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NASA Technical Memorandum 4769
Thermostructural Behavior of a
Hypersonic Aircraft Sandwich
Panel Subjected to Heating onOne Side
William L. Ko
Dryden Flight Research Center
Edwards, California
National Aeronautics and
Space Administration
Office of Management
Scientific and Technical
Information Program
1997
https://ntrs.nasa.gov/search.jsp?R=19970017836 2018-06-04T08:28:02+00:00Z
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 .................................................................. 6Thermal 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 tem-
perature 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) dome-
shaped-temperature profile, which approximates the actual surface temperature distribution associatedwith 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 ther-
mal 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 heat-
ing and edge conditions. This technical report presents comprehensive, three-dimensional graphical dis-
plays 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
TU
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 com-
plexity (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
fthermal 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 sand-
wich 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 thermo-
structural 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 iden-
tify 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 t s . 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 typesof 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 sub-
structures 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 x-
and 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 finite-
element 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 thermostruc-
tural analysis. The panel face sheets were modeled with E43 elements (quadrilateral membrane and bend-
ing 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, pin-
ended 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 stiff-
ness 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 ITable 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 sandwichpanel 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" sec-
tion. 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 sand-
wich 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 gener-
ated 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 dome-
shaped 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 calculat-
ed from equation (1) falls pictorially on that calculated from the finite-element method (for the flat tem-
perature 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,andalsointheadequacyof thefinite-elementmodelused.
Thedeflectionequation(1) andthefinite-elementmodelswerealsousedto studytheeffectof trans-verseshearonpaneldeflections.Table4 lists thepanelmaximumdeflectionsWma 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 condi-
tions.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
Dome0.3050 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 sad-
dle 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 fixed-
and free-edge cases (figs. 12 and 15) are distorted bell-shaped within each quarter-panel region. The mag-
nitude 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 compres-
sive 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 fixed-
edge 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 free-
edge 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 sand-
wich 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 concen-
trations 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 trans-
verse 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 bound-
ary of the central plateau zone and not at the panel's edges. The shear stress distributions for the 4S fixed-
and 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 tem-
perature 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
Edgecondition 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/in2condition "r'xz" Xyz ' "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 every-where 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 condi-
tions) 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 Sand-
wich 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 Com-
posite Sandwich Panels Under Different Thermal Environments, NASA TM-4321, September1991.
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," Proceed-
ings 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 panelregion 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 1E22"-1 _-E4
(a) 4S edge condition (fixed).
7
k960443
JzX
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 t0-12 -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
-100a x ,
-75ib/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 _ Oy960451
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 210
5
0
Figure 15. Distribution of X,xyT 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,_ ooib/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 LIb/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
0X
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 point25[ Oy = -45,801 Ib/in2
-100Oy,
Ib/in2-50
-25 /-Panel0 ,/ comer
Oy_ Oy96O460
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 15Z, Xxy1°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
<°x96O462
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
-75Ib/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 210
5Panel
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.
125Peak tensile stress point
100 ox = 25,671 Ib/in275
.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 OyT 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
7Y 0o,, Y _ 0_____ l_
y ---_Oy96O466
in the lower face sheet; 4S flee-edge condition; flat temperature profile;
_xy'
Ib/in2
Figure 27. Distribution of XxyT u = 900 °F, T 1 = 200 °F.
28
30 x 103 "¢xy= 23,755 Ib/in2
"_xy = -23,755 Ib/in225
20
15
10
5Panel
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 oX
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 fOy, 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
2O1; ,
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 103r"
125 _ _ Peak tensile stress point
100
°x' 75Ib/in2
50
/- Panel250 / 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, 75Ib/in2
50
/- Panel250 / corner
Oy__=_..Oy960472
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 f1;xY' 20 "_xy < 219 Ib/in2
ib/in2 15
!0 (+) _z, Xxy Panel5_ ___¢_/x _ c°rner 7
_l;xy960473
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 condi-
tion; fiat temperature profile; T u = 900 °F, T 1 = 200 °F.
2.5 x 103 /-'_yz = 1,798 Ib/in 2
1.5
"_yz' 1.0Ib/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 condi-
tion; 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
Panelcorner
960476
Figure 36. Distribution of transverse shear stress Xxz in sandwich core; 4C fixed- or 4C free-edge condi-
tion; 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 condi-
tion; 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 /- Panel0 / 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
_-Panelcorner
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/in230 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 PanelIb/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 20
25
50
Peak compression point
Oy = -25,576 Ib/in 2
y Oy
k_ Panelcorner
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 / cornerAxes 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 oX
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
-25Panel
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, -75Ib/in2
-50
-25
0
_- Panelcorner
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 temperatureprofile; 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, -75ib/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 2r
, 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 Panelcorner
0
<°x960490
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/in2Oy,
-75Ib/in2
-50 _ " _-_ /-Panel-25
0 x ,._/ corner
Oy.._::__Oy960491
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/in225 _, , "_.,,,= -19,242 Ib/in2-,
5 Panel0 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
Panelcorner
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°x960496
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 _ Oy960497
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 temperatureprofile; 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 250 _m_l___ Panel
YOy --_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 ofsymmetry
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 condi-
tion; dome temperature profile; Tu = 900 °F, T l = 200 °F.
2.5 x 103
2.0
1.5
_yz' 1.0Ib/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 condi-
tion; 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' 1.0Ib/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' 1.0Ib/in z
.5
-.5
= 88 Ib/in2 FI_
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
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April 1997 Technical Memorandum4.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 CenterP.O. Box 273
Edwards, California 93523-02"73
9.SPONSORING/MONOTORINGAGENCYNAME(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/MONITORINGAGENCY 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 heatsinks, which are generally not considered in the classical analysis. One side of the panel was heated tohigh temperature to simulate aerodynamic heating during hypersonic flight. Two types of surfaceheating 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 distributionassociated with the existence of edge heat sinks. The finite-element method was used to calculate thedeformation 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 theirlocations change with different heating and edge conditions. This technical report presents compre-hensive, 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 quickvisualization 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
A0420, LIMITATION OF ABSTRACT
Unlimited
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