Collapse by ponding of pneumatic elastic spherical caps under distributed loads

1983 ◽  
Vol 10 (4) ◽  
pp. 740-747 ◽  
Author(s):  
G. Ahmadi ◽  
P. G. Glockner
Keyword(s):  
Numerical Solutions ◽  
Graphical Form ◽  
Nonuniform Load ◽  
Spherical Caps ◽  
Load Intensity ◽  
Range Of Values ◽  
Central Load

The problem of collapse by ponding of air-supported elastic spherical caps subjected to a distributed axisymmetric central load is investigated. Cases of uniform and nonuniform load intensity are considered and the expressions for the critical intensities for the onset of collapse are derived. Numerical solutions are obtained for a range of values of the parameters and the results are presented in graphical form. The interpretation of the results in terms of some initial depressions filled with a ponding fluid is also discussed.

A Comparison of Five Methods of Calculating Aerodynamic Stagnation-Point Heat Transfer at Velocities of 25,000 to 40,000 fps

1963 ◽  
Vol 30 (3) ◽  
pp. 430-434 ◽  
Author(s):  
Stefan Schreier
Keyword(s):  
Heat Transfer ◽  
Stagnation Point ◽  
The Other ◽  
Graphical Form ◽  
Equilibrium Flow ◽  
Enthalpy Method ◽  
Range Of Values

Five methods of calculating aerodynamic stagnation-point heat transfer at velocities of 25,000 to 40,000 fps are considered. Three of these methods are simple extrapolations of techniques previously developed for calculations below 25,000 fps. The other two are methods especially developed for velocities above 25,000 fps. The five methods are: The method of Fay and Riddell [1]; the method of Scala [2]; the reference enthalpy method [3]; the method of Adams [4]; and the method of Cohen [5]. Methods [4] and [5] are the methods developed for the higher velocities. The results are presented in graphical form. It is found that the extrapolation of the reference enthalpy method and the correlation formula of Fay and Riddell yield results so close to those of Cohen that, in view of the uncertainties involved in the latter method, using the former two methods over the range of values considered in the present paper yields results at least as satisfactory as those of Cohen for equilibrium flow. Furthermore it is found that extrapolation of the formula of Fay and Riddell for frozen flow yields results sufficiently close to those obtained by the method of Adams that, in view of the uncertainties of the latter method, the advantage of its use over the former in the range of values under consideration is questionable.

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.

Cavity flows driven by buoyancy and shear

1972 ◽  
Vol 51 (2) ◽  
pp. 221-231 ◽  
Author(s):  
K. Torrance ◽  
R. Davis ◽  
K. Eike ◽  
P. Gill ◽  
D. Gutman ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Temperature Fields ◽  
Navier Stokes ◽  
Cavity Flows ◽  
Navier Stokes Equations ◽  
Moving Wall ◽  
Aspect Ratios ◽  
Range Of Values

Fluid motion driven by the combined effects of a moving wall and natura convection is examined for rectangular cavities with heightlwidth ratios of ½, 1 and 2. The Reynolds number and Prandtl number are held fixed at Re = 100 and Pr = 1; the Grashof number is varied over the range of values Gr = 0, ±104, ±106. Flow and temperature fields obtained from numerical solutions of the Navier-Stokes equations reveal a marked influence of buoyancy for the larger aspect ratios when Gr = ±106 and the dominance of buoyancy for all aspect ratios when Gr = ± 106. Results are compared with earlier work where possible and some observations are offered on the convergence of the numerical solutions.

The Effects of Fluid Inertia Forces in Parallel Circular Squeeze Film Bearings Lubricated With Pseudo-Plastic Fluids

1986 ◽  
Vol 108 (2) ◽  
pp. 282-287 ◽  
Author(s):  
Hiromu Hashimoto ◽  
Sanae Wada
Keyword(s):  
Numerical Solutions ◽  
Momentum Equation ◽  
Mean Value ◽  
Squeeze Film ◽  
Graphical Form ◽  
Shear Strain Rate ◽  
Fluid Inertia ◽  
Film Pressure ◽  
Inertia Forces ◽  
Plastic Fluids

The effects of fluid inertia forces in parallel circular squeeze film bearings lubricated with pseudo-plastic fluids are examined theoretically. In the derivation of lubrication equation, the cubic equation obtained from the empirical flow curves for pseudo-plastic fluids is used as the relation between shear stress and shear strain rate, and the inertia term in the momentum equation is approximated by the mean value averaged across the film thickness. Numerical solutions for the film pressure of circular bearings lubricated with Newtonian and pseudo-plastic fluids under the sinusoidal squeeze motion are presented in graphical form and the effects of inertia forces on the film pressure are determined.

Hiemenz flow of a micropolar viscoelastic fluid in hydromagnetics

2005 ◽  
Vol 83 (10) ◽  
pp. 1007-1017 ◽  
Author(s):  
S MM El-Kabeir
Keyword(s):  
Numerical Solutions ◽  
Transverse Magnetic ◽  
Shooting Technique ◽  
Electrically Conducting ◽  
Boundary Layer Equations ◽  
Viscoelastic Parameters ◽  
Governing System ◽  
Hiemenz Flow ◽  
Range Of Values ◽  
Numerical Integration Procedure

Boundary-layer equations are solved for the hydromagnetic problem of two-dimensional Hiemenz flow, for a micropolar, viscoelastic, incompressible, viscous, electrically conducting fluid, impinging perpendicularly onto a plane in the presence of a transverse magnetic field. The governing system of equations is first transformed into a dimensionless form. The resulting equations then are solved by using the Runge–Kutta numerical integration procedure in conjunction with shooting technique. Numerical solutions are presented for the governing momentum and angular-momentum equations. The proposed approximate solution, although simple, is nevertheless sufficiently accurate for the entire investigated range of values of the Hartman number. The effect of micropolar and viscoelastic parameters on Hiemenz flow in hydromagnetics is discussed.PACS No.: 46.35

The Five-Point Loading Shear Stiffness Test

1962 ◽  
Vol 66 (621) ◽  
pp. 591-591 ◽  
Author(s):  
H. B. Howard
Keyword(s):  
Shear Stiffness ◽  
Bending Stiffness ◽  
Loading Test ◽  
Central Deflection ◽  
Straight Line ◽  
Range Of Values ◽  
Central Load

The shear stiffness of a beam in bending is commonly determined by measuring the central deflection δ in a three-point loading test for a range of values of the span L under a constant central load. The value of bending stiffness, EI, and shear stiffness, GA, can then be obtained by plotting δ/L against L2 and drawing the best straight line through the points so obtained. The slope of this line for unit central load is then 1/48EI and its intercept on the δ/L axis is 1/4GA on the simple “Engineer's” theory.

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.

Qualitative theory for hyperbolic characteristic initial value problems

1983 ◽  
Vol 94 (1-2) ◽  
pp. 15-24 ◽  
Author(s):  
Kurt Kreith ◽  
Gordon Pagan
Keyword(s):  
Initial Value Problems ◽  
Numerical Solutions ◽  
Hyperbolic Equations ◽  
Nodal Line ◽  
Qualitative Theory ◽  
Graphical Form ◽  
Initial Value ◽  
New Criteria ◽  
Oscillation Properties

SynopsisCharacteristic initial value problems associated with hyperbolic equations of the form uxy + g(x, y)u = 0 are considered for (x, y)∈ℝ+× ℝ+. New criteria for the existence of a nodal line asymptotic to the axes are established, as are criteria for the existence of a zero beyond such a nodal line. Some numerical solutions are presented in graphical form and discussed relative to what is known about oscillation properties of such problems.

Green-Haar method for fractional partial differential equations

2019 ◽  
Vol 37 (4) ◽  
pp. 1473-1490
Author(s):  
Muhammad Ismail ◽  
Mujeeb ur Rehman ◽  
Umer Saeed
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Haar Wavelet ◽  
Graphical Form ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Wavelet Method ◽  
Content Type ◽  
Haar Wavelet Method

Purpose The purpose of this study is to obtain the numerical scheme of finding the numerical solutions of arbitrary order partial differential equations subject to the initial and boundary conditions. Design/methodology/approach The authors present a novel Green-Haar approach for the family of fractional partial differential equations. The method comprises a combination of Haar wavelet method with the Green function. To handle the nonlinear fractional partial differential equations the authors use Picard technique along with Green-Haar method. Findings The results for some numerical examples are documented in tabular and graphical form to elaborate on the efficiency and precision of the suggested method. The obtained results by proposed method are compared with the Haar wavelet method. The method is better than the conventional Haar wavelet method, for the tested problems, in terms of accuracy. Moreover, for the convergence of the proposed technique, inequality is derived in the context of error analysis. Practical implications The authors present numerical solutions for nonlinear Burger’s partial differential equations and two-term partial differential equations. Originality/value Engineers and applied scientists may use the present method for solving fractional models appearing in applications.

Atomic Imaging of Crystals using Large-Angle Electron Scattering in STEM

1990 ◽  
Vol 48 (1) ◽  
pp. 74-75
Author(s):  
D.E. Jesson ◽  
S. J. Pennycook
Keyword(s):  
Wave Function ◽  
Electron Scattering ◽  
Numerical Solutions ◽  
Large Angle ◽  
Real Space ◽  
High Angle ◽  
Analytical Treatment ◽  
Order Zero ◽  
Experimental Conditions ◽  
Ewald Sphere

It is well known that conventional atomic resolution electron microscopy is a coherent imaging process best interpreted in reciprocal space using contrast transfer function theory. This is because the equivalent real space interpretation involving a convolution between the exit face wave function and the instrumental response is difficult to visualize. Furthermore, the crystal wave function is not simply related to the projected crystal potential, except under a very restrictive set of experimental conditions, making image simulation an essential part of image interpretation. In this paper we present a different conceptual approach to the atomic imaging of crystals based on incoherent imaging theory. Using a real-space analysis of electron scattering to a high-angle annular detector, it is shown how the STEM imaging process can be partitioned into components parallel and perpendicular to the relevant low index zone-axis.It has become customary to describe STEM imaging using the analytical treatment developed by Cowley. However, the convenient assumption of a phase object (which neglects the curvature of the Ewald sphere) fails rapidly for large scattering angles, even in very thin crystals. Thus, to avoid unpredictive numerical solutions, it would seem more appropriate to apply pseudo-kinematic theory to the treatment of the weak high angle signal. Diffraction to medium order zero-layer reflections is most important compared with thermal diffuse scattering in very thin crystals (<5nm). The electron wave function ψ(R,z) at a depth z and transverse coordinate R due to a phase aberrated surface probe function P(R-RO) located at RO is then well described by the channeling approximation;

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