NASA Technical Memorandum 4769

Thermostructural Behavior of a

Hypersonic Aircraft Sandwich

Panel Subjected to Heating on

One Side

William L. Ko

Dryden Flight Research Center

Edwards, California

National Aeronautics and

Space Administration

Office of Management

Scientific and Technical

Information Program

1997

CONTENTS

ABSTRACT ....................................................................... 1

NOMENCLATURE ................................................................ 1

INTRODUCTION ................................................................... 2

DESCRIPTION OF PROBLEMS ...................................................... 3

FINITE-ELEMENT ANALYSIS ...................................................... 4

Finite-Element Modeling .......................................................... 4

Numerical Input Values ........................................................... 4

DISPLACEMENT FIELD ............................................................ 5

RESULTS ........................................................................ 6

Displacements .................................................................. 6

Thermal Stresses ................................................................. 7

Flat Temperature Profile ....................................................... 7

Upper Face Sheet .......................................................... 7

Lower Face Sheet .......................................................... 8

Sandwich Core ............................................................ 8

Dome Temperature Profile ..................................................... 9

Upper Face Sheet .......................................................... 9

Lower Face Sheet .......................................................... 9

Sandwich Core ............................................................ 9

Peak Stress Summary ......................................................... 10

CONCLUSIONS .................................................................. 10

REFERENCES ................................................................... 12

TABLES

1. Geometry of a panel ............................................................ 5

2. Face sheet properties ............................................................ 5

3. Honeycomb core (properties at 600 °F) .............................................. 5

4. Maximum deflections at center of sandwich panel's middle plane; T u = 900 °F,

T l = 200 °F ................................................................... 7

5. Peak thermal stresses in face sheets of sandwich panel; T u = 900 °F, T 1 = 200 °F

(yield stress = 126,000 lb/in 2) ..................................................... 10

6. Peak transverse shear stresses in sandwich core; T u = 900 °F, T 1 = 200 °F ................ 10

°°°

111

ABSTRACT

Thermostructural analysis was performed on a heated titanium honeycomb-core sandwich panel. The

sandwich panel was supported at its four edges with spar-like substructures that acted as heat sinks,

which are generally not considered in the classical analysis. One side of the panel was heated to high temperature to simulate aerodynamic heating during hypersonic flight. Two types of surface heating were

considered: (1) fiat-temperature profile, which ignores the effect of edge heat sinks, and (2) domeshaped-temperature profile, which approximates the actual surface temperature distribution associated

with the existence of edge heat sinks. The finite-element method was used to calculate the deformation

field and thermal stress distributions in the face sheets and core of the sandwich panel. The detailed thermal stress distributions in the sandwich panel are presented, and critical stress regions are identified. The

study shows how the magnitudes of those critical stresses and their locations change with different heating and edge conditions. This technical report presents comprehensive, three-dimensional graphical displays of thermal stress distributions in every part of a titanium honeycomb-core sandwich panel subjected

to hypersonic heating on one side. The plots offer quick visualization of the structural response of the

panel and are very useful for hot structures designers to identify the critical stress regions.

NOMENCLATURE

i

a

b

E

E cx

Ecy

E cz

E22

E43

Gcxy

a cxz

G cyz

h

h c

JLOC

m

SPAR

$81

T

T l

length of sandwich panel, in.

width of sandwich panel, in.

modulus of elasticity of sandwich face sheets, lb/in 2

effective modulus of elasticity of sandwich core in x-direction, lb/in 2

effective modulus of elasticity of sandwich core in y-direction, lb/in 2

effective modulus of elasticity of sandwich core in z-direction, lb/in 2

beam element for which the intrinsic stiffness matrix is given

quadrilateral combined membrane and bending element

effective shear modulus of sandwich core in xy-plane, lb/in 2

effective shear modulus of sandwich core in xz-plane, lb/in 2

effective shear modulus of sandwich core in yz-plane, lb/in 2

depth of sandwich panel, in.

depth of sandwich core, in.

joint location (or grid point or node) of finite-element model

number of deformation half waves in x-direction

structural performance and resizing finite-element computer program

hexahedron (or brick) element

temperature, °F

temperature of lower face sheet, °F
T

U

t S

W

Wmax

x, y, z

X t

(X

Ctcx

cy

(_¢z

(Z l

_u

AT

Yxz' Yyz

'V

Vcxy ' Vcxz ' Vcyz

Phc

Ox

Oy

Zxy

"_xz ' "_yz

temperature of upper face sheet for the flat-temperature profile, or temperature of

upper-face-sheet plateau zone for the dome-temperature profile, °F

thickness of sandwich face sheets, in.

deflection at arbitrary point of middle plane of sandwich panel, in.

maximum deflection at center of sandwich panel, in.

rectangular Cartesian coordinates, in.

shifted x-coordinate (x' = x + a/2), in.

coefficient of thermal expansion of solid plate or sandwich face sheets, in/in-°F

coefficient of thermal expansion of sandwich core in x-direction, in/in-°F

coefficient of thermal expansion of sandwich core in y-direction, in/in-°F

coefficient of thermal expansion of sandwich core in z-direction, in/in-°F

coefficient of thermal expansion of sandwich face sheets at temperature TI, in/in-°F

coefficient of thermal expansion of sandwich face sheets at temperature Tu, in/in-°F

temperature differential between upper and lower face sheets (AT = T u - T l ), °F

transverse shear strains of sandwich panel in xz- and yz-plane, in/in.

Poisson ratio of sandwich face sheets

Poisson ratios of sandwich core

density of sandwich core, lb/in 3

normal stress in x-direction, lb/in 2

normal stress in y-direction, lb/in 2

shear stress in xy-plane, lb/in 2

transverse shear stresses in sandwich core in xz- and yz-planes, respectively, lb/in 2

INTRODUCTION

A sandwich panel fabricated with titanium face sheets bonded to titanium honeycomb core through

enhanced diffusion bonding process is a potential candidate for application to hypersonic aircraft outer

skin structural panels (ref. 1). This type of sandwich structure can operate at elevated temperature levels

approaching 1000 °F. When applied as a structural component of hypersonic flight vehicles, this type of

sandwich panel is fastened to relatively cool substructures that act as heat sinks. Even under uniform

surface heating, the induced panel surface temperature distribution could be nonuniform because of those

edge heat sinks. Most analyses do not include the heat sink effects because of added mathematical complexity (refs. 2 through 8). The heated sandwich surface temperature profile is generally a truncated dome

shape, with temperature nearly constant in the central plateau zone, tapering down toward the cooler

edges. Because the panel is supported by relatively cool substructures and constrained from free

expansion, considerable thermal stresses could build up in the panel. The most critical stresses are the

compressive stresses. Excessive magnitude of compressive stress built up in the heated face sheet could

cause thermal bending caused by thermal moments; thermal buckling; thermal yielding; thermal creep;

2
f

thermal crack after cooling down; and other effects. One-sided heating, under certain temperature

profiles and edge conditions, also could induce high-intensity transverse shear stress in the sandwich core

near the panel corner, which could cause potential shear debonding between the face sheets and the sandwich core. Thus, loss of structural integrity could result.

Ko and Jackson conducted extensive studies, in recent years, concerning the mechanical and thermal

buckling characteristics of titanium sandwich panels (refs. 2 through 6) and metal-matrix composite

sandwich panels (refs. 7 and 8). Extensive information about thermomechanical buckling characteristics

of such sandwich structures have been documented (refs. 2 through 8). To fully understand the thermostructural response of the sandwich panels in actual applications under which the panel is constrained by

the substructures and subjected to one-sided heating, detailed thermal stress analyses are needed to identify the critical stress regions.

This report presents the results of finite-element thermal stress analyses of the sandwich panel under

different one-sided heating conditions and edge constraints. The detailed deformation fields and thermal

stress fields generated in the sandwich panel are presented graphically for easy visualization of the

critical stress regions.

DESCRIPTION OF PROBLEMS

Figure 1 shows the honeycomb-core sandwich panel, which has length a, width b, and depth h (depth

of sandwich core hc). The upper and the lower face sheets have the same thickness of ts . The panel is

subjected to one-sided heating of AT = T u - TI, the temperature differential between the upper-face-sheet

temperature T u and the lower-face-sheet temperature T l. The temperature differential AT has two types

of profiles (i.e., distributions): flat (fig. 2), for which AT is constant over the panel surface, and dome

shaped (fig. 3), for which AT is constant only in the panel central region and decreases linearly to zero at

the panel edges. The flat temperature profile heating is for the case when the heat sinks at the panel edges

are neglected. The dome-shaped temperature profile heating is for the case when there exist cooler substructures at the panel edges. The temperature profile in figure 3 is actually a truncated pyramid and

approximates the actual dome-shaped temperature profile (fig. 4), measured during a thermal ground test

of a titanium sandwich panel heated on one side at 10 °F/sec heating rate (ref. 9).

In the thermostructural analysis, the extensional and bending stiffnesses of the sandwich panel were

provided by the two face sheets, and the transverse shear stiffness by the sandwich core. The sandwich

panel was supported under four edge conditions to study different thermal deformation and thermal stress

fields generated in the panel:

.

o

.

.

4S fixed-edge condition---conventional simply supported edge condition in which the four edges

cannot move in the x-, y-, or z-directions.

4S free-edge condition--simply supported edges in which the four edges can move freely in the xand y- directions only.

4C fixed-edge condition---conventional clamped edge condition in which the four edges have zero

slopes and cannot move in the x-, y-, or z-directions.

4C free-edge condition----clamped edges with zero edge slopes in which the four edges can move

freely in the x- and y-directions only.

3
FINITE-ELEMENT ANALYSIS

This section describes the finite-element models and numerical input values used in the analysis.

Finite-Element Modeling

The structural performance and resizing (SPAR) finite-element computer program (ref. 10) was used

in the thermostructural analysis of the sandwich panel. Because the panel is symmetrical with respect to

the x- and y-axes (fig. 1), only a quarter-panel was modeled. Figure 5 shows the quarter-panel finiteelement model constructed for the sandwich panel. The SPAR constraint commands, SYMMETRY

PLANE = 1 and SYMMETRY PLANE = 2, were then used to generate the whole panel for thermostructural analysis. The panel face sheets were modeled with E43 elements (quadrilateral membrane and bending elements), and the sandwich core was modeled with a single layer of $81 elements (hexahedron or

brick elements) that connect to the upper- and lower-face-sheet E43 elements.

For the 4S fixed edge (fig. 6(a)) and 4S free edge conditions, the four edges must rotate freely with

respect to the corresponding edges of the middle plane. To simulate the 4S boundary condition, pinended rigid rods were attached to the panel edge to connect the two face sheets. The midpoints of these

rigid rods were pin-jointed to points (fixed or movable in the x- and y-directions) lying in the hypothetical

middle plane (fig. 6(a)). Each pin-ended rigid rod was modeled with two identical E22 elements (beam

element for which the intrinsic stiffness matrix is given). To simulate the rigidity of the rods, extensional

and transverse shear stiffnesses of the E22 elements were made very large. The pin-jointed condition at

the face sheet edges was simulated by assigning zero values to the rotational spring constants in the stiffness matrix for the E22 elements. The pin-jointed condition at the hypothetical middle-plane points was

simulated by eliminating the three rotational constraints. One node of each E22 element was connected to

the associated node of E43 element, and the other node was connected to the hypothetical middle-plane

point. The quarter-panel model (fig. 5) for the 4S fixed- and free-edge conditions (to be called 4S model)

has 1,299 joint locations (JLOCs), 98 E22 elements for the edge rigid rods, 1,152 E43 elements for the

face sheets, and 576 $81 elements for the sandwich core, as shown in the figure.

For the 4C fixed-edge condition (fig. 6(b)), the E22 elements at the panel edges may be neglected.

However, when the E22 elements were attached at the panel edges (i.e., using the 4S model) and enforced

the zero-edge slopes, the finite-element solutions remained the same as those in which the E22 elements

were not used. Retaining the E22 elements requires added computational penalty. For the 4C free-edge

condition, the E22 elements were attached at the panel edges to enforce zero-edge slopes and allow free

in-plane translations.

Numerical Input Values

The dimensions and the material properties used in this study (tables 1 through 3) are identical to the

titanium honeycomb-core sandwich panel previously used in thermostructural simulation tests at NASA

Dryden Flight Research Center (ref. 9).

4
_ H I

Table 1. Geometry of a panel.

a = b=24in.

h = 0.75 in.

ts = 0.06 in.

Table 2. Face sheet properties.

200 °F 900 °F

E, lb/in 2 15.4 x 106 13.1 x 106

v 0.31 0.31

c_, in/in-°F 4.3 x 10 -6 5.35 x 10-6

Table 3. Honeycomb core (properties at 600 °F).

Ecx = 2.7778 x 104 lb/in 2

Ecy = 2.7778 x 104 lb/in 2

Ecz = 2.7778 x 105 lb/in 2

Gcxy = 0.00613 lb/in 2

Gcy z = 0.81967 x 105 lb/in 2

Gcx z = 1.81 x 105 lb/in 2

Vcxy = 0.658 x 10-2

Vcy z = 0.643 x 10-6

Vcxz = 0.643 x 10-6

O_cx = 5.37 x 10-6 in/in-°F

C_cy = 5.37 x 10 --6 in/in-°F

C_cz = 5.37 × 10-6 in/in-°F

Phc = 3.674 x 10 -3 lb/in 3

The temperature loadings on the sandwich panel are T u = 900 °F for the upper face sheets (entire

regions (fig. 2) or central regions (fig. 3)) and T l = 200 °F for the lower face sheet.

DISPLACEMENT FIELD

A theoretical equation describing the displacement field of a solid rectangular plate was modified to

make it applicable to sandwich panels. This equation was required to evaluate the transverse shear effect

on the sandwich panel deflection.

The following equation, taken from reference 11, describes the deflection field of a simply supported

solid isotropic rectangular plate under differential heating.

5
w xy,=4o a2 1+ ,sin / c°sh /

m= .... COS 

where the origin of the coordinates for this equation is at x = -a/2, y = 0; namely,

a

x' = x + _. (2)

When the transverse shear effect of the sandwich core is neglected (i.e., 7xz = _'yz = 0), the sandwich

panel behaves like a solid plate, and therefore, the above equation could be user to approximate the

deflection field of the sandwich plate. The validity of equation (1) is addressed later in the "Results" section. To apply.equation (1) for the sandwich plate, the thermal bending term etAT must be replaced with

sAT = auTu- etlT l (3)

The displacement field calculated from equation (1) using equation (3), is then compared with that

calculated from the finite-element method for only the case when the transverse shear effect of the sandwich core is neglected.

RESULTS

Displacements

Figures 7(a) and 7(b) show the half-panel plots of the deformed shapes of the sandwich panel under

different edge conditions subjected to flat temperature profile heating. These half-panel plots were generated from the quarter-panel plots by using the SYMMETRY command. The panel's deformed shapes

under fixed and free edges are the same; however, as will be seen later, the induced thermal stress fields

are quite different. Notice that under the 4C edge condition (fixed or free, fig. 7(b)), the panel deflection

is zero (i.e., the deformed panel remains flat).

Figures 8(a) and 8(b) show the similar half-panel plots for the case when the heating is of the domeshaped temperature profile. Again, the deformed shapes for the fixed- and free-edge cases are identical.

Unlike the previous case, the panel deflection away from the boundaries under the 4C edge condition,

fixed or free, (fig. 8(b)) is nonzero.

Figure 9 shows the deflection curves of the sandwich panel's middle plane center line, along the

x-axis, for different heating cases. The figure also shows the deflection curve calculated from

equation (1) up to 10 terms summation for flat temperature profile heating. The deflection curve calculated from equation (1) falls pictorially on that calculated from the finite-element method (for the flat temperature case) neglecting the transverse shear effect (i.e., by setting 7xz = ?yz = 0, namely by making

Gcx z and Gcy z very large). The maximum deflection at the center of sandwich panel middle plane Wma x

calculated from equation (1) using 10-terms series summation is Wma x = 0.2931 in., and that calculated

from the finite-element method (for Txz = 7yz = 0) is Wma x = 0.2920 in. The close correlation between
thesetwo valuesgivesconfidencein theapplicabilityof equation(1) for thesandwichpanel,andalsoin

theadequacyof thefinite-elementmodelused.

Thedeflectionequation(1) andthefinite-elementmodelswerealsousedto studytheeffectof transverseshearonpaneldeflections.Table4 liststhepanelmaximumdeflectionsWma x for different heating

and edge conditions. The Wma x values in parentheses are applicable when the transverse shear effect

is neglected (i.e., Yxz = "Yyz = 0). The Wma x value calculated from equation (1) (10 terms summation) is

also shown in brackets for comparison. Notice that by neglecting the transverse shear effect, the panel

deflection could be underpredicted by 3 to about 11 percent depending on the edge and heating conditions.In practical application, the panel is under dome temperature profile heating and 4C edge condition

(closer to fixed edges rather than free edges). For this case, the maximum deflection is only Wma x =

0.0576 in. Such a small panel deflection greatly minimizes any concern that the deformed panel could

severely disturb the airflow field and, therefore, alter the surface heating rate.

Table 4. Maximum deflections at center of sandwich panel's middle plane;

T u = 900 °F, T l = 200 °F.

Temperature profile

W ma x , in.

4S fixed 4S free 4C fixed 4C free

Flat

0.3305 0.3305

(0.2920) (0.2920)

[0.2931]

0 0

Dome

0.3050 0.3050 0.0576 0.0576

(0.2745) (0.2745) (0.0557) (0.0557)

Thermal Stresses

This section presents thermal stress results for flat and dome-shaped temperature heating applied to

the sandwich panel under the various edge conditions.

Flat Temperature Profile

Upper Face Sheet

Figures 10 through 21 show various distributions of normal stresses {Ox, Oy }, which are negative

(i.e., compression), and the shear stress ('txy), in the upper face sheet of the sandwich panel induced by

fiat-temperature-profile heating. Again, these half-panel plots were generated from quarter-panel plots

using the SYMMETRY command. The figures show the peak stress points and values of peak stress. For

the 4S fixed- and free-edge cases, the distributions of {Ox, Oy } (figs. 10, 11, 13, and 14) are slightly saddle shaped, and the peak compression points of {Ox, Oy } are at the midpoints of the panel edges, y = b/2

7
andx = a/2, respectively. The distributions of the shear stress Xxy in the upper face sheet for the 4S fixedand free-edge cases (figs. 12 and 15) are distorted bell-shaped within each quarter-panel region. The magnitude of "r,xy reaches its peak value near the panel corners and decreases steeply to zero at the panel edges

and rapidly to zero at the two axes of symmetry. By freeing the panel edges from the fixed constraint, the

magnitudes of compressive stresses {Ox, Oy} could be reduced considerably (figs. 10, 11, 13, and 14);

however, the distributions of shear stress rxy remained almost the same (figs. 12 and 15). For the 4C

fixed-edge case, the compressive stresses {Ox, Oy } in the upper face sheet(figs. 16 and 17) are constant

everywhere, and the shear stress "txy is zero everywhere (fig. 18). For the 4C free-edge case, the compressive stresses {Ox, Oy } are almost constant over the upper face sheet (figs. 19 and 20), and the shear stress

•rxy induced in the upper face sheet (fig. 21) is nearly zero.

Lower Face Sheet

Figures 22 through 33 show various distributions of {Ox, Oy, Xxy } induced in the lower face sheet of

the sandwich panel under different edge conditions for flat-temperature-profile heating. For the fixededge cases (4S and 4C), {Ox, oy } are negative (i.e., compression); however, for the free-edge cases (4S

and 4C), {Ox, Oy } are positive (i.e., tension). For the 4S fixed-edge case, the peak compression points of

{Ox, Oy } (figs. 22 and 23) are no longer located at the edge midpoints like the upper-face-sheet case

(figs. 10 and 11). For the 4S free-edge case, similar to the upper-face-sheet case for which {Ox, Oy } are

negative (figs. 13 and 14), the peak tensile stress points of {Ox, Oy } (figs. 25 and 26), are at the midpoints

of the panel edges. The distributions of shear stress "rxy in the lower face sheet for the 4S fixed- and freeedge cases (figs. 24 and 27) are very similar to those for the upper-face-sheet case (figs. 12 and 15);

however, the sign of Yxy is reversed. For the 4C fixed-edge case, the compressive stresses {Ox, Oy } are

identical and constant everywhere in the lower face sheet (figs. 28 and 29), but the magnitude is much

lower than that in the upper face sheet (figs. 16 and 17), and the shear stress "rxy in the lower face sheet

(fig. 30), like the upper face sheet case (fig. 18), is zero everywhere. For the 4C free-edge case, {Ox, Oy }

in the lower face sheet are both positive and nearly constant (figs. 31 and 32), and the shear stress Xxy

induced in the lower face sheet (fig. 33) is at an insignificant level similar to the case for the upper face

sheet (fig. 21).

Sandwich Core

Figures 34 and 35 show the distributions of transverse shear stresses {Xxz, "Cyz} induced in the sandwich core under 4S fixed- or 4S free-edge condition subjected to flat-temperature-profile heating. Each

transverse shear stress value used in the plots is the average of the eight stress values at the eight nodes of

the $81 element. Both the 4S fixed- and 4S free-edge cases induced identical transverse shear stresses.

The shape of "rxz plot (fig. 34) is like an airplane wing with winglets; for "ryz (fig. 35) the shape is like

fox ears near the panel's edge. The values of {Xxz, Xyz} are quite low in the core central region and rises

steeply to their respective peak values at the comers of the core (i.e., the transverse shear stress concentrations occur at the panel's comers). The levels of {'Cxz, _:yz} stress concentrations are relatively low;

however, they might cause the thin honeycomb walls to buckle in shear.

Under flat-temperature-profile heating, both the 4C fixed- and 4C free-edge cases induced no

transverse shear stresses {'rxz, "ryz} in the sandwich core, as shown in figures 36 and 37. For actual

8
application, the panel's edge condition is closer to the 4C fixed-edge condition, which induces no transverse shears. Therefore, under the present heating level, no concern about stress concentration caused by

transverse shear is warranted.

Dome Temperature Profile

Upper Face Sheet

Figures 38 through 49 show the distributions of {Ox, Oy, Xxy } in the upper face sheet of the sandwich

panel induced by the dome-temperature-profile heating. The distributions of the compressive stresses

{Ox, Oy } for the 4S fixed- and free-edge cases (figs. 38, 39, 41, and 42) and 4Cfixed- and free-edge cases

(figs. 44, 45, 47, and 48), are hat shaped, reflecting partly the shape of the dome temperature profile.

Unlike the flat-temperature-profile case, the peak compression points of {o x, Oy } are now at the boundary of the central plateau zone and not at the panel's edges. The shear stress distributions for the 4S fixedand free-edge cases (figs. 40 and 43) are similar to those of the flat-temperature-profile case (figs. 12 and

15) but with slightly higher peak magnitudes. For the 4C fixed- and free-edge cases, the shear stress "Cxy

(figs. 46 and 49), is zero only at the two axes of symmetry and the panel's comers (the plotted comer

points are not exactly at the panel's corners, and therefore, show finite values) but nonzero at the panel

edges because of the nonuniform thermal expansions. The peak magnitudes of "txy are lower than those

for the 4S fixed- and free-edge cases (figs. 40 and 43) and are in the vicinity of the panel's corners.

Lower Face Sheet

Figures 50 through 61 show various distributions of {o x, Oy, Txy } in the lower face sheet induced by

the dome-temperature-profile heating. The stress distributions are very similar to those for the fiat temperature profile and, unlike the upper face sheet, they do not reflect the dome temperature profile. Those

figures also indicate the peak stress points. For the 4C fixed and 4C free cases (figs. 56 through 61), the

distributions of {o x, Oy, r_xy} stresses in the lower face sheets are slightly wavy in shape with peak stress

points at the edges.

Sandwich Core

Figures 62 and 63, respectively, show the distributions of transverse shear stresses {_xz, Xyz } induced

in the sandwich core for the 4S fixed- and 4S free-edge Cases under dome-temperature-profile heating.

Both the 4S fixed- and 4S free-edge case give identical {Xxz, a:yz} distributions. The "txz plot (fig. 62)

also looks like an airplane wing with winglets, and the "tyz plot (fig. 63) looks like cat ears near the

panel's edge. The peak magnitudes of {Zxz, "tyz} are now at the core edges and near the core comers--not

exactly at the core corners like the previous case. The {'txz, Xyz } stress concentrations are less severe for

the dome-temperature-profile case (figs. 62 and 63), as compared with the fiat-temperature-profile case

(figs. 34 and 35). For dome-temperature-profile heating, the magnitudes of transverse stresses {Xxz, Xyz}

induced in the sandwich core under both 4C fixed- and 4C free-edge conditions (figs. 64 through 67) are

quite close and very small--not exactly zero like for fiat-temperature-profile heating (figs. 36 and 37).

9
Peak Stress Summary

Table 5 lists the peak values of the thermal stresses {Ox, Oy, l:xy } (positive or negative) induced in the

upper and lower face sheets of the sandwich panel. Table 6 lists the peak values of the transverse shear

stresses {_xz, Xyz} induced in the sandwich core.

Table 5. Peak thermal stresses in face sheets of sandwich panel; T u = 900 °F, T l = 200 °F (yield stress =

126,000 lb/in2).

Upper face sheet

Flat temperature profile Dome temperature profile

Edge

condition o x, lb/in 2 oy, lb/in 2 Xxy, lb/in 2 o x, lb/in 2 Oy, lb/in 2 "txy , lb/in 2

4S fixed

4S free

4C fixed

4C free

-89,245 -87,430 23,827

-26,161 -25,783 23,904

-107,470 -107,470 0

-46,177 -45,801 219

-75,961 -75,796 28,579

-26,140 -25,576 30,917

-96,192 -96,087 12,984

-45,488 -44,996 14,062

Lower face sheet

4S fixed

4S free

4C fixed

4C free

-62,948 -64,010 23,827

25,671 22,931 23,755

-19,190 -19,190 0

44,339 44,393 219

-53,433 -54,553 19,242

21,084 18,251 17,086

-29,399 -28,160 2,115

36,994 36,743 2,757

Table 6. Peak transverse shear stresses in sandwich core; T u = 900 °F, T l = 200 °F.

Flat temperature profile Dome temperature profile

Edge lb/in2 lb/in2 lb/in2 lb/in2 condition "r'xz" Xy z ' "r'xz' "r'yz'

4S fixed

4S free

4C fixed

4C free

2,216 1,798

2,216 1,798

0 0

0 0

1,339 1,065

1,339 1,065

134 86

142 88

CONCLUSIONS

Finite-element thermal stress analyses were performed on a titanium honeycomb-core sandwich

panel supported at its edges under four different edge conditions, and heated on one side under both flat

and dome-shaped temperature profiles. Detailed deformation and thermal stress fields induced in the

10
sandwichpanelwere presented graphically for easy visualization. The key results of the thermostructural

analyses are as follows:

o

.

If the transverse shear effect of a sandwich core is neglected, the maximum deflection of the

sandwich panel was underpredicted by 3 to about 11 percent, depending on edge conditions and

heating temperature profiles.

Under the flat-temperature-profile heating:

(a) The classical deflection equation for a simply supported rectangular flat plate adequately

describes the deformation field of a simply supported sandwich panel for which the transverse

shear effect of the sandwich core is neglected, as validated by the finite-element solutions.

(b) For the 4S fixed- and 4S free-edge conditions, the peak stress points of the normal stresses

{Ox, Oy } are at the edges of the face sheets; the peak stress points of the shear stress "gxy are at

the diagonal lines and near the comers of the face sheets; and the peak stress points of the

transverse shear stresses {_xz, Xyz } are right at the comers of the sandwich core.

(c) For the 4C fixed-edge condition, the normal stresses {Ox, Oy } in both of the face sheets are

constant everywhere, and the shear stress Xxy in both of the face sheets is zero everywhere.

For the 4C free-edge condition, the normal stresses {Ox, Oy } in both of the face sheets are

almost constant, and the shear stress Xxy in both of the face sheets is negligibly low. For both

4C fixed- and 4C free-edge conditions, the transverse shear stresses {Xxz , -Cyz} are zero everywhere in the sandwich core.

. Under the dome-temperature-profile heating:

(a) For all four edge conditions, the peak stress points of normal stresses {Ox, Oy } in the upper

face sheet are at the boundary of the temperature plateau zone--not at the face sheet edges.

The peak stress points of the shear stress Xxy in the upper face sheet (for all the edge conditions) and in the lower face sheet (for 4S fixed- and 4S free-cases only) are on the diagonal

lines and near the comers of the face sheets.

(b) The distributions of {Ox, Oy } in the lower face sheet for the 4S fixed and 4S free cases are

very similar to those for the flat-temperature-profile case and do not reflect the temperature

profile applied to the upper face sheet. For the 4C fixed and 4C free cases, the distributions of

{Ox, Oy, Xxy} stresses in the lower face sheets are slightly wavy in shape with peak stress

points at the edges of the lower face sheet.

(c) For 4S fixed and 4S free cases, the peak stress points of the transverse shear stresses {_xz,

Xyz } in the sandwich core are at the core edges and very near the core comers. For the 4C

fixed and 4C free cases, the transverse shear stresses {Xxz , _yz} induced in the sandwich core

have extremely low magnitudes.

Dryden Flight Research Center

National Aeronautics and Space Administration

Edwards, California, May 3, 1996

11
REFERENCES

°

.

.

.

5

.

.

.

.

i0.

11.

Tenney_ D.R., W.B. Lisagor, and S.C. Dixon, "Materials and Structures for Hypersonic Vehicles,"

J. Aircraft, vol. 26, no. 11, November 1989, pp. 953-970.

Ko, William L. and Raymond H. Jackson, Thermal Behavior of a Titanium Honeycomb-Core Sandwich Panel, NASA TM-101732, January 1991.

Ko, William L. and Raymond H. Jackson, "Combined Compressive and Shear Buckling Analysis of

Hypersonic Aircraft Structural Sandwich Panels," AIAA Paper No. 92-2487-CP, presented at the

33rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference,

Dallas, Texas, April 13-15, 1992; NASA TM-4290, May 1991.

Ko, William L., "Mechanical and Thermal Buckling Analysis of Sandwich Panels Under Different

Edge Conditions," Proc. l st Paciftc International Conference on A erospace Science and Technology,

Tainan, Taiwan, Dec. 6-9, 1993.

Ko, William L., Mechanical and Thermal Buckling Analysis of Rectangular Sandwich Panels Under

Different Edge Conditions, NASA TM-4585, April 1994.

Ko, William L., Predictions of Thermal Buckling Strengths of Hypersonic Aircraft Sandwich Panels

Using Minimum Potential Energy and Finite Element Methods, NASA TM-4643, May 1995.

Ko, William L. and Raymond H. Jackson, Combined-Load Buckling Behavior of Metal-Matrix Composite Sandwich Panels Under Different Thermal Environments, NASA TM-4321, September

1991.

Ko, William LI and Raymond H. Jackson, "Compressive and Shear Buckling Analysis of Metal

Matrix Composite Sandwich Panels Under Different Thermal Environments," Composite Structures,

vol. 25, July 1993, pp. 227-239. Also NASA TM-4492, June 1993.

Richards, W. Lance and Randolph C. Thompson, "Titanium Honeycomb Panel Testing," Proceedings Structural Testing Technology at High Temperature Conference, Dayton, Ohio, Nov. 4-6,

1991, Society for Experimental Mechanics, Inc., June 1992.

Whetstone, W.D., SPAR Structural Analysis System Reference Manual, System Level 13A, vol. 1,

Program Execution, NASA CR-158970-1, December 1978.

Timoshenko, S. and S. Woinowsky-Krieger, Theory of Plates and Shells, McGraw-Hill Book Co.,

Inc., New York, 1959, p. 164.

12
960440

Figure 1. Honeycomb-core sandwich panel under one-sided thermal loading.

13
AT

I

960441

Figure 2. Heating under flat temperature profile; AT = T u - T l .

nol

960442

Figure 3. Heating under dome temperature profile; AT = T u - T l .

14
Temperature,

oF

600

500

400

300

200

100

0

24 ir

\

911067

Figure 4. Measured temperature distribution in upper surface of titanium honeycomb-core sandwich panel,

heated on upper side at 10 °F/sec heating rate, with four edges supported by test fixtures (heat sink).

15
/

Z

Sandwich Quarter panel

region modeled

Y

X

Z

Y

E43 elements 1152

$81 elements 576 x

970047

Figure 5. Quarter-panel, finite-element model for sandwich panel.

16
i  ̧ /

O" Pin joint

Rigid bar-_ Maximum Yxz

lz

_. /-E4

E22-1 1

E22"-1 _-E4

(a) 4S edge condition (fixed).

7

k

960443

Jz

X

960444

(b) 4C edge condition (fixed).

Figure 6. Simulation of different edge conditions.

17
(a) 4S edge condition (fixed and free).

960445

96O446

(b) 4C edge condition (fixed and free).

Figure 7. Deformed shapes of sandwich panel under heating on one side; fiat temperature profile; T u

900 °F, T l = 200 °F; half-panel plots.

.m

18
(a)4Sedgecondition(fixed andfree).

960447

960448

(b) 4C edge condition (fixed and free).

Figure 8. Deformed shapes of sandwich panel under heating on one side; dome temperature profile; T u =

900 °F, T l = 200 °F; half-panel plots.

19
.4

Wj

in..3

.2

.1

III

.5

Flat temperature profile

Dome temperature profile

No transverse shear effect-flat temp. = equation (1)

No transverse shear effect-dome temp.

- --"" I I I t

0

-12 -8 -4 0 4 8 12

x, in.

I

16

960449

Figure 9. Deflections of sandwich panel's middle plane along x-axis; T u = 900 °F, T l =200 °F.

2O
Normal and Shear Stress Distributions in Upper Face SheetmFlat Temperature Proffie

21
-150 x 103

Peak compression point

-125 o x = -89,245 Ib/in 2

-100

a x ,

-75

ib/in 2 _'_

-50 / Panel

0 x

96045O

Figure 10. Distribution of o x in the upper face sheet; 4S fixed-edge condition; flat temperature profile;

Tu = 900 °F, T l = 200. °F.

-150 x 103

Peak compression point

-125 ay = -87,430 Ib/in 2

-100

Oy,

ib/in2 -75

-50

Panel

-25 corner

0

Oy _ Oy

960451

Figure 11 Distribution of o in the upper face sheet; 4S fixed-edge condition; flat temperature profile;

"o o Y

T u =900 F,T l--200 F.

30 x 103 _- 1;xy = -23,827 Ib/in 2 = 23,827 Ib/in 2

25 &-) 1;_

'b/in2 11_ /Fca_i/e r

Axes of J .........

symmetry_

_Xxy

960452

Figure 12. Distribution of T,xy in the upper face sheet; 4S fixed-edge condition; flat temperature profile;

T u = 900 °F, T I = 200 °F.

22
-150 x 103

0 X,

Ib/in2

-125 _ Peak compression point

-1O0 °'x = -26,161 Ib/in 2

-75

-50 _lz, o x

-250

O x°X

Figure 13. Distribution of o x

T u = 900 °F, T l = 200 °F.

Panel

corner- 7

in the upper face sheet; 4S free-edge condition; fiat temperature profile;

O'y,

Ib/in2

-150 x 103

-125 1 _ Peak compression point

-100 p Oy = -25,783 Ib/in 2

F

-75 z, Oy

-50 t __I Panel

-250 7

°Y"-,c=-_ Oy

Figure 14. Distribution of Oy

T u = 900 °F, T l = 200 °F.

960454

in the upper face sheet; 4S free-edge condition; flat temperature profile;

30 x 103 _-'_xy = -23,904 Ib/in 2

A _ /-Panel

_/ corner

sAXyeS°let ry _,,,,,___ __ _"

25

20

_xy'

15

Ib/in 2

10

5

0

Figure 15. Distribution of X,xy

T u = 900 °F, T l = 200 °F.

960455

in the upper face sheet; 4S free-edge condition; flat temperature profile;

23
Figure 16. Distribution of o x

T u = 900 °F; T l = 200 °F.

-150 x 103 /- ° x = -107,470 Ib/in2

__i2_s_,__ eVerywhere

-125

ox, _ oo

ib/in2 -75

-5O

-25

0

Panel

96O456

in the upper face sheet; 4C fixed-edge condition; flat temperature profile;

Ib/in2

Figure 17. Distribution of Oy

T u = 900 °F, T l = 200 °F.

-150 x 103 Oy = -107,470 Ib/in2

-125 -1O0

Oy, -75 /

Y 0

-y

-5O

-25

0

Panel

960457

in the upper face sheet; 4C fixed-edge condition; flat temperature profile;

30 x 103

25 _xy = 0 even/where

"_xy' 20 i

2 15 L

Ib/in Az, x_ t

10 _ I-'-xy L Panel

5r ____t_x [. corner-]

96O458

Figure 18. Distribution of Xxy in the upper face sheet; 4C fixed-edge condition; flat temperature profile;

T u = 900 °F, T l = 200 °F.

24
) '

-150 x 103

-125 f _Peak compression point

°x' -100 [ °x = -46,177 Ib/in2

ib/in2 -75

-50

-25

0

X

OS °x

Figure 19. Distribution of o x

T u = 900 °F, T 1 = 200 °F.

_ /--Panel

._/ corner

960459

in the upper face sheet; 4C free-edge condition; flat temperature profile;

-150 x 103

L _Peak compression point 25 [ Oy = -45,801 Ib/in2

-100

Oy,

Ib/in2

-50

-25 /-Panel

0 ,/ comer

Oy_ Oy

96O460

Figure 20. Distribution of Oy in the upper face sheet; 4C free-edge condition; flat temperature profile;

T u = 900 °F, T l = 200 °F.

30 x 103

ib/in2 15

Z, Xxy 1°1" ¢+) / / Panel

5t" _x r _c°rner7

/

"_ Xxy

960461

Figure 21. Distribution of "_xy in the upper face sheet; 4C free-edge condition; flat temperature profile;

T u = 900 °F, T l = 200 °F.

25
Normal and Shear Stress Distributions in Lower Face Sheet--Flat Temperature Profile

26
-150 x 103

Peak compression point

-125 ox = -62,948 Ib/in 2

-100

0 x,

ib/in2 -75

-50

Panel

-25 corner

0

<°x 96O462

Figure 22. Distribution of o x in the lower face sheet; 4S fixed-edge condition; flat temperature profile;

T u = 900 °F, T l = 200 °F.

-150 x 103

Peak compression point

-125

Oy = -64,010 Ib/in 2

-100

-75

Ib/in 2

-50 J_"_

_ _'__- Panel

-25 corner

0

Oy _ Oy

96O463

Figure 23. Distribution of Oy in the lower face sheet; 4S fixed-edge condition; fiat temperature profile;

T u = 900 °F, T l = 200 °F.

- -¢xy = 23,827 Ib/in2

30 x 103 _(+) _'_

• xy = -23,827 Ib/in2

25

20 (-)

_x'y'

15

Ib/Jn 2

10

5

Panel

0 corner

_:xy of symmetry

960464

Figure 24. Distribution of Xxy in the lower face sheet; 4S fixed-edge condition; fiat temperature profile;

T u = 900 °F, T l = 200 °F.

27
150 x 103

_X _

Ib/in2

Figure 25. Distribution of o

T u = 900 _F, T l = 200 °F.

125

Peak tensile stress point

100 ox = 25,671 Ib/in2

75

.50 _ iZ,Ox

0

<Ox

Panel

corner -7

96O465

in the lower face sheet; 4S free-edge condition; flat temperature profile;

O'y,

Ib/in2

Figure 26. Distribution of Oy

T u = 900 °F, T 1 = 200 °F.

150 x 103

125 f

100 -"

75

50

25

0

Peak tensile stress point

Oy = 22,931 Ib/in2 i

/

Az,o,, . k

__ Panel

7

Y 0

o,, Y _ 0_____ l_

y ---_Oy

96O466

in the lower face sheet; 4S flee-edge condition; flat temperature profile;

_xy'

Ib/in2

Figure 27. Distribution of Xxy

T u = 900 °F, T 1 = 200 °F.

28

30 x 103 "¢xy= 23,755 Ib/in2

"_xy = -23,755 Ib/in2

25

20

15

10

5

Panel

0 corner

_xy -Axes of symmetry

960467

in the lower face sheet; 4S free-edge condition; fiat temperature profile;
-150 x 103

-125

-100

Ox,

ib/in2 -75

-50

-25

0

Figure 28. Distribution of o

X

T u = 900 °F, T l = 200 °F.

So x = -19,190 Ib/in 2

everywhere t

"__ z' °x x [" Panel

in the lower face sheet; 4C fixed-edge condition; flat temperature profile;

-150 x 103

-125

-100 SOy =-19,190 Ib/in 2 f

Oy, everywhere

-75

Ib/in2- = / _z, 0 I_

-50 Y x Pane_

-25

0

Oy _Oy

96O469

Figure 29. Distribution of Oy in the lower face sheet; 4C fixed-edge condition; flat temperature profile;

T u = 900 °F, T l = 200 °F.

30 x 103

25

2O

1; ,

xy 1_ b /-'rv,, = 0 everywhere

i;i 

[ ._ t z, 1;xy Panel

5 t. __l_R_/_-xr corner--/

96O470

Figure 30. Distribution of "_xy in the lower face sheet; 4C fixed-edge condition; flat temperature profile;

T u = 900 °F, T l = 200 °F.

29
150 x 103

r"

125 _ _ Peak tensile stress point

100

°x' 75

Ib/in2

50

/- Panel

250 / corner

960471

Figure 31. Distribution of o x in the lower face sheet; 4C free-edge condition; flat temperature profile;

T u = 900 °F; T l = 200 °F.

150 x 103

,t

125 _ _ Peak tensile stress point

100

Oy, 75

Ib/in2

50

/- Panel

250 / corner

Oy__=_..Oy

960472

Figure 32. Distribution of Oy in the lower face sheet; 4C free-edge condition; flat temperature profile;

T u = 900 °F, T l = 200 °F.

30 x 103

I f

1;xY' 20 "_xy < 219 Ib/in2

ib/in2 15

!0 (+) _z, Xxy Panel

5_ ___¢_/x _ c°rner 7

_l;xy

960473

Figure 33. Distribution of Xxy in the lower face sheet; 4C free-edge condition; flat temperature profile;

T u = 900 °F, T l = 200 °F.

3O
Transverse Sheer Stress Distributions in Sandwich Core--Flat Temperature Profile
2.5 x 103

2.0

1.5

a:xz' 1.0

Ib/in2

.5

Y

= 2,216 Ib/in2

Panel

-.5 0 corner

0 "_xz

2,216 Ib/in2

96O474

Figure 34. Distribution of transverse shear stress r,xz in sandwich core; 4S fixed- or 4S free-edge condition; fiat temperature profile; T u = 900 °F, T 1 = 200 °F.

2.5 x 103 /-'_yz = 1,798 Ib/in 2

1.5

"_yz' 1.0

Ib/in2

.5

0

_-- Panel

-.5 corner

t0 Ty-z

960475

Figure 35. Distribution of transverse shear stress "_yz in sandwich core; 4S fixed- or 4S free-edge condition; fiat temperature profile; T u = 900 °F, T l = 200 °F.

32
3.0 x 103

2.5

"_xz' 2.0 [

Ib/in2 1.5 \'_xz = 0 everywhere

.50 X __

0 l:xz

Panel

corner

960476

Figure 36. Distribution of transverse shear stress Xxz in sandwich core; 4C fixed- or 4C free-edge condition; fiat temperature profile; T u = 900 °F, T l = 200 °F.

q

3.0 x 10"

2.5

2.0 f

"_yz' 1.5 \'_yz = 0 everywhere

F,.o 1z' 'z I.

.50 x ' _-Panel

comer

96O477

Figure 37. Distribution of transverse shear stress X,yz in sandwich core; 4C fixed- or 4C free-edge condition; fiat temperature profile; T u = 900 *F, T l = 200 °F.

33
Normal and Shear Stress Distributions in Upper Face SheetmDome Temperature Profile
• k

OX J

Ib/in2

-150 x 103

-125 i

-100

-75

-50

Peak compression point

o x = -75,961 Ib/in2

-25 /- Panel

0 / comer

Y

96O478

Figure 38. Distribution of o x in the upper face sheet; 4S fixed-edge condition; dome temperature profile;

Tu = 900 °F, T l = 200 °F.

-150 x 103

Peak compression point

-125 Oy = -75,796 Ib/in2

-100

O'y,

ib/in2 -75

-50

-25

_-Panel

corner

960479

Figure 39. Distribution of Oy in the upper face sheet; 4S fixed-edge condition; dome temperature profile;

T u = 900 °F, T l = 200 °F.

/-'_xy = -28,579 Ib/in2

30 x 103 _, "¢ = 28,579 Ib/in2

,b

111 /--Panel / corner

Axes of symmetry-_,/_

_ _ ,_ _l;xy

96O48O

Figure 40. Distribution of x,x in the upper face sheet; 4S fixed-edge condition; dome temperature

profile; T u = 900 °F, T l = 20_°F.

35
-100 x 103

Peak compression point

-75 o x = -26,140 Ib/in 2

-5o _ I z'°x F

°x' -25 ___mmll=_'_X r Panel

Ib/in2 J _ corner- I

25

50

96O481

Figure 41. Distribution of o x in the upper face sheet; 4S free-edge condition; dome temperature profile;

T = 900 °F, T l = 200 °F.

v /'i -100 x 103

-75

-50

Oy, -25

Ib/in 2

0

25

50

Peak compression point

Oy = -25,576 Ib/in 2

y Oy

k_Panel

corner

960482

Figure 42. Distribution of Oy in the upper face sheet; 4S free-edge condition; dome temperature profile;

T u = 900 °F, T! = 200 °F.

_- _x-y = -30,917 Ib/in2

30 x 103 _ F'_ = 30,917 Ib/in 2

Sl I_B/-Panel

0 / corner

Axes of symmetry-_J_

" " >" _'_xy

96O483

Figure 43. Distribution of Xxy in the upper face sheet; 4S free-edge condition; dome temperature profile;

T u = 900 °F, T l = 200 °F.

36
.-: i

Or x ,

Ib/in2

Figure 44. Distribution of o X

T u --900 °F, T l = 200 °F.

-150 x 103

f _ Peak compression point -125 °x = -96,192 Ib/in2

-100 r

-75 f

-50

-25 Panel

0 corner

960484

in the upper face sheet; 4C fixed-edge condition; dome temperature profile;

-150 x 103 _ Peak compression point

Oy = -96,087 Ib/in2

-125 z, Oy

-100

Oy, -75

Ib/in2

-50

-25

0

_- Panel

corner

96o485

Figure 45. Distribution of Oy in the upper face sheet; 4C fixed-edge condition; dome temperature profile;

T u = 900 °F, T l = 200 °F.

20 x 103 F "_xy= -12,984 Ib/in2 _xy = 12,984 Ib/in2

15 ._) \ " xy'

ib/in2 1_ /-Panel

o corner

Axes of symmetry-_"_

_l:xy

960486

Figure 46. Distribution of x x in the upper face sheet; 4C fixed-edge condition; dome temperature

profile; T u = 900 °F, T l = 20_°F.

37
-125 x 103

-100 _ Peak compression point

-75 °x = -45,488 Ib/in 2

ib/in2 -50

-25

Panel

,0 f

corner

960487

Figure 47. Distribution of o x in the upper face sheet; 4C free-edge condition; dome temperature profile;

T u = 900 °F, T l = 200 °F.

-125 x 103

Peak compression point

-1O0 Oy = -44,996 Ib/in2

Oy, -75

ib/in2 -50

-25

0

25

O'y corner

96O488

Figure 48. Distribution of Oy in the upper face sheet; 4C free-edge condition; dome temperature profile;

T u = 900 °F, T l = 200 °F.

20 x 103 r'_xy = -14,062 Ib/in 2

r

, 15_ _ (_) \_xy=

14,062 Ib/in2

_2 101- _ (+_

Ib/in 5 _ /-Panel

o ./ corner

Axes of symmetry-_/_

" " _" _'xy

960489

Figure 49. Distribution of "_xy in the upper face sheet; 4C free-edge condition; dome temperature profile;

T u = 900 °°F, T l = 200 °F.

38
Normal and Shear Stress Distributions in Lower Face SheetmDome Temperature Profile

39
-150 x 103

Peak compression point

-125 o x = -53,433 Ib/in 2

-100

O x,

ib/in2 -75

-50

-25 Panel

corner

0

<°x 960490

Figure 50. Distribution of o x in the lower face sheet; 4S fixed-edge condition; dome temperature profile;

T u = 900 °F, T 1 = 200 °F.

-150 x 103

-125 { Peak compression point

-100 Oy = -54,553 Ib/in2

Oy, -75

Ib/in2

-50 _ " _-_ /-Panel -25

0 x ,._/ corner

Oy.._::__Oy

960491

Figure 51. Distribution of Oy in the lower face sheet; 4S fixed-edge condition; dome temperature profile;

T u = 900 °F, T 1 = 200 °F.

30 x 103

-Cxy= 19,242 Ib/in2

25 _, , "_.,,,= -19,242 Ib/in2-,

5 Panel 0 S corner

Axes of symmetry-_ _g__ _

- - 7 _xx, y

96049"2

Figure 52. Distribution of x x in the lower face sheet; 4S fixed-edge condition; dome temperature

profile; T u = 900 °F, T l = 20_°F.

,_ 40
150 x 103

O x ,

Ib/in2

125

100

75

5O

25

0

Peak tensile stress point

o x = 21,084 Ib/in2

I _ I Z, 0 x

Y x

Panel

corner

96O493

Figure 53. Distribution of o x in the lower face sheet; 4S free-edge condition; dome temperature profile;

T u = 900 °F, T l = 200 °F.

150 x 103

125

100

Oy, 75

Ib/in250

25

0

Peak compression point

Oy = 18,251 Ib/in2

z, Oy

Panel

Oy _Oy

96O494

Figure 54. Distribution of Oy in the lower face sheet; 4S free-edge condition; dome temperature profile;

T u = 900 °F, T l = 200 °F.

30 x 103 1;xy = 17,086 Ib/in2

2025 "_xy = -17,086 Ib/?

"l:xy,

ib/in215 (-)

10

5 Panel

0 corner

Axes of

96O495

Figure 55+ Distribution of "_xy in the lower face sheet; 4S free-edge condition; dome temperature profile;

T u = 900 °F, T l = 200 °F.

41
-150 x 103

-125 Peak compression point

-100 o x = -29,399 Ib/in2

°x, °x f

-75

Ib/in2 -50 x

-25

0 _ _- Pane/er

_.-_x°

960496

Figure 56. Distribution of o x in the lower face sheet; 4C fixed-edge condition; dome temperature profile;

T u = 900 °F; T l = 200 °F.

-150 x 103

-125!

Peak compression point

-100 Oy = -28,160 Ib/in2 r

°_' -_ _ Iz'°_ I

Ib/in2 -50 __ x.. I. Panel

-250

Oy _ Oy

960497

Figure 57. Distribution of Oy in the lower face sheet; 4C fixed-edge condition; dome temperature profile;

T u = 900 °F, T l = 200 °F.

25 x 103

Xxy,

Ib/in2

20 _ Peak shear point

15 _:xy =+2,115 Ib/in2

10

5

__'_xy '" "LAxes of

0

-5

symmetry

Panel

corner-]

960498

Figure 58. Distribution of "r,x in the lower face sheet; 4C fixed-edge condition; dome temperature

profile; T u = 900 F, T l = 20_°F.

42
150 x 103

O x ,

Ib/in 2

125 _ Peak tensile stress point

100 ax = 36,994 Ib/in 2

75

50

25

0

Y

Panel

96O499

Figure 59. Distribution of o x in the lower face sheet; 4C free-edge condition; dome temperature profile;

T u = 900 °F, T l = 200 °F.

150 x 103

125 _ Peak tensile stress point

100 Oy = 36,743 Ib/in 2 r

Oy, 75

ib/in 2

50 _m_l___ Panel

Y

Oy --_c:=_..Oy

Figure 60. Distribution of oy in the lower face sheet; 4C free-edge condition; dome temperature profile;

T u = 900 °F, T l = 200 °F.

30 x 103

25 / _ Peak shear point _.

_xy' 20V l:xy= +2,757 Ib/in 2 [_

Ib/in2 11_I , (+) _ Panel

"¢xy Axes of

symmetry

960501

Figure 61. Distribution of -Cxy in the lower face sheet; 4C free-edge condition; dome temperature profile;

T u = 900 °F, T ! = 200 °F.

43
Transverse Shear Stress Distributions in Sandwich Core---Dome Temperature Profile

44
2.5 x 103

l;xz = 1,339 Ib/in 2

1.5 1;xz = 1,339 Ib/in2

TXZ,

Ib/in 2 1.0

.5 X

_-Panel

-.5 corner

96O502

Figure 62. Distribution of transverse shear stress Xxz in sandwich core; 4S fixed- or 4S free-edge condition; dome temperature profile; Tu = 900 °F, T l = 200 °F.

2.5 x 103

2.0

1.5

_yz' 1.0

Ib/in 2

.5

0

-.5

f'Cyz = 1,065 Ib/in2

/__ t:yz = -1,065 Ib/in2//7

.,__ _- Paoneler

t_t "_yz _-Axes of symmetry [

96O5O3

Figure 63. Distribution of transverse shear stress "gyz in sandwich core; 4S fixed- or 4S free-edge condition; dome temperature profile; T u = 900 °F, T l = 200 °F.

45
;i  ̧ ̧

L

WI

2.5 x 103

l:xz' 1.0

Ib/in2 .5

xz = 134 Ib/in2 i

134 Ib/in 2

__0_ _- Paneler

960504

Figure 64. Distribution of transverse shear stress "txz in sandwich core; 4C fixed-edge condition; dome

temperature profile; T u = 900 °F, T l = 200 °F.

2.5 x 103

2.0

1.5

"tYZ' 1.0

Ib/inz

.5

-.5

/-'t:y z = 86 Ib/in2 I

.U 1 r

-86 Ib/in2

_- Panr_er

960505

Figure 65. Distribution of transverse shear stress Xy z in sandwich core; 4C fixed-edge condition; dome

temperature profile; T u = 900 °F, T l = 200 °F.

': 46
2.5 x 103

2"0 f

1.5 "txz = 142 Ib/in 2

Ib/in2 " / _ I -" /

Y 0

-.5 _ _ 0 _ corner

O_xz _'_

960506

Figure 66. Distribution of transverse shear stress "txz in sandwich core; 4C free-edge condition; dome

temperature profile; T u = 900 °F, T l = 200 °F.

2.5 x 103

2.0

1.5

a:YZ' 1.0

Ib/in z

.5

-.5

= 88 Ib/in2 F

I_ Tz''z [

-88 Ib/in2

__- Panel

0 _ corner

960507

Figure 67. Distribution of transverse shear stress "_yz in sandwich core; 4C free-edge condition; dome

temperature profile; T u = 900 °F, T l = 200 °F.

47

• _i_ _ _ •

REPORT DOCU MENTATION PAGE FormApproved

OMB No. 0704-0188

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gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis

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J1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORTTYPE AND DATES COVERED

April 1997 Technical Memorandum

4.TITLE AND SUBTITLE 5. FUNDING NUMBERS

Thermostructural Behavior of a Hypersonic Aircraft Sandwich Panel

Subjected to Heating on One Side

S. AUTHOR(S)

William L. Ko

7.PERFORMINGORGANIZATIONNAME(S)ANDADDRESS(ES)

NASA Dryden Flight Research Center

P.O. Box 273

Edwards, California 93523-02"73

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

National Aeronautics and Space Administration

Washington, DC 20546-0001

WU 505-63-50-00-RS-00-000-01

8, PERFORMING ORGANIZATION

REPORT NUMBER

H-2103

10, SPONSORING/MONITORING

AGENCY REPORTNUMBER

NASA TM-4769

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABIUTY STATEMENT

Unclassified--Unlimited

Subject Category 39

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

Thermostructural analysis was performed on a heated titanium honeycomb-core sandwich panel.

The sandwich panel was supported at its four edges with spar-like substructures that acted as heat

sinks, which are generally not considered in the classical analysis. One side of the panel was heated to

high temperature to simulate aerodynamic heating during hypersonic flight. Two types of surface

heating were considered: (1) flat-temperature profile, which ignores the effect of edge heat sinks, and

(2) dome-shaped-temperature profile, which approximates the actual surface temperature distribution

associated with the existence of edge heat sinks. The finite-element method was used to calculate the

deformation field and thermal stress distributions in the face sheets and core of the sandwich panel.

The detailed thermal stress distributions in the sandwich panel are presented, and critical stress

regions are identified. The study shows how the magnitudes of those critical stresses and their

locations change with different heating and edge conditions. This technical report presents comprehensive, three-dimensional graphical displays of thermal stress distributions in every part of a titanium

honeycomb-core sandwich panel subjected to hypersonic heating on one side. The plots offer quick

visualization of the structural response of the panel and are very useful for hot structures designers to

identify the critical stress regions.

14. SUBJECTTERMS

Heat-sink effect, One-sided heating, Sandwich panels, Thermal deformations,

Thermal stress analysis, Thermal stress distributions

17. SECURITY CLASSIFICATION 118. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION

OF REPORT OFTHIS PAGE OF ABSTRACT

Unclassified Unclassified Unclassified

NSN 7540-01-280-5500 Available from the NASA Center for AeroSpace Information, 800 Elkridge Landing Road,

Linthicum Heights, MD 21090; (301)621-0390

15. NUMBER OF PAGES

52

16. PRICE CODE

A04

20, LIMITATION OF ABSTRACT

Unlimited

Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18

298-102
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