NASA Technical Memorandum 107288

AIAA-96-2550

/i

/

Minimum Weight Design of a

Genetic Axisymmetric Inlet

Shaft-Beth Nadell

Lewis Research Center

Cleveland, Ohio

Prepared for the

32nd Joint Propulsion Conference

cosponsored by AIAA, ASME, SAE, and ASEE

Lake Buena Vista, Florida, July 1-3, 1996

National Aeronauticsand

Space Administration

MINIMUM WEIGHT DESIGN OF A

GENERIC AXISYMMETRIC INLET

Shari-Beth Nadell"

NASA Lewis Research Center, Cleveland, Ohio 44135

Abstract

A new minimum weight design method for highspeed axisymmetric inlets was demonstrated on a

generic inlet. The method uses Classical Beam Theory

and shell buckling to determine the minimum required

equivalent isotropic thickness for a stiffened shell based

on prescribed structural design requirements and load

conditions. The optimum spacing and equivalent

isotropic thickness of ring frame supports are computed

to prevent buckling. The method thus develops a

preliminary structural design for the inlet and computes

the structural weight. Finite element analyses were

performed on the resulting inlet design to evaluate the

analytical results. Comparisons between the analytical

and finite element stresses and deflections identified

areas needing improvement in the analytical method.

The addition of the deflection due to shear and a

torsional buckling failure mode to the new method

brought its results in line with those from the finite

element analyses. Final validation of the new method

will be made using data from actual inlets.

Nomenclature

E

Fscr

G

Knon-opt

L

n

Nxy

r,R

S

t

tbuck

teomp

tframe

modulus of elasticity, lb/in 2

design allowable shear stress to prevent

torsional buckling, lb/in 2

shear modulus of elasticity, lb/in 2

non-optimum weight factor

shell length for torsional buckling, in

load factor

shear stress resultant, lb/in

shell radius, in

surface area, in 2

thickness; equivalent isotropic thickness, in

minimum equivalent isotropic thickness of shell

to prevent radial buckling, in

minimum equivalent isotropic thickness of shell

to prevent compression failure, in

minimum equivalent isotropic thickness of

frame, in

ho,g minimum equivalent isotropic thickness of shell

to prevent longitudinal buckling, in

tmg minimum gage thickness of the shell, in

train minimum equivalent isotropic thickness of shell,

in

tshc_ minimum equivalent isotropic thickness of shell

to prevent shear failure, in

tt_,sion minimum equivalent isotropic thickness of shell

to prevent tensile failure, in

ttorsion minimum equivalent isotropic thickness of shell

to prevent torsional buckling, in

W weight, lb

W._eg segment weight, ib

Wst_ structural weight, lb

x x coordinate value, in

7 unit shear strain

_5 bending deflection, in

A shear deflection, in

rt 3.14159

p material density, tb/in 3

_x bending stress, lb/in 2

_y hoop stress, lb/in 2

"_ shear stress, lb/in 2

Subscripts

i analysis station counter

k sum variable

Introduction

Current aeropropulsion systems studies are

focusing on advanced concepts that very often do not

draw on current and past design practices enough to

permit the use of empirically based design and weight

analysis methods. New methods for the conceptual

design and analysis of advanced engine components

must therefore be developed and tested. These new

methods can also provide a bridge between conceptual

level design and more detailed, complex preliminary

design activities.

" Aerospace Engineer, Member AIAA
Toaddressthisissueintheareaofhigh-speed

inletdesignandweightanalysis, aminimumweight

designmethodwasdevelopedbasedonanalytical

principles. 1Theanalytical methodrequiresasinput

onlyinformationthatisavailablefromconceptual

flowpathanalysis.Usingthisinformation, theanalytical

method, calledtheAxisymmetricInletMinimum

WeightDesignMethod,orAXIDES,developsaninitial

structural designandcomputesthestructural weightof

theinlet.Themethodassumesstiffenedshell

constructionoftheinletstructure.Varioustypesof

stiffenercross-sections canbespecified, including

truss-corehoneycombconstruction. Classical Beam

Theoryandshellradialbucklinganalysisduetoan

external loadareemployedtodeterminetheminimum

requiredequivalent isotropicthicknessforthestiffened

shellbasedonprescribedstructural designrequirements

andloadconditions.Theoptimumspacingand

equivalent isotropicthicknessofringframesupportsare

computedtopreventpanelbuckling.Additionalweight

forsystemsisaddedtothestructural weight,resulting

inanestimateforthetotalweightoftheinlet.

TheAXIDES method was demonstrated using a

generic Mach 2.4 axisymmetric inlet. The resulting

minimum weight inlet design was then evaluated using

finite element analyses (FEA). The goals of the

evaluation included identifying possible deficiencies in

the new analytical method as well as measuring its

accuracy. Any deficiencies were then corrected by

modifying the AXIDES method.

This paper gives a brief description of the

minimum weight design method and then discusses the

application of the method to a generic Mach 2.4

axisymmetric inlet. The development of finite element

models based on the analytical design results is

presented along with a comparison of the deflection and

stress results between the two analyses. Modifications

made to the analytical method as a result of the FEA

evaluation are described.

Design Method Summary

The general strategy used in the Axisymmetric

Inlet Minimum Weight Design Method is similar to that

used by Ardema for the minimum weight design of

arbitrary fuselage bodies. 2 In essence, the method

determines the minimum "smeared" thickness, which is

the minimum equivalent isotropic thickness, of a

stiffened panel structure required to prevent failure.

The weight of the structure is then calculated based on

this smeared thickness value. A detailed description of

the AXIDES method can be found in reference 1. The

method is summarized below.

The AXIDES method assumes stiffened shell

construction, i.e., shells or panels stiffened by

longitudinal members and ring frames (Figure 1). Nine

different structural concepts are available for the design.

The cross-section of the ring frames is assumed to be Zshaped for all of the structural concepts. To simplify

the inlet structure, it is divided into three components:

centerbody, internal cowl, and external cowl (Figure 2).

It is then assumed that each of these structures can be

designed and analyzed separately from the others.

While there is no question that these structures actually

do interact, this simplification was felt to be reasonable

for conceptual level design.

The first step in the minimum weight design

process is the definition of the inlet geometry. An

initial geometric definition of the inlet flowpath is

obtained from conceptual level performance analyses.

This geometry is refined using parametric cubic curves

to produce a smooth surface that is integrated to find

surface areas, volumes, and center of gravity locations.

A loads analysis is then performed at equally spaced

stations along the length of each inlet component.

Various combinations of internal and external loads,

including inertial loads, internal pressures, and

aerodynamic loads, are considered. The AXIDES

method requires that normal operating and

hammershock pressures be supplied at each geometric

coordinate of the inlet flowpath. Hammershock

pressures result from dynamic flow distortion that

causes the engine to surge. This results in a shock wave

that moves forward out of the inlet, leaving behind

pressures that are significantly higher than the inlet

pressure before the distortion. 3 External pressures are

likewise required at each geometric coordinate defining

the external cowl structure.

Eight different design load cases incorporating

the inlet pressures and loads are used to determine the

maximum loads to which the structure will be designed.

These are: landing, yaw maneuver, lateral load with

nose left yawing moment, vertical load with nose down

pitching moment, wind gust, asymmetric hammershock,

normal operating pressure, and axisymmetric

hammershock. Each is assumed to occur independent

of the others. The maximum loads for all of the design

load cases are based on ultimate load requirements.

Each design load case produces some combination of

bending, shear, axial, and radial loads. For the

calculation of bending and shear loads, the structure is

assumed to act like a cantilever beam, fixed at a

location approximating the centerline of the support

struts that would be present in an actual inlet (Figure 2).

Computation of axial and radial loads assumes that the

2
structureactslikeathin-walledcylindrical shell.The

finalmaximumloadsateachanalysisstationarechosen

bycomparingthosecomputedforeachdesignload

case.Thefinalloaddistributionisthereforenotbased

solelyononeloadcondition, butonacombinationof

thosethatproducethemostsevereloadsthathe

structurewillbesubjecttoduringalllevelsof

operation.

Assumingelasticbehaviorforallstructures, the

minimumallowablesmearedthicknessofthe

shell/longitudinal stiffeners(tmi,)iscomputedateach

stationbasedonthemaximumloadsappliedatthat

station.Fivepossiblefailuremodesareconsideredin

thecalculationoftrain- These are tension, compression

without buckling, shear, longitudinal buckling, and

radial buckling. The last of these is only considered in

the design of the inlet centerbody, which is subject to

external pressure loads. Maximum stress failure theory

is applied for all failure modes. A minimum gage

constraint, due to either manufacturing considerations

or Foreign Object Damage (FOD) requirements, is

included as an additional design requirement. Six

values for t,,in are therefore computed at each analysis

station, one for each failure mode and one for minimum

gage. The final minimum smeared thickness at each

analysis station is determined by comparing those from

each failure mode, or

train = max(ttension,tcomp,tlong,tshear,tbuck,tmg ) (1)

An iterative process is used to determine the

optimum spacing and smeared thickness of the ring

frames; alternatively, the frame spacing may be input to

the method, and the appropriate frame smeared

thickness (t;,a=,) will then be computed. The thickness

and spacing of the ring frames are based on the Shanley

criterion. 4 This assumes that the frames act as elastic

supports for a wide column with an equal probability of

general instability or local buckling failure. The

spacing and minimum equivalent thickness of the

frames is then based on panel failure due to buckling,

since this is the simpler approach of the two.

The total structural weight of each inlet

component is found by multiplying t,,_, and ty,_m_by the

material density and surface area of each analysis

segment:

Wstr=[lr_(ptmin+Ptframe)S](l+gnon_opt) (2)

where K,o,.opt is a non-optimum weight factor that is

applied to the structural weight of the inlet to account

for structural items such as fasteners and bolts, extra

weld material, uniform gages, etc., that are not modeled

in the structural analysis. This factor also corrects for

some of the inaccuracies introduced by the simplifying

assumptions made during the design process. The total

structural weight of the inlet is the sum of the weight of

the centerbody, internal cowl, and external cowl

structures. Finally, additional weight is added to

account for inlet actuators, controls, and bypass

systems. This weight is interpolated from data used in

the INSTAL pro_am. 5

The last action performed by the AXIDES

program is the computation of the deflections, using the

Moment-Area method 6, of the internal surfaces of the

inlet. This is important because the optimum

performance of a high-speed inlet is dependent on

maintaining the proper throat area and internal flowpath

geometry during normal inlet operation. Similar to the

inlet design, the inlet components are assumed to act as

cantilever beams for the deflection calculations. Limit

loads due to normal inlet operation were used for these

calculations.

Generic Inlet Description

The AXIDES program was demonstrated using a

generic Mach 2.4 axisymmetric inlet generated in-house

at the NASA Lewis Research Center. The total length

of the inlet (Figure 3), from centerbody tip to

compressor face, is 169.48 in, and the cowl lip radius is

29.2 in. The inlet normal operating and hammershock

pressures are plotted in Figure 4 along with the external

pressure assumed to act on all external surfaces.

The inlet was designed using Titanium alloy Ti6AI-4V. The material properties can be found in

reference 7. Since the AXIDES program does not

perform a thermal stress analysis, the effect of high

temperatures on the inlet structure is introduced by

degrading the material properties so they are consistent

with the approximate continuous operating temperature

on a standard day for a Mach 2.4 inlet.

The structural concept used in AXIDES for the

generic inlet was Z-stiffened shell with frames designed

for best buckling behavior. A fixed frame spacing of 10

in was specified. This value was chosen based on a

trade study that compared inlet weight with frame

spacing. 8

Analytical Design Results

The total weight of the generic inlet, as computed

by the AXIDES method, was 2773.79 lb. The inlet
centerbody, internalcowl,andexternal cowlweights

were645.26lb,413.00lb,and454.96lb,respectively.

Twentypercentoftheseweightswereduetothenonoptimumweightpenalty.Theinletsystemsaccounted

for 1260.58lbofthetotalinletweight.

Theminimumequivalent shellthicknesses forthe

inletcenterbody, internalcowl,andexternal cowlare

showninFigure5. FODrequirements dictatedthe

valueoft_, at the forward part of the centerbody as

well as at the cowl lip. The critical failure mode along

most of the centerbody was radial buckling due to

axisymmetric hammershock pressure loads. The

internal cowl structure consisted of both minimum gage

and shear critical equivalent shells. The structure for

the external cowl was designed entirely by minimum

gage constraints. The unit weight of all three inlet

components is shown in Figure 6. All frame structures

were designed based on minimum gage constraints,

indicating the possibility that the Z-shaped cross-section

may not have been optimum for this inlet design.

The maximum deflections of the centerbody and

internal cowl occurred at the centerbody tip (x=0.0 in)

and the cowl lip (Figures 7 and 8). The maximum

deflection of the centerbody was -.01617 in; the

maximum deflection of the internal cowl was -.00176

in. Both of these values fell within the acceptable

deflection limits as defined in the AXlDES program and

in reference 9.

Finite Element Evaluation

Finite Element Analysis

frames and the non-optimum shell and frame weights,

was included on the element property cards (PSHELL

cards). Therefore, the correct inertial load was applied

to the structure. QUAD4 two-dimensional elements

were used to model the equivalent shell structure. The

inlet centerbody was modeled using 2503 QUAD4

elements. The internal and external cowls were

modeled using 1392 and 1624 QUAD4 elements,

respectively. The finite element models for the inlet

centerbody, internal cowl, and external cowl are shown

in Figure 9. Symmetric boundary conditions were used

to reduce the size of the models. Fixed boundary

conditions were applied at the aft nodes of each model

to mimic the fixed cantilever end and to prevent

warping of the final cross-section. These fixed

boundary conditions are comparable to a rigid inlet

mount.

The four design load cases, representative of the

different types of loading, chosen for use in the method

evaluation are the normal operating limit pressure load

case, the landing load case, the axisymmetric

hammershock load case, and the asymmetric

hammershock load case. Each of these four load cases

included the inertial load of the structure. This was

modeled using the gravitational (GRAV) load card.

Pressure loads were modeled using the PLOAD2 card.

GENESIS does not support varying pressure loads

across an individual element. Therefore, the pressure

variations along the inlet axis were applied as a step

function, with the changes occurring at each analysis

station coordinate. This introduces small stress

discontinuities across the nodes located at each analysis

station.

The minimum weight structural design of the

generic axisymmetric inlet developed using AXIDES

was used to generate three models for finite element

analysis. One model was created for each inlet

component. These models were used to evaluate the

stresses and deflections predicted by the analytical

minimum weight design method for four of the design

load cases. The MSC/PATRAN pre- and postprocessor 1° was used to generate the finite element

models and evaluate the FEA results. The GENESIS

finite element analysis program H was used to perform

linear static analyses for each load case described

below.

The AXIDES method assumes that the smeared

shell structure carries all of the primary loads, with the

ring frames providing stability. The structure modeled

for the FEA analysis therefore only represented the

equivalent shell structure from the analytical method.

Nonstructural mass, including the weight of the ring

Comparison of FEA and AXIDES Results

The evaluation of the AXIDES method consisted

not only of comparing the analytical data with that from

the finite element analyses, but also of identifying

deficiencies in the analytical method, and improving the

method to eliminate or reduce the impact of these

deficiencies. Selected AXIDES stress and deflection

results were compared with those obtained from the

finite element analyses, as described below. Problem

areas and the resulting modifications are discussed.

The analytical bending and hoop stresses for the

individual load cases were computed using the AXIDES

minimum weight design results. The finite element

deflection results were recovered at the nodes in the x-z

plane (y=0). Finite element stress results were

recovered for the QUAD4 elements located at the top

(3'>0, z=O) and bottom (y<0, z=O) of the models.

Assuming beam behavior, these locations should give

4
themaximumtensileandcompressive stressesinthe

model.It wasassumedthathecompressive bending

stresseswouldhavegeaterimpactontheinletdesign

thanthetensilebendingstresses; therefore, onlythe

compressivebendingstresses, orthosealongthebottom

ofthestructure, arecompared. GENESISproduces

stressresultsatthetop(Z1)andbottom(Z2)facesof

theQUAD4plateelements, wherethetopfaceisinthe

positivedirectionofthenormalvectoroftheelement.

Forallthreefiniteelement models,thepositivenormal

vectorwasinthenegativeradialdirection.BothZ1 and

Z2 results are given in the figures presenting FEA stress

results.

Deflections (6) caused by limit normal operating

pressure and gravitational loads were compared for the

inlet centerbody and internal cowl structures. Bending

stresses (G) due to landing gravitational loads, bending

and hoop stresses (G) resulting from axisymmetric

hammershock pressures and gravitational loads, and

bending stresses caused by asymmetric hammershock

and _avitational loads were compared for all three inlet

components.

Limit Normal Operating Deflection

Bending Deflection

The analytical and FEA centerbody deflection in

the y-direction caused by the limit normal operating

inertial load are compared in Figure 7. The maximum

deflection from AXIDES, -0.01617 in, was

approximately 11.6 percent less than the -0.0183 in

obtained using the GENESIS finite element program.

This is good agreement given the assumptions made in

the analytical method.

A comparison of the deflection results for the

internal cowl structure can be seen in Figure 8. The

maximum deflection obtained from AXIDES was

-0.00176 in, while that obtained from GENESIS was

-0.00287 in. The analytical result is approximately 38.7

percent less than the finite element result. One possible

explanation for this difference is the influence of the

shear loads on the deflection of the structure. In

general, the deflection due to shear is small for beams

with large length to diameter ratio. However, as the

length to diameter (L/D) ratio becomes small (the

average length to diameter of the generic axisymmetric

inlet cowl is approximately 1.98), the deflection due to

shear becomes a larger part of the overall beam

deflection. _2 The computation of the deflection due to

shear for the inlet is discussed in the following section.

Shear Deflection

The deflection due to shear was computed for the

inlet structure using the following simplified method.

The only load considered for this load case is the

inertial load of the structure. It was assumed that the

weight of each shell segment, where the length of one

segment was equal to the distance between analysis

stations, was distributed uniformly over the length of

the segment. Furthermore, it was assumed that the

weight of the segment acted at the forward edge of the

segment, instead of at the center of gravity location of

the segment. Assuming that

A = vc = -- (3)

G

the maximum shear stress for a hollow circular crosssection is given by

Wn(t + r)

= (4)

_r2t

Starting at the last (aft) segment of the shell and moving

forward, the shear deflection at each analysis station

was defined as the sum of the shear deflection of the

previous station plus the shear deflection at the current

station due to all of the segment weights ahead of that

station:

A i = Ai+ 1 +

1Wsegrt1 (5) ;_ri2t mini G

The deflections due to shear computed from

Equation (5) for the inlet centerbody and intemal cowl

are presented in Figures 7 and 8, respectively. As seen

in Figure 7, the addition of the shear deflection to the

bending deflection gave a modest improvement in the

analytical results for the inlet centerbody, which were

already within 12 percent of the FEA results. The total

maximum centerbody deflection increased from -.01617

in to -.01706 in. This new value is 6.8 percent lower

than that computed by GENESIS. The addition of the

shear deflection to the internal cowl bending deflection

(Figure 8) decreased the difference between the

AXIDES and FEA results from 38.7 percent to 21.6

percent. The new value of the total maximum internal

cowl deflection was -.00225 in.

Though the addition of the shear deflection

improved the comparison between the analytical and

FEA analyses for this load case, Figure 8 shows that
thereisstillaconsiderabledifferenceintheinternal

cowldeflections. Acorrectionfactor,whosevalueis

givenas2.0forhollowcylindricalcross-sections, is

appliedintheliteraturewhencomputingshear

deflection. _2Applyingthisfactortothesheardeflection

oftheinternalcowlandaddingthebendingdeflection

givesthetotaldeflectionresultshowninFigure8.As

canbeseen,themaximumdeflection, andtheshapeof

thedeflectioncurve,ismuchclosertotheFEAresults

withthecorrectionfactorincluded.Thismaximum

deflectionis-.00275in,4.2percentlessthanthefinite

element value.Increasingthecorrectionfactorto2.25

givesalmostexactagreement betweentheanalytical

andFEAresults,withamaximumdeflectionof-.00287

in(Figure8,"B+(S'2.25)").

Theresultsofsimilarincreasesintheinlet

centerbodysheardeflectionareshowninFigure7.

Multiplyingthecenterbodysheardeflectionby2.0

resultsinamaximumdeflectionof-.01797in,only1.8

percentlessthanthatfortheFEAmodel,whereas

multiplyingby2.25givesalmostexactlythesame

resultsastheFEA,withamaximumdeflectionof

-.0182in.

Basedontheprecedingdiscussion, thedeflection

analysisoftheAXIDESmethodwasmodifiedto

includethedeflectionduetoshearmultipliedbya

correctionfactorof2.25.Thenewmethodcanthus

predictthedeflectionsoftheinletcenterbodyand

internalcowlmoreaccurately. Comparisonwith

predefineddeflectionlimitsontheinletwill leadto

betterinformationfortheuserofthemethodregarding

theneedtoredesigntheinletgeometry.

Landing Bending Stress

The landing load case is a pure bending situation,

including only the inertial load of the structure. A

comparison of the AXIDES and GENESIS bending

stresses for the centerbody is shown in Figure 10. Good

agreement between the results, like that seen in Figure

10, is also obtained for the internal and external cowl

structures. The influence of the fixed boundary

conditions on the finite element model can be seen at

the aft end (x=169.48 in), where the FEA bending

stresses vary suddenly from the expected distribution.

This is strictly a result of the finite element method and

does not reflect a real, physical condition.

Axisvmmetric Hammershock Bending and Hoop

Stresse....._s

The analytical and finite element hoop stresses

caused by the axisymmetric hammershock pressure

loads compare well with one another, as seen for the

internal cowl in Figure 11. The effect of the FEA aft

fixed boundary conditions are once again evident for all

components.

Comparisons of the bending stresses for this

same load case show a large difference between the

analytical and FEA results. The bending stresses for the

internal cowl are shown in Figure 12. A closer look at

the FEA models indicates that local deformation of the

QUAD4 elements due to the axisymmetric pressure

loads are the major contributor to the bending stresses

seen in the FEA results. The magnitudes of these local

deformations are small, and the Von Mises stresses are

much lower than the material yield stress. These local

deformations are therefore not causing failure of the

structure. They are a result of the way in which the

FEA model was constructed, using equivalent thickness

shells, and are, therefore, not necessarily indicative of

the stresses in an actual inlet, which would be

constructed using discrete structural elements.

Comparing the finite element bending stresses due to

only the inertia load with the analytical results shows

good agreement similar to that found for the landing

load case. No modifications to the computation of the

bending stresses in AXIDES for this load case were

deemed necessary due to the influence of the model

technique on the results.

Asymmetric Hammershock Bending Stress

Linear Static Analysis

Comparison of the bending stresses computed for

the inlet centerbody using AXIDES and GENESIS for

the asymmetric hammershock load case indicates fairly

good agreement, though not as close as the previous two

bending load cases. Those for the internal and external

cowls, however, do not show good agreement, as seen

for the internal cowl in Figure 13. Furthermore, the

bending stress plot for the internal cowl (Figure 14),

and similarly for the external cowl, did not show the

expected distribution with the largest tensile and

compressive stresses at the top and bottom of the

structure, respectively. For example, Figure 14 shows

that the largest stresses in the internal cowl occur at

approximately 65 and 120 degrees around the

circumference of the shell.

The maximum FEA deflections of the internal

and external cowl structures for the asymmetric

hammershock load case were 36.6 and 17.5 in,

respectively. The finite element linear static analysis is

based on small displacement theory; the large maximum

deflections seen in these results and the large stress
variationaroundthecircumference ofthecowlshells

wereindicationsthatthesestructureswerenotbehaving

inalinearfashion.Therefore, nonlinearbuckling

analyseswereperformedonthesestructures. Thisis

presentedinthefollowingsection.Themaximum

deflectionofthecenterbodystructureforthisloadcase

was2.2inatthecenterbodytip. TheVonMises

stressesindicatednostructural yield,andnofurther

analysisonthecenterbodywasperformed.

Nonlinear Buckling Analysis

Two changes were made to improve both the

internal and external cowl FEA models before

performing the nonlinear analyses. The first change

involved increasing the mesh density from 1392 to 5568

elements for the internal cowl, and 1624 to 6496

elements for the external cowl. The second change

made involved the application of the pressure loads to

the elements. Whereas in the linear static analyses the

pressure was applied uniformly over each element,

resulting in a step function distribution along the length

of the inlet, it was decided that improved accuracy

could be obtained by varying the pressure linearly over

each element, giving a smoother load distribution.

The GENESIS finite element program does not

support varying pressure loads over an element. It was

therefore necessary to switch to a different finite

element analysis method. The NASTRAN finite

element program 13was chosen. NASTRAN supports

the same QUAD4 element as GENESIS. The pressures

on the elements were applied using the PLOAD4 card,

which varies the pressure linearly across the QUAD4

element. All boundary conditions were applied in the

same manner as for the linear static analysis FEA

models.

The nonlinear buckling analysis of the inlet cowl

structures showed that the internal cowl was only able

to carry 27.8 percent of the applied asymmetric

hammershock pressure loads, and the external cowl

could carry only 2.8 percent. At these percentages of

the load, the shear stresses in shells reach the critical

value for buckling. Figure 15 shows the buckled shape

of the internal cowl. As seen in this figure, the buckling

is a rippling in the aft portion of the shell, rather than an

obvious rupture. The buckled area of the internal cowl

can also be seen in the shear stress distribution at the

critical load, Figure 16, as a subtle difference in the

shear stress distribution in the lower aft portion of the

shell.

This deflection pattern is similar to that seen for

the buckling of thin cylinders subject to torsion. 14 A

method for designing the structure to prevent this type

of failure was investigated. An efficiency equation,

similar to those already included in the AXIDES

method to design for longitudinal and radial buckling,

was found in Reference 15. For the design of a

monocoque shell of intermediate length

( 10x/tx_ < L/R < 3_-R-_- ) subject to torsional buckling:

Nxy = 741(t/9/44 IR/y2

RE " t,R) \L)

(6)

where the critical shear stress is

Fsc r =.74 \--_) _--_)

(7)

for a simply supported shell. Rearranging Equation 6 to

give a relation for the minimum thickness required to

prevent torsional buckling for a given shear stress

resultant, material, and geometry results in

(8)

Assuming a simply supported shell and analyzing

stiffened shells as monocoque with a length equal to the

frame spacing, Equation 8 was added to the AXIDES

method as an additional failure mode used to compute

the smeared shell thickness required at each analysis

station. New values of trainwere then computed for both

the internal and external cowl structures (Figure 17).

Nonlinear analyses using these new values for

t,_ were performed for both the internal and external

cowl structures. The internal cowl FEA model using

the new values for t,,i_ converged to carry 100 percent

of the applied load. Figure 18 compares the FEA

bending stress from the converged nonlinear analysis

with that computed analytically using the new values for

tmi,. The comparison is much better than that resulting

from the linear static analysis (Figure 13). The bending

stresses exhibit the expected distribution with tensile

stresses on the top of the structure, and compressive

stresses on the bottom.

Results from the nonlinear analysis of the

redesigned external cowl were not as favorable. The

structure buckled under only 4.7 percent of the load.

The shear stress distribution of the external cowl

(Figure 19) shows a different deformation pattern than
thatoftheinternalcowl(Figure16).Large

deformations occurattheexternal cowllipwith

virtuallynodeformationintheaftportionoftheshell.

Thereasonforthedifferencesbetweentheinternaland

external cowlbucklingdeformationisduetodiffering

loadapplications. All ofthepressuresontheinternal

cowl,normalandhammershock, areappliedtothe

internalsurfaceofthestructure.However, duetothe

differencebetweentheexternal pressureandthe

internalleakagepressures, normalandhammershock,

thenormalpressuresintheasymmetrichammershock

loadcaseareappliedtotheexternal surfaceofthe

external cowl,whilethehammershock pressures are

appliedtotheinternalsurface.Thisresultsinthelarge

twistevidentinFigure19,causingtheexternal cowl

shelltobuckleatsuchalowpercentageoftheapplied

load.Theexternalcowlresultsarediscussedfurther

below.

Method Assumptions

Detail design of an axisymmetric inlet would

entail determining the dimensions of each panel,

stiffener, frame, actuator, etc., for a specific inlet

required to meet specific load conditions. This is called

a point design. At the conceptual level of design,

performing a point design of an inlet is infeasible as

well as impractical. Assumptions are therefore made to

simplify the structure for quick analysis. In the

development of the AXIDES minimum weight design

method, many simplifying assumptions were made. The

first concerned the type of construction that would be

used to design the inlet. This was assumed to be

stiffened shell construction. This limits the application

of the method to those inlet types whose structure can

reasonably be described using this type of construction.

Using AXIDES to design inlets that contain

components designed using slats and seals, instead of

some type of stiffened panel construction, would

produce questionable results. Correction factors could

be determined to adjust the weight computed by

AXIDES for these types of inlets, however, by

comparing with existing inlet data.

The second important assumption, or

simplification, made to the inlet involved using smeared

structural dimensions instead of discrete values for the

design of the shell and longitudinal stiffeners and for

the ring frames. As a result, the inlet design produced

by AXIDES is not what would ultimately be

manufactured. In some cases, the structure designed by

AXIDES could not be built. For example, it is highly

improbable that a panel would be constructed with a

thickness that changes every four inches. This is

essentially what is predicted by the analytical method by

computing the smeared thickness at analysis stations

spaced closer together than the stabilizing frames.

However, this simplification makes it possible to

consider many variations of an inlet design in a short

amount of time, and with little input data.

The structure of the inlet was further simplified

for the finite element analyses, where only the smeared

shell was modeled, without any stiffeners or frames.

Unlike the AXIDES method, which includes analyses

based on a stiffened panel and shell structure, and

therefore "knows" what the structure really looks like,

the finite element methods have no "knowledge" that

any stiffening of the structure exists. They "see" the

inlet components as no more than large thin shells. This

became important for the axisymmetric hammershock

load case evaluated above. As discussed, the FEA

bending stress for the inlet structures included that due

to local deformation of the elements. While this type of

deformation might take place in a "real" inlet, stiffeners

and supports would be included in a discrete design to

ensure it did not lead to structural failure. Since the

FEA deformations were small and well below the elastic

limit of the material, and considering the simplifications

made in the model, the decision was made not to try to

correct the AXIDES method for these local

deformations.

The third major assumption made in the

development of the AXIDES method was that of

Classical Beam behavior. The inlet structures were

modeled as hollow cylindrical cantilever beams. Since

the analysis of these types of beams is relatively simple

and well documented, this further enabled the method to

produce a minimum weight design quickly and with a

small amount of input data. The assumption of beam

behavior worked well for the inlet centerbody; however,

the FEA deflection and asymmetric pressure load case

stress results for the cowl show greater evidence of shell

behavior. This is not a surprising result, as the L/D

value for the cowl is considerably lower than that given

in the literature as the limit for the application of beam

theory. It was possible to correct the deflection

calculation in AXIDES to account for shell behavior by

including the deflection due to shear, as above. It was

also possible to better model the internal cowl structure

by including an additional failure mode, that of

torsional buckling.

The FEA deformation and stresses of the external

cowl under asymmetric hammershock loads, however,

were not easily modeled by the analytical method.

Considering again the assumptions made in the

development of the FEA models as compared with the

construction of a real inlet, one can see that it is likely
that the FEA deformations and stresses would not be

present in a structure designed using discrete elements.

To modify the analytical method to match the current

FEA results exactly for this case would not be

reasonable. Final evaluation of the AXIDES method

will have to be made by comparing the analytical results

with real in service inlets, or with study inlets that have

been advanced to the detail design phase. This will be

the next, and final, step in validating the new analytical

minimum weight design method.

Conclusion

A new method for developing a minimum weight

design of a high-speed axisymmetric inlet was

demonstrated using a generic Mach 2.4 axisymmetric

inlet. The method, AXIDES, uses analytical principles

to determine the minimum equivalent isotropic

thicknesses of a stiffened shell structure and transverse

ring frames. The GENESIS and NASTRAN finite

element programs were used to evaluate the deflections

and stresses predicted by the AXIDES method.

After modifications were made to include the

calculation of shear stresses and a torsional buckling

failure mode, the AXIDES method was demonstrated to

develop a minimum weight structure that meets all of

the defined load requirements with the exception of

asymmetric hammershock pressure. The shell behavior

of the inlet external cowl model under the asymmetric

hammershock loads is not indicative of the behavior of

a real inlet built with discrete structural elements.

Comparisons with real inlets will be necessary to

completely verify the design of the external cowl and

determine necessary correction factors to be applied in

the AXIDES method.

The final step in evaluating the new AXIDES

method will be applying it to existing inlets and

comparing the computed weights with actual values.

Once this has been completed, the method will be ready

to use in systems studies supporting the aeronautics

project offices at the National Aeronautics and Space

Administration as well as the aeronautics industry.

References

1. Nadell, S.B.: Axisymmetric Inlet Minimum

Weight Design Method. NASA TM-106948, Aug.,

1995.

2. Ardema, M.D.: Body Weight of Hypersonic

Aircraft: Part 1. NASA TM-101028, Oct., 1988.

.

4.

.

.

7.

.

.

10.

11.

12.

13.

14.

15.

Seddon, J.; Goldsmith, E.L.: Intake Aerodynamics.

AIAA, Inc. 1985.

Shanley, F.R.: Weight-Strength Analysis of

Aircraft Structures. Dover Publications, Inc.

1960.

Kowalski, E.J.: A Computer Code for Estimating

Installed Performance of Aircraft Gas Turbine

Engines, Vols. I-III. NASA CR159691-3. Dec.,

1979.

Timoshenko, S.: Strength of Materials Part 1. D.

Van Nostrand Company, Inc., 1955.

Military Standardization Handbook. Metallic

Materials and Elements for Aerospace Vehicle

Design. MIL-HDBK-5E, 1987.

Nadell, S.B.: Investigation of Methods for the

Structural Weight Analysis of a Mach 2.4

Axisymmetric Inlet. NASA TM-106693, Aug.,

1994.

Koncsek, J.L.; Gerstle, J.H.; MacKinnon, M.I.K.:

Inlet Type Screening for High Speed Civil

Transport with Turbine Bypass Engine. The

Boeing Commercial Airplane Company. NAS3-

25963. CR101006. Mar., 1993.

MSC/PATRAN Release 1.4-1 Users Manual. The

MacNeal-Schwendler Corporation, Los Angeles,

CA.

GENESIS Users Manual. VMA Engineering,

Colorado Springs, CO.

Roarke, R.J.; Young, W.C.: Formulas for Stress

and Strain. Fifth Edition. McGraw-Hill, Inc.,

1975.

NASTRAN Users Manual. The MacNealSchwendler Corporation, Los Angeles, CA.

Donnell, L.H.: Beams, Plates, and Shells.

McGraw-Hill, Inc., 1976.

Crawford, R.F.; Burns, A.B: Strength, Efficiency,

and Design Data for Beryllium Structures. N63-

10645. Feb., 1962.
Frames

Panels

Longitudinal

Stiffeners

Figure 1. Stiffened Shell Geometry

Centerbody --7 /

/ /

/

/

_-- Extemal cowl

/

Intemal cowl --_

Figure 2. Axisymmetric Inlet Components

175

150

125

_, 100

>" 75

!

50 t

25

0 -'-""_ I --_-----+-------_

0 25 50 75 100 125 150 175

X (in)

Figure 3. Generic Axisymmetric lnlet Geometry

Centerbody Normal Pressure

...... Centerbody Hammershock Pressure

Internal Cowl Normal Pressure

Internal Cowl Hammershock Pressure

- External Pressure

50 F

!

40

C

-_ 30

._ 2o

=

O.

10

!

I

o

: f

/

0 4 .... t---- I - t -{

0 50 100 150 200

X (in)

Figure 4. Generic Axisymmetric lnlet Pressures

10
0.30

0.25

A

.E 0.20

r_

0.15

•: 0.10 I0.05

0.00

+

Centerbody

...... Internal Cowl

---- External Cowl

.°.-"

I I I I I I

30 60 90 120 150 180

X (in)

Figure 5. Minimum Equivalent lsotropic

Shell Thickness

60

5.0

4.0

v

_30

.m

_: 2.0

C

1.0

0.0

Centerbody

...... Internal Cowl

-- External Cowl

..°.--"

Figure 6

I I I ) I b I

0 25 50 75 100 125 150 175

x (in)

Generic Axisymmetric lnlet Unit Weight

Bending -- Shear

_ Bending+Shear ...... GENESIS

.... B+(S'2.25)

0.000

-0.005 ,

' -o.o10

-0.015

J

-0.020 i i i t i _ b I

0 25 50 75 100 125 150 175

X(in)

Bending -- Shear

_Bending+Shear ...... GENESIS

.... B+(S'2.25)

0.0000

-0.0010

c

O

U

-0,0020

-0.0030 b q I q t

50 75 100 125 150 175

X (in)

Figure 7.

Centerbody

Centerbody Deflection Figure 8. Internal Cowl Deflection

Internal Cowl External Cowl

Figure 9. lnlet Finite Element Models

11
-5OO

A-1000

-1500

_-2000

-2500

-3000

-3500

-4000 I I

0 25 50

_AXlDES

...... GENESIS (Z1)

.... GENESIS (Z2)

t

I i I--_

75 100 125 150 175

X (in)

Figure 10. Centerbody Landing Load Case

Bending Stress

8000 !

6000

4000 i

E

. 2000i!ili, i'

-2000 _

-4000

-6000 _ 4 I ---+-----_

AXIDES

...... GENESIS (Z1)

.... GENESIS (Z2)

50 75 100 125 150 175

X(In)

Figure 12. Internal Cowl Axisymmetric Hammershock

Load Case Bending Stress

35147'5.1

304167. •

162246.1

1148311. l

67631. l

_x

=i

-74_1, •

-121598. •

-16_05. •

-216212. •

-31O827.nun!

-358134, ._

Figure 14. Internal Cowl Asymmetric Hammershock

Load Case Bending Stress Distribution

40000

35000

30000

25000

20000

15000

10000

5000

Figure 11.

AXIDES

...... GENESIS (Bottom, Z1)

.... GENESIS (Bottom, Z2)

-- -- -- GENESIS (Top, Z1)

.... GENESIS (Top, Z2)

!

I

0 t---- t i I I

50 75 1oo 125 150 175

X (In)

Internal Cowl Axisymmetric Hammershock

Load Case Hoop Stress

60000

_AXIDES

...... GENESIS (Z1)

.... GENESIS (Z2)

A 40000 '.,.. . _.i_ _--=_" 20000 " "-'""

" ,,.._J 5 o

_ -20000 \.,,, I

-40000

-60000

-80000 -

50 75 100 125 150 175

X (in)

Figure 13. Internal Cowl Asymmetric Hammershock

Load Case Bending Stress

Figure 15.

X

Internal Cowl Buckling Deformation

At Critical Load

12
19061. n

17706.

16350.

14995. _

13639. I

12284..

10929. _

9573. I

8218.

6862.

5507.

4152.

2796.

1441.

85.30 i

=

-1270. -

0.16

0.12

A

C

v

01

t: 00a

O,m

el-"

0.04

Internal Cowl

...... External Cowl

0.00 I b I I

50 75 100 125 150 175

X (in)

Figure 16. Internal Cowl Shear Stress At

Buckling Limit Load

Figure 17. Internal and External Cowl tmi,,

Including Design For Torsional Buckling

10000

_'-10000

"_-20000

_-30000

-40000

-50000

--AXlDES (Zl)

...... NASTRAN

.... NASTRAN (Z2)

k

o

a

I t I I i

50 75 100 125 150 175

X (in)

1743.

1499. I

1255.

1011. + :

766.8

522.6 I

278.5 _

34.31

-209.8

--454,0

-698.2

-942.3

-1186.

-1431.

-1675. i

-1919.

Figure 18. lnternal Cowl Bending Stress Using

Design For Torsional Buckling

Figure 19. External Cowl Critical Shear Stress

Distribution

13
Form Approved

REPORT DOCUMENTATION PAGE OMBNo.0704-0188

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE

August 1996

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Minimum Weight Design of a Generic Axisymmetric Inlet

s. AUTHOR(S)

Shari-Beth Nadell

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135-3191

9. SPONSORING/MONITORING AGENCYNAME(S)ANDADDRESS(ES)

National Aeronautics and Space Administration

Washington, D.C. 20546-0001

3. REPORT TYPE AND DATES COVERED

Technical Memorandum

WU-505--69-50

8. PERFORMING ORGANIZATION

REPORT NUMBER

E-10363

10. SPONSORING/MONITORING

AGENCY REPORTNUMBER

NASA TM- 107288

AIAA-96-2550

11. SUPPLEMENTARY NOTES

Prepared for the 32nd Joint Propulsion Conference cosponsored by AIAA, ASME, SAE, and ASEE, Lake Buena Vista,

Florida, July 1-3, 1996. Responsible person, Shari-Beth NadeU, organization code 2420, (216) 977-7035.

12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified -Unlimited

Subject Category 07

This publiealion is available from the NASA Center for AeroSpace Information, (301) 621-0390.

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

A new minimum weight design method for high-speed axisymmetric inlets was demonstrated on a generic inlet. The

method uses Classical Beam Theory and shell buckling to determine the minimum required equivalent isotropic thickness

for a stiffened shell based on prescribed structural design requirements and load conditions. The optimum spacing and

equivalent isotropic thickness of ring frame supports are computed to prevent buckling. The method thus develops a

preliminary structural design for the inlet and computes the structural weight. Finite element analyses were performed on

the resulting inlet design to evaluate the analytical results. Comparisons between the analytical and finite element stresses

and deflections identified areas needing improvement in the analytical method. The addition of the deflection due to shear

and a torsional buckling failure mode to the new method brought its results in line with those from the finite element

analyses. Final validation of the new method will be made using data from actual inlets.

14. SUBJECT TERMS

Air-intakes; Axisymmetric inlets; Supersonic inlets; Design methods; Structural design;

Structural weight; Engine design

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