent. Ocvirk’s short bearing series approximation—for finite bearing aspect ratio—is shown to become singular in the limit as the eccentricity ratio approaches unity. The one term π film Ocvirk solution is shown to be a nonconservative approximation to the journal bearing load capacity. A method to extend the accuracy of the short bearing approximation for partial-arcs and slider bearings is then presented.

A stochastic operational matrix method for numerical solutions of multi-dimensional stochastic Itô–Volterra integral equations

2020 ◽  
Vol 28 (3) ◽  
pp. 209-216
Author(s):  
S. Singh ◽  
S. Saha Ray
Keyword(s):  
Integral Equations ◽  
Numerical Solutions ◽  
Operational Matrix ◽  
Approximate Solutions ◽  
Volterra Integral Equations ◽  
Numerical Examples ◽  
Operational Matrix Method ◽  
Block Pulse Functions ◽  
Stochastic Operational Matrix ◽  
Block Pulse Function

AbstractIn this article, hybrid Legendre block-pulse functions are implemented in determining the approximate solutions for multi-dimensional stochastic Itô–Volterra integral equations. The block-pulse function and the proposed scheme are used for deriving a methodology to obtain the stochastic operational matrix. Error and convergence analysis of the scheme is discussed. A brief discussion including numerical examples has been provided to justify the efficiency of the mentioned method.

scholarly journals High-resolution particle separation by inertial focusing in high aspect ratio curved microfluidics

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Javier Cruz ◽  
Klas Hjort
Keyword(s):  
High Resolution ◽  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Biological Fluids ◽  
Essential Feature ◽  
Particle Separation ◽  
Size Difference ◽  
Inertial Focusing ◽  
Complex Samples ◽  
Wide Range

AbstractThe ability to focus, separate and concentrate specific targets in a fluid is essential for the analysis of complex samples such as biological fluids, where a myriad of different particles may be present. Inertial focusing is a very promising technology for such tasks, and specially a recently presented variant, inertial focusing in High Aspect Ratio Curved systems (HARC systems), where the systems are easily engineered and focus the targets together in a stable position over a wide range of particle sizes and flow rates. However, although convenient for laser interrogation and concentration, by focusing all particles together, HARC systems lose an essential feature of inertial focusing: the possibility of particle separation by size. Within this work, we report that HARC systems not only do have the capacity to separate particles but can do so with extremely high resolution, which we demonstrate for particles with a size difference down to 80 nm. In addition to the concept for particle separation, a model considering the main flow, the secondary flow and a simplified expression for the lift force in HARC microchannels was developed and proven accurate for the prediction of the performance of the systems. The concept was also demonstrated experimentally with three different sub-micron particles (0.79, 0.92 and 1.0 µm in diameter) in silicon-glass microchannels, where the resolution in the separation could be modulated by the radius of the channel. With the capacity to focus sub-micron particles and to separate them with high resolution, we believe that inertial focusing in HARC systems is a technology with the potential to facilitate the analysis of complex fluid samples containing bioparticles like bacteria, viruses or eukaryotic organelles.

Heat transfer characteristics of nanofluids from a sinusoidal corrugated cylinder placed in a square cavity

2021 ◽  
pp. 095440622110272
Author(s):  
Salaika Parvin ◽  
Nepal Chandra Roy ◽  
Litan Kumar Saha ◽  
Sadia Siddiqa
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Heat Transfer Characteristics ◽  
Number Range ◽  
Transfer Characteristics ◽  
Wide Range

A numerical study is performed to investigate nanofluids' flow field and heat transfer characteristics between the domain bounded by a square and a wavy cylinder. The left and right walls of the cavity are at constant low temperature while its other adjacent walls are insulated. The convective phenomena take place due to the higher temperature of the inner corrugated surface. Super elliptic functions are used to transform the governing equations of the classical rectangular enclosure into a system of equations valid for concentric cylinders. The resulting equations are solved iteratively with the implicit finite difference method. Parametric results are presented in terms of streamlines, isotherms, local and average Nusselt numbers for a wide range of scaled parameters such as nanoparticles concentration, Rayleigh number, and aspect ratio. Several correlations have been deduced at the inner and outer surface of the cylinders for the average Nusselt number, which gives a good agreement when compared against the numerical results. The strength of the streamlines increases significantly due to an increase in the aspect ratio of the inner cylinder and the Rayleigh number. As the concentration of nanoparticles increases, the average Nusselt number at the internal and external cylinders becomes stronger. In addition, the average Nusselt number for the entire Rayleigh number range gets enhanced when plotted against the volume fraction of the nanofluid.

scholarly journals Entanglement entropy in cubic gravitational theories

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Elena Cáceres ◽  
Rodrigo Castillo Vásquez ◽  
Alejandro Vilar López
Keyword(s):  
Entanglement Entropy ◽  
Gravitational Theory ◽  
Riemann Tensor ◽  
Holographic Entanglement Entropy ◽  
Gravitational Theories ◽  
Entropy Functional ◽  
Wide Range ◽  
Splitting Problem ◽  
Range Of Values

Abstract We derive the holographic entanglement entropy functional for a generic gravitational theory whose action contains terms up to cubic order in the Riemann tensor, and in any dimension. This is the simplest case for which the so-called splitting problem manifests itself, and we explicitly show that the two common splittings present in the literature — minimal and non-minimal — produce different functionals. We apply our results to the particular examples of a boundary disk and a boundary strip in a state dual to 4- dimensional Poincaré AdS in Einsteinian Cubic Gravity, obtaining the bulk entanglement surface for both functionals and finding that causal wedge inclusion is respected for both splittings and a wide range of values of the cubic coupling.

scholarly journals Strength Analysis of Alternative Airframe Layouts of Regional Aircraft on the Basis of Automated Parametrical Models

Aerospace ◽  
2021 ◽  
Vol 8 (3) ◽  
pp. 80
Author(s):  
Dmitry V. Vedernikov ◽  
Alexander N. Shanygin ◽  
Yury S. Mirgorodsky ◽  
Mikhail D. Levchenkov
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
High Performance ◽  
Strength Analysis ◽  
Labor Input ◽  
Aerodynamic Loading ◽  
Aspect Ratios ◽  
Wide Range ◽  
Parametrical Design

This publication presents the results of complex parametrical strength investigations of typical wings for regional aircrafts obtained by means of the new version of the four-level algorithm (FLA) with the modified module responsible for the analysis of aerodynamic loading. This version of FLA, as well as a base one, is focused on significant decreasing time and labor input of a complex strength analysis of airframes by using simultaneously different principles of decomposition. The base version includes four-level decomposition of airframe and decomposition of strength tasks. The new one realizes additional decomposition of alternative variants of load cases during the process of determination of critical load cases. Such an algorithm is very suitable for strength analysis and designing airframes of regional aircrafts having a wide range of aerodynamic concepts. Results of validation of the new version of FLA for a high-aspect-ratio wing obtained in this work confirmed high performance of the algorithm in decreasing time and labor input of strength analysis of airframes at the preliminary stages of designing. During parametrical design investigation, some interesting results for strut-braced wings having high aspect ratios were obtained.

scholarly journals A Comparison of Some Methods of Deriving the Instantaneous Unit Hydrograph

1985 ◽  
Vol 16 (1) ◽  
pp. 1-10 ◽  
Author(s):  
V. P. Singh ◽  
C. Corradini ◽  
F. Melone
Keyword(s):  
Peak Flow ◽  
Central Italy ◽  
Effective Rainfall ◽  
Unit Hydrograph ◽  
Time To Peak ◽  
Wide Range ◽  
Instantaneous Unit Hydrograph ◽  
Similar Accuracy ◽  
Two Parameters ◽  
Range Of Values

The geomorphological instantaneous unit hydrograph (IUH) proposed by Gupta et al. (1980) was compared with the IUH derived by commonly used time-area and Nash methods. This comparison was performed by analyzing the effective rainfall-direct runoff relationship for four large basins in Central Italy ranging in area from 934 to 4,147 km2. The Nash method was found to be the most accurate of the three methods. The geomorphological method, with only one parameter estimated in advance from the observed data, was found to be little less accurate than the Nash method which has two parameters determined from observations. Furthermore, if the geomorphological and Nash methods employed the same information represented by basin lag, then they produced similar accuracy provided the other Nash parameter, expressed by the product of peak flow and time to peak, was empirically assessed within a wide range of values. It was concluded that it was more appropriate to use the geomorphological method for ungaged basins and the Nash method for gaged basins.

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