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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

A Study of Nucleate Boiling with Forced Convection in Microgravity

The ultimate objective of basic studies of flow boiling in microgravity is to improve the understanding of the processes involved, as manifested by the ability to predict its behavior. This is not yet the case for boiling heat transfer even in earth gravity, despite the considerable research activity over the past 30 years. The elements that constitute the nucleate boiling process - nucleation, growth, motion, and collapse of the vapor bubbles (if the bulk liquid is subcooled) - are common to both pool and flow boiling. It is well known that the imposition of bulk liquid motion affects the vapor bubble behavior relative to pool boiling, but does not appear to significantly influence the heat transfer. Indeed, it has been recommended in the past that empirical correlations or experimental data of pool boiling be used for design purposes with forced convection nucleate boiling. It is anticipated that such will most certainly not be possible for boiling in microgravity, based on observations made with pool boiling in microgravity. In earth gravity buoyancy will act to remove the vapor bubbles from the vicinity of the heater surface regardless of how much the imposed bulk velocity is reduced, depending, of course, on the geometry of the system. Vapor bubbles have been observed to dramatically increase in size in pool boiling in microgravity, and the heat flux at which dryout took place was reduced considerably below what is generally termed the critical heat flux (CHF) in earth gravity, depending on the bulk liquid subcooling. However, at heat flux levels below dryout, the nucleate pool boiling process was enhanced considerably over that in earth gravity, in spite of the large vapor bubbles formed in microgravity and perhaps as a consequence. These large vapor bubbles tended to remain in the vicinity of the heater surface, and the enhanced heat transfer appeared to be associated with the presence of what variously has been referred to as a liquid microlayer between the bubble and the heater surface. The enhancement of the boiling process with low velocities in earth gravity for those orientations producing the formation of a liquid macrolayer described above, accompanied by "sliding" vapor bubbles, has been demonstrated. The enhancement was presented as a function of orientation, subcooling, and heated length, while a criterion for the heat transfer for mixed natural/forced convection nucleate boiling was given previously. A major unknown in the prediction and application of flow boiling heat transfer in microgravity is the upper limit of the heat flux for the onset of dryout (or critical heat flux - CHF), for given conditions of fluid-heater surfaces, including geometry, system pressure and bulk liquid subcooling. It is clearly understood that the behavior in microgravity will be no different than on earth with sufficiently high flow velocities, and would require no space experimentation. However, the boundary at which this takes place is still an unknown. Previous results of CHF measurements were presented for low velocity flow boiling at various orientations in earth gravity as a function of flow velocity and bulk liquid subcooling, along with preliminary measurements of bubble residence times on a flat heater surface. This showed promise as a parameter to be used in modeling the CHF, both in earth gravity and in microgravity. The objective of the work here is to draw attention to and show results of current modeling efforts for the CHF, with low velocities in earth gravity at different orientations and subcoolings. Many geometrical possibilities for a heater surface exist in flowing boiling, with boiling on the inner and outer surfaces of tubes perhaps being the most common. If the vapor bubble residence time on and departure size from the heater surface bear a relationship to the CHF, as results to be given indicate, it is important that visualization of and access to vapor bubble growth be conveniently available for research purposes. In addition, it is desirable to reduce the number of variables as much as possible in a fundamental study. These considerations dictated the use of a flat heater surface, which is rectangular in shape, 1.91 cm by 3.81 cm (0.75 x 1.5 inches), consisting either of a 400 Angstrom thick semi-transparent gold film sputtered on a quartz substrate which serves simultaneously as a heater and a resistance thermometer, or a copper substrate of the same size. The heater substrate is a disc which can be rotated so that the heated length in the flow direction can be changed from 1.91 to 3.81 cm (0.75 to 1.5 inches). The fluid is R-113, and the velocities can be varied between 0.5 cm/s and 60 cm/s. For a sufficiently low velocity the CHF can be modeled reasonably well at various orientations by the correlation for pool boiling corrected for the influence of bulk liquid subcooling, multiplied by the square root of q, the angle relative to horizontal. This arises from equating buoyancy and drag forces in the inverted positions where the vapor bubbles are held against the heater surface as they slide. A distortion of the measurements relative to pool boiling occurs as the flow velocity increases. In modeling this effect at different levels of subcooling it appeared appropriate to estimate the volumetric rate of vapor generation, using measurements of bubble frequency (or residence time), void fraction and average bubble boundary layer thickness. These were determined with the use of a platinum hot wire probe 0.025 mm in diameter by 1.3 mm long, applying a constant current to distinguish between contact with liquid or vapor. Two-dimensional spatial variations are obtained with a special mechanism to resolve displacements in increments of 0.025 mm. From such measurements it was determined that the fraction of the surface heat transfer resulting in evaporation varies inversely with the subcooling correction factor for the CHF. The measured inverse bubble residence time is normalized relative to that predicted for an infinite horizontal flat plate at the CHF, and is correlated well with the CHF normalized relative to that for pool boiling, for various orientation angles and subcooling levels. This correspondence is then combined with a normalizing factor for the energy flux leaving the heater surface at the CHF and the computed bubble radius at departure, determined from the balance between the outward velocity of the interface due to evaporation and the buoyance induced velocity of the center of mass of the bubble. The product of the CHF and the corresponding residence time was determined to be a constant for all orientations at a given bulk flow velocity and liquid subcooling, and must be determined empirically for each velocity and subcooling at present. It then becomes possible to predict the CHF for the different orientations, velocities, and subcoolings. These are compared with normalized measurements of the CHF for velocities ranging from 4 cm/s to 55 cm/s, subcoolings from 2.8 to 22.2 K, over orientations angles of 360 degrees.

Merte, Herman, Jr.↗
NASA NTRS1974

A viscous/potential flow interaction analysis method for multi-element infinite swept wings, volume 1

An analysis method and computer program have been developed for the calculation of the viscosity dependent aerodynamic characteristics of multi-element infinite swept wings in incompressible flow. The wing configuration consisting at the most of a slat, a main element and double slotted flap is represented in the method by a large number of panels. The inviscid pressure distribution about a given configuration in the normal chord direction is determined using a two dimensional potential flow program employing a vortex lattice technique. The boundary layer development over each individual element of the high lift configuration is determined using either integral or finite difference boundary layer techniques. A source distribution is then determined as a function of the calculated boundary layer displacement thickness and pressure distributions. This source distribution is included in the second calculation of the potential flow about the configuration. Once the solution has converged (usually after 2-5 iterations between the potential flow and boundary layer calculations) lift, drag, and pitching moments can be determined as functions of Reynolds number.

Dvorak, F. A.↗
NASA NTRS1993

Modeling the reflectance of CO2 frost with new optical constants: Application to Martian south polar cap spectra

New measurements of the absorption coefficients of CO2 ice, in most of the spectral range 0.2 to 3.9 microns where absorption coefficients are below 1.5 per cm, have recently been made. Although these measurements are preliminary, they contain spectral detail not seen previously in the literature. Therefore, it is useful to combine these new data with older data from spectral regions of stronger absorption and reformulate models of the albedo or reflectance of CO2 frost. These models can then be adjusted in an attempt to match measurements of Martian polar deposits, such as the set of spectra returned by the IRS instrument on Mariner 7 (1969). The new absorption coefficients of CO2 ice were measured on several samples of 41-mm thickness at 150-155 K. A portion of the spectrum from 1.9 to 3.9 microns wavelength is shown in the form of imaginary coefficient of refraction ( = linear absorption x wavelength / 4 pi). The data above 3x10(exp -5) are obtained from, except for the absorption line at 3.32 micrometers, which is extrapolated in a way that is consistent with laboratory frost measurements, but the peak level is still highly uncertain. This new imagary coefficient, combined with the real coefficient, can be immediately applied to the models for hemispherical albedo, resulting in markedly different results from those in that study. The results for an infinite optical depth layer and solar incidence of 60 degrees are plotted for a range of mean particle radii from 0.03 to 3 mm.

Hansen, Gary B.↗
NASA NTRS1996

Sound Transmission through a Cylindrical Sandwich Shell with Honeycomb Core

Sound transmission through an infinite cylindrical sandwich shell is studied in the context of the transmission of airborne sound into aircraft interiors. The cylindrical shell is immersed in fluid media and excited by an oblique incident plane sound wave. The internal and external fluids are different and there is uniform airflow in the external fluid medium. An explicit expression of transmission loss is derived in terms of modal impedance of the fluids and the shell. The results show the effects of (a) the incident angles of the plane wave; (b) the flight conditions of Mach number and altitude of the aircraft; (c) the ratios between the core thickness and the total thickness of the shell; and (d) the structural loss factors on the transmission loss. Comparisons of the transmission loss are made among different shell constructions and different shell theories.

Tang, Yvette Y.↗
NASA NTRS1998

Radiation-Driven Warping: Nonisothermal Disks - 2

Recent work by Pringle and by Maloney, Begelman, & Pringle has shown that geometrically thin, optically thick, accretion disks are unstable to warping driven by radiation torque from the central source. This work was confined to isothermal (i.e., surface density Sigma varies as R(sup -3/2) disks. In this paper we generalize the study of radiation-driven warping to include general power-law surface density distributions, Sigma varies as R(sup -delta).We consider the range from Delta = 3/2 (the isothermal case) to Delta = -3/2, which corresponds to a radiation-pressure-supported disk; this spans the range of surface density distributions likely to be found in real astrophysical disks. In all cases there are an infinite number of zero-crossing solutions (i.e., solutions that cross the equator), which are the physically relevant modes if the outer boundary of the disk is required to lie in a specified plane. However, unlike the isothermal disk, which is the degenerate case, the frequency eigenvalues for Delta does not equal 3/2 are all distinct. In all cases the location of the zero moves outward from the steady state (pure precession) value with increasing growth rate; thus, there is a critical minimum size for unstable disks. Modes with zeros at smaller radii are damped. The critical radius and the steady state precession rate depend only weakly on Delta. An additional analytic solution has been found for Delta = 1. The case Delta = 1 divides the solutions into two qualitatively different regimes. For Delta greater than or equal to 1, the fastest growing modes have maximum warp amplitude, close to the disk outer edge, and the ratio of Beta(sub max) to the warp amplitude at the disk inner edge, Beta(sub o), is much greater than 1. For Delta less than 1, Beta(sub max/Beta(sub o) approximately equals 1, and the warp maximum steadily approaches the origin as Delta decreases. This implies that nonlinear effects must be important if the warp extends to the disk inner edge for Delta greater than or equal to 1, but for Delta less than 1 nonlinearity will be important only if the warp amplitude is large at the origin. Because of this qualitative difference in the shapes of the warps, the effects of shadowing of the central source by the warp will also be very different in the two regimes of Delta. This has important implications for radiation-driven warping in X-ray binaries, for which the value of Delta characterizing the disk is likely to be less than unity. In real accretion disks the outer boundary condition is likely to be different from the zero-crossing condition that we have assumed. In accretion disks around massive black holes in active galactic nuclei, the disk will probably become optically thin before the outer disk boundary is reached, whereas in X-ray binaries there will be an outer disk region (outside the circularization radius) in which the inflow velocity is zero but angular momentum is still transported. We show that in both these cases the solutions are similar to the zero-crossing eigenfunctions.

Maloney, Philip R.↗
NASA NTRS2005

Buckling of Carbon Nanotube-Reinforced Polymer Laminated Composite Materials Subjected to Axial Compression and Shear Loadings

A multi-scale method to predict the stiffness and stability properties of carbon nanotube-reinforced laminates has been developed. This method is used in the prediction of the buckling behavior of laminated carbon nanotube-polyethylene composites formed by stacking layers of carbon nanotube-reinforced polymer with the nanotube alignment axes of each layer oriented in different directions. Linking of intrinsic, nanoscale-material definitions to finite scale-structural properties is achieved via a hierarchical approach in which the elastic properties of the reinforced layers are predicted by an equivalent continuum modeling technique. Solutions for infinitely long symmetrically laminated nanotube-reinforced laminates with simply-supported or clamped edges subjected to axial compression and shear loadings are presented. The study focuses on the influence of nanotube volume fraction, length, orientation, and functionalization on finite-scale laminate response. Results indicate that for the selected laminate configurations considered in this study, angle-ply laminates composed of aligned, non-functionalized carbon nanotube-reinforced lamina exhibit the greatest buckling resistance with 1% nanotube volume fraction of 450 nm uniformly-distributed carbon nanotubes. In addition, hybrid laminates were considered by varying either the volume fraction or nanotube length through-the-thickness of a quasi-isotropic laminate. The ratio of buckling load-to-nanotube weight percent for the hybrid laminates considered indicate the potential for increasing the buckling efficiency of nanotube-reinforced laminates by optimizing nanotube size and proportion with respect to laminate configuration.

Riddick, J. C.↗
NASA NTRS1977

The crack-contact and the free-end problem for a strip under residual stress

The plane problem for an infinite strip with two edge cracks under a given state of residual stress is considered. The residual stress is compressive near and at the surfaces and tensile in the interior of the strip. If the crack is deep enough to penetrate into the tensile zone, then the problem is one of crack-contact where the depth of the contact area is an unknown which depends on the crack depth and the residual stress profile. The problem has applications to the static fatigue of glass plates and is solved for three typical residual-stress profiles. In the limiting case of the crack's crossing the entire plate thickness, the problem becomes a stressfree end problem for a semiinfinite strip under a given residual-stress state away from the end. This is a typical stress diffusion problem in which decay behavior of the residual stress near and the nature of the normal displacement at the end of the semiinfinite strip are of special interest. For two typical residual-stress states the solution is obtained, and some numerical results are given.

Bakioglu, M.↗
NASA NTRS1986

Tension strength of a thick graphite/epoxy laminate after impact by a 1/2-in. radius impactor

NASA is developing graphite/epoxy filament-wound cases for solid rocket motors of the space shuttle. They are wet-wound with AS4W graphite fiber and HBRF-55A epoxy. The membrane region is about 1.4 inches thick. Two 30-inch-diameter by 12-inch-long cylinders were impacted every two inches of circumference with 1/2-inch radius impactors that were dropped from various heights. One cylinder was empty and the other was filled with inert propellant. Two-inch-wide test specimens were cut from the cylinders. Each was centered on an impact site. The specimens were x-rayed and loaded to failure in uniaxial tension. Rigid body mechanics and the Hertz law were used to predict impact force, local deformations, contact diameters, and contact pressures. The depth of impact damage was predicted using Love's solution for pressure applied on part of the boundary of a semi-infinite body. The predictions were reasonably good. The strengths of the impacted specimens were reduced by as much as 37 percent without visible surface damage. Even the radiographs did not reveal the nonvisible damage.

Poe, C. C., Jr.↗
NASA NTRS1985

On the electromagnetic scattering from infinite rectangular conducting grids

The study and development of two numerical techniques for the analysis of electromagnetic scattering from a rectangular wire mesh are described. Both techniques follow from one basic formulation and they are both solved in the spectral domain. These techniques were developed as a result of an investigation towards more efficient numerical computation for mesh scattering. These techniques are efficient for the following reasons: (a1) make use of the Fast Fourier Transform; (b2) they avoid any convolution problems by converting integrodifferential equations into algebraic equations; and (c3) they do not require inversions of any matrices. The first method, the SIT or Spectral Iteration Technique, is applied for regions where the spacing between wires is not less than two wavelengths. The second method, the SDCG or Spectral Domain Conjugate Gradient approach, can be used for any spacing between adjacent wires. A study of electromagnetic wave properties, such as reflection coefficient, induced currents and aperture fields, as functions of frequency, angle of incidence, polarization and thickness of wires is presented. Examples and comparisons or results with other methods are also included to support the validity of the new algorithms.

Christodoulou, C.↗
NASA NTRS1990

Derivation of generalized transition/boundary conditions for planar multiple-layer structures

Infinite-order generalized impedance boundary conditions (GIBCs) and generalized sheet transition conditions (GSTCs) for planar multilayer configurations are developed via the Taylor series expansion method. The conditions are derived in a matrix product form where each matrix corresponds to a specific layer. An overall composite boundary/transition condition is obtained by making finite-order approximations to the elements of each matrix for the cases of 'low-contrast' and 'high-contrast' material layers. The accuracy of the truncated boundary conditions is examined by comparing their implied reflection and transmission coefficients with the corresponding exact coefficients. Design curves are also given which relate the maximum order of the conditions required to simulate a coating or layer of specific thickness and contrast. Expressions are then derived for the reflection and transmission coefficients of the GIBC/GSTC sheets, and these are compared to exact coefficients to demonstrate the validity of the derived GIBCs/GSTCs.

Ricoy, M. A.↗
NASA NTRS1996

Performance Analysis of Two Early NACA High Speed Propellers with Application to Civil Tiltrotor Configurations

The helicopter industry is vigorously pursuing development of civil tiltrotors. One key to efficient high speed performance of this rotorcraft is prop-rotor performance. Of equal, if not greater, importance is assurance that the flight envelope is free of aeroelastic instabilities well beyond currently envisioned cuise speeds. This later condition requires study at helical tip Match numbers well in excess of 1.0. Two 1940's 'supersonic' propeller experiments conducted by NACA have provided an immensely valuable data bank with which to study prop-rotor behavior at transonic and supersonic helical tip Mach numbers. Very accurate 'blades alone' data were obtained by using nearly an infinite hub. Tabulated data were recreated from the many thrust and power figures and are included in two Appendices to this report. This data set is exceptionally well suited to re-evaluating classical blade element theories as well as evolving computational fluid dynamic (CFD) analyses. A limited comparison of one propeller's experimental results to a modem rotorcraft CFD code is made. This code, referred to as TURNS, gives very encouraging results. Detailed analysis of the performance data from both propellers is provided in Appendix A. This appendix quantifies the minimum power required to produce usable prop-rotor thrust. The dependence of minimum profile power on Reynolds number is quantified. First order compressibility power losses are quantified as well and a first approximation to design air-foil thickness ratio to avoid compressibility losses is provided. Appendix A's results are applied to study high speed civil tiltrotor cruise performance. Predicted tiltrotor performance is compared to two turboprop commercial transports. The comparison shows that there is no fundamental aerodynamic reason why the rotorcraft industry could not develop civil tiltrotor aircraft which have competitive cruise performance with today's regional, turboprop airlines. Recommendations for future study that will insure efficient prop-rotor performance to well beyond 400 knots are given.

Harris, Franklin D.↗
NASA NTRS1975

Shear flow aerodynamics - Lifting surface theory

A lifting surface theory based on a parallel shear flow model is presented for steady, incompressible flows. The theory is intended to account approximately for the presence of a boundary layer. The method of Fourier transforms is used to calculate the pressure on a surface of infinite extent and arbitrary contour. Immediately above the surface is a region of sheared flow (the boundary layer), outside of which the flow velocity is constant. The Fourier transform of the pressure on this surface is used to derive the shear flow equivalent to the kernel function of classical potential flow lifting surface theory. The kernel function provides an integral relation between the upwash at a given point on the surface and the pressure everywhere on the surface. This relation is treated as an integral equation for the pressure, and is solved numerically. Computations are presented for the lift and pitching moment on a flat plate in two-dimensional flow, and for flat, rectangular wings of aspect ratio 1, 2, and 5. As expected, the shear layer decreases the lift curve slope; however, the shear layer (whose thickness is constant along the wing chord) has little effect on the center of pressure.

Ventres, C. S.↗
NASA NTRS1988

Simulated impact damage in a thick graphite/epoxy laminate using spherical indenters

The extent of fiber damage due to low-velocity impacts was determined for very thick graphite/epoxy laminates. The impacts were simulated by pressing spherical indenters against the laminates. After the forces were applied, the laminate was cut into smaller pieces so that each piece contained a test site. Then the pieces were deplied and the individual plies were examined to determine the extent of fiber damage. Broken fibers were found in the outer layers directly beneath the contact site. The locus of broken fibers resembled cracks. The cracks were more or less oriented in the direction of the fibers in the contiguous layers. The maximum length and depth of the cracks increased with increasing contact pressure and indenter diameter. The length and depth of the cracks were also predicted using maximum compression and shear stress criteria. The internal stresses were calculated using Hertz's law and Love's solution for pressure applied on part of the boundary of a semi-infinite body. The predictions and measurements were in good agreement.

Poe, C. C., Jr.↗
DOE OSTI2024

Vortex in superconducting thin-film strips of arbitrary width

We report the currents and field distributions of a vortex in a thin superconducting strip of a width W are considered. It is shown that unlike infinite films where the vortex field crosses the film only in one direction (say, from the half-space under the film to the half-space above it), in strips (as well as in finite size film samples of any shape) the field lines go back to the lower half-space not only out of the sample but also through certain strip parts. The strip patches where the magnetic lines 'dive' back to the space under the strip are situated mostly near the strip edges, at the strip and out of it. The magnetic flux through the strip associated with the vortex is shown to be less than the flux quantum and depends on the vortex position. The suppression of the vortex flux is strong in narrow strips with W $\ll$ Λ = 2λ 2 /d where λ is the bulk London penetration depth and d is the film thickness. The vortex energy scales roughly with W/Λ and depends on vortex position.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1947

Wing plan forms for high-speed flight

It is pointed out that, in the case of an airfoil of infinite aspect ratio moving at an angle of sideslip, the pressure distribution is determined solely by that component of the motion in a direction normal to the leading edge. It follows that the attachment of plane waves to the airfoil at near-sonic or supersonic speeds (Ackeret theory) may be avoided and the pressure drag may be reduced by the use of plan forms in which the angle of sweepback is greater than the Mach angle. The analysis indicates that for aerodynamic efficiency, wings designed for flight at supersonic speeds should be swept back at an angle greater than the Mach angle, and the angle of sweepback should be such that the component of velocity normal to the leading edge is less than the critical speed of the airfoil sections. This principle may also be applied to wings designed for subsonic speeds near the speed of sound, for which the induced velocities resulting from the thickness might otherwise be sufficiently great to cause shock waves.

Jones, Robert J↗
NASA NTRS1987

Strength of a thick graphite/epoxy rocket motor case after impact by a blunt object

The National Aeronautics and Space Administration is developing graphite/epoxy filament-wound cases (FWC) for the solid rocket motors of the Space Shuttle. The membrane region is about 36 mm thick. A study was made to determine the reduction in strength of the FWC due to accidental damage caused by low-velocity impacts. Two 76.2 cm diameter by 30.5 cm long cylinders were impacted every 5 cm of circumference with 1.27 cm radius impacters of various mass. The impacters represented tools and equipment dropped from various heights. One cylinder was empty and the other was filled with inert propellant. Five cm wide test specimens were cut from the cylinder. Each was centered on an impact sight. The specimens were X-rayed and loaded to failure in uniaxial tension. The strengths and depths of impact damage were analyzed in terms of maximum impact force. Rigid body mechanics and the Hertz law were used to derive an equation for impact force in terms of kinetic energy and the masses of the impacter and target. The depth of damage was predicted in terms of impact force using Love's solution of pressure applied on part of the boundary of a semi-infinite body.

Poe, C. C., Jr.↗
NASA NTRS1989

Strength of a thick graphite/epoxy rocket motor case after impact by a blunt object

The National Aeronautics and Space Administration is developing graphite/epoxy filament-wound cases (FWC) for the solid rocket motors of the Space Shuttle. The membrane region is about 36 mm thick. A study was made to determine the reduction in strength of the FWC due to accidental damage caused by low-velocity impacts. Two 76.2 cm diameter by 30.5 cm long cylinders were impacted every 5 cm of circumference with 1.27 cm radius impacters of various mass. The impacters represented tools and equipment dropped from various heights. One cylinder was empty and the other was filled with inert propellant. Five cm wide test specimens were cut from the cylinder. Each was centered on an impact site. The specimens were X-rayed and loaded to failure in uniaxial tension. The strengths and depths of impact damage were analyzed in terms of maximum impact force. Rigid body mechanics and the Hertz law were used to derive an equation for impact force in terms of kinetic energy and the masses of the impacter and target. The depth of damage was predicted in terms of impact force using Love's solution of pressure applied on part of the boundary of a semi-infinite body.

Poe, Clarence C., Jr.↗
NASA NTRS1939

Stress Concentration Around an Open Circular Hole in a Plate Subjected to Bending Normal to the Plane of the Plate

An aluminum-alloy plate containing an open circular hole of diameter large compared with the thickness of the plate was subjected to bending forces normal to the plane of the plate. Deflection and strain measurements were taken for two different loads. Stress concentrations occurred at the edge of the hole and the maximum stresses were tangential to the hole at the ends of the transverse diameter. The maximum stress at the edge of the hole was 1.59 times the computed stress on the net section and 1.85 times the computed stress in a solid plate of the same dimensions subjected to the same bending forces. The maximum deflections were about 20 percent greater than the corresponding deflection for a solid plate of the same size subjected to the same bending forces. The smallest edge distance was equal to 2-1/2 times the diameter of the hole and the stress concentration on this side of the hole was the same as on the side where the edge distance was about 4-1/2 diameters. A theoretical analysis of the problem shows that, for an aluminum plate of infinite width, the stress concentration at the edge of the hole would be 1.87 times the stress in a solid plate, which is substantially the same relation obtained for the plate tested.

Dumont, C↗