U.S. patent number 3,663,347 [Application Number 05/055,537] was granted by the patent office on 1972-05-16 for honeycomb panels formed of minimal surface periodic tubule layers.
Invention is credited to Alan H. Schoen.
United States Patent |
3,663,347 |
Schoen |
May 16, 1972 |
HONEYCOMB PANELS FORMED OF MINIMAL SURFACE PERIODIC TUBULE
LAYERS
Abstract
Panels including honeycomb cores formed of minimal surface
periodic tubule layers are described. Each tubule layer is defined
as being formed of minimal surface elements that orthogonally
intersect all of the faces of a kaleidoscopic cell at least once.
In other words, for purposes of definition, the tubule layers are
broken into elemental sections. The elemental sections are defined
as minimal surface elements, i.e., elements having a mean curvature
at all points on the surface that is equal to zero. These elements
are further defined inside of kaleidoscopic cells wherein they
orthogonally intersect all faces of the kaleidoscopic cell with
which they are associated at least once. The minimal surface
elements are smoothly interconnected to form tubule layers which
are stacked in a reflection image-like manner to form a honeycomb
core having no internal discontinuities.
Inventors: |
Schoen; Alan H. (West Concord,
MA) |
Assignee: |
|
Family
ID: |
21998512 |
Appl.
No.: |
05/055,537 |
Filed: |
July 16, 1970 |
Current U.S.
Class: |
428/116; 52/80.1;
52/DIG.10; 428/542.2; 482/35; D25/117; 428/178 |
Current CPC
Class: |
E04C
2/3405 (20130101); Y10T 428/24149 (20150115); Y10T
428/24661 (20150115); Y10S 52/10 (20130101) |
Current International
Class: |
E04C
2/34 (20060101); B32b 003/12 () |
Field of
Search: |
;156/197 ;161/68,69,127
;29/455LM ;52/61S,80 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Goolkasian; John T.
Assistant Examiner: Epstein; Henry F.
Claims
What is claimed is:
1. A honeycomb core panel comprising:
first and second parallel boundary surfaces; and,
a honeycomb core located between said first and second parallel
boundary surfaces, said honeycomb core comprising at least one
minimal surface periodic tubule layer, said minimal surface tubule
layer being defined by a plurality of approximately minimal surface
elements formed in a smooth continuous manner, each of said minimal
surface elements being definable within a kaleidoscopic cell.
2. A honeycomb core panel as claimed in claim 1 wherein the outer
boundary of said honeycomb core intersects said first and second
parallel boundary surfaces in simple closed curves.
3. A honeycomb core panel as claimed in claim 2 wherein said simple
closed curved intersections between said honeycomb core and said
first and second parallel boundary surfaces are substantially
orthogonal at all points.
4. A honeycomb core panel as claimed in claim 3 wherein said
honeycomb core comprises a plurality of tubule layers, said layers
being stacked in an image-like manner whereby no internal
discontinuities are formed in said honeycomb core at the junctions
between said layers.
5. A honeycomb core panel as claimed in claim 4 wherein said
plurality of minimal surface periodic tubule layers is two in
number.
6. A honeycomb core panel as claimed in claim 4 wherein said
plurality of minimal surface periodic tubule layers is three in
number.
7. A honeycomb core panel as claimed in claim 3 wherein said simple
closed curved intersections between said honeycomb core and said
first and second parallel boundary surfaces are approximately
circular.
8. A honeycomb core panel as claimed in claim 1 wherein said
honeycomb core comprises a plurality of tubule layers, said layers
being stacked in an image-like manner whereby no internal
discontinuities are formed in said honeycomb core at the junctions
between said layers.
9. A honeycomb core panel as claimed in claim 8 wherein said
plurality of minimal surface periodic tubule layers is two in
number.
10. A honeycomb core panel as claimed in claim 8 wherein said
plurality of minimal surface periodic tubule layers is three in
number.
11. A honeycomb core panel as claimed in claim 1 wherein the outer
surface of said honeycomb core terminally intersects said first and
second parallel boundary surfaces substantially orthogonally at all
points.
12. A honeycomb core panel as claimed in claim 1 wherein each of
said minimal surface elements intersects each surface of said
kaleidoscopic cell at least once and each intersection is
orthogonal.
13. A honeycomb core panel as claimed in claim 1 wherein said
kaleidoscopic cell is a rectangular parallelopiped.
14. A honeycomb core panel as claimed in claim 1 wherein said
kaleidoscopic cell is an equilateral triangular prism.
15. A honeycomb core panel comprising:
first and second parallel boundary surfaces; and
a honeycomb core located between said first and second parallel
surfaces, said honeycomb core comprising at least one constant mean
curvature periodic tubule layer, said constant mean curvature
periodic tubule layer being defined by a plurality of approximately
constant mean curvature elements formed in a smooth continuous
manner, each of said constant means curvature elements being
definable within a kaleidoscopic cell.
16. A honeycomb core panel as claimed in claim 15 wherein said
constant is zero.
17. A honeycomb core panel as claimed in claim 15 wherein said
honeycomb core comprises a plurality of tubule layers, said layers
being stacked in an image-like manner, whereby no internal
discontinuities are formed in said honeycomb core at the junctions
between said layers.
Description
ORIGIN OF THE INVENTION
The invention described herein was made by an employee of the
United States Government and may be manufactured and used by or for
the Government for governmental purposes without the payment of any
royalties thereon or therefor.
BACKGROUND OF THE INVENTION
This invention relates to honeycomb core panels and more
particularly, to honeycomb core panels that are light in weight
while possessing high strength and rigidity.
Various types of honeycomb core panels have been proposed and are
in use. They are used as walls and floors in constructing
buildings, for example. In addition, they have been used as desk
tops and other panels in furniture manufacture. In other words, any
place where it is desired to have a relatively thick panel that is
light in weight for its size, yet possesses high strength and
rigidity, a honeycomb core panel is useful.
Various types of honeycomb core panels of different design have
been constructed from a variety of materials, such as pressed
paper, plastic, or metal. Many honeycomb core designs utilize
corrugated sheets stacked in a parallel planar manner whereby
hollows are formed in the resultant honeycomb core. This honeycomb
core is then joined to boundary planar panels to form the resultant
honeycomb core panel. The major disadvantage of honeycomb core
panels of this nature is that discontinuities are created where the
corrugated sheets intersect one another and where they intersect
the outer panels. These discontinuities create "weak" points where
rupture of the honeycomb core panel is likely. Hence, the honeycomb
core panel is not as strong as desirable for its weight. More
recently, honeycomb core panels utilizing curved cellular members
that tend to eliminate internal intersections have been produced.
While curved cellular core panels have improved the
strength-to-weight ratio of honeycomb core panels, they have not
been entirely satisfactory. More specifically, curved cellular
cores are usually formed in planes and very often the intersection
between the planes is discontinuous, whereby weak points are
created. Moreover, the curves of the cellular cores do not provide
core panels that have an optimum strength-to-weight ratio.
Therefore, it is an object of this invention to provide a new and
improved honeycomb core panel.
It is a further object of this invention to provide new and
improved honeycomb core panels that have an optimum
strength-to-weight ratio.
It is a still further object of this invention to provide panels
having honeycomb cores that have no internal discontinuities, are
light in weight, and have a maximum strength-to-weight ratio.
SUMMARY OF THE INVENTION
In accordance with the principles of this invention, panels
including honeycomb cores located between boundary surfaces are
provided. The honeycomb cores are formed of minimal surface
periodic tubule layers. The minimal surface tubule layers are
defined as being formed of minimal surface elements that
orthogonally intersect all of the faces of a kaleidoscopic cell at
least once. In other words, for purposes of definition, the tubule
layers are broken into minimal surface elements. Each minimal
surface element is defined as having mean curvature at all points
on its surface equal to zero. These elements are further defined
inside of kaleidoscopic cells wherein they orthogonally intersect
all faces of their related kaleidoscopic cell at least once. These
minimal surface elements are smoothly interconnected to form an
overall tubule layer that has no discontinuities except at the
edges of the layers. In other words, the entire tubule layer has a
minimal surface form and will be subsequently referred to as a
minimal surface periodic tubule layer.
In accordance with a further principle of the invention, the
boundaries of the honeycomb cores intersect the boundary surfaces
orthogonally. As described above, the minimal surface periodic
tubule layers forming the honeycomb cores are composite and
sheet-like in form, not a structure of individual elements.
In accordance with still further principles of this invention, a
plurality of minimal surface periodic tubule layers are stacked in
a reflection image-like manner to form a relatively thick honeycomb
core between the boundary surfaces of the overall panel
structure.
It will be appreciated from the foregoing brief summary of the
invention that panels formed of layers having no internal
discontinuities are provided by the invention. Because of the lack
of discontinuities, structural weak points are eliminated. Further,
because the minimal surface tubule layers intersect the surfaces of
the overall honeycomb core panel structure at 90.degree., optimum
strength at the boundary discontinuity intersections are provided
by the invention. In addition, the invention has the versatility of
providing relatively thick panels, also with no internal
discontinuities, by stacking the tubule layers of the invention in
an image-like manner.
It will also be appreciated by those skilled in the art and others
that because the invention uses minimal surface honeycomb cores, it
optimizes core strength for the weight of the core material
involved. More specifically, the honeycomb core structures are
based on minimal surface forms in doubly curved surface
configurations whereby the mechanism of membrane action is
operative. This action leads to the maximum diffusion of applied
loads throughout the entire structure away from the point of load
application. Hence, maximum strength for a given weight is provided
by the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
The foregoing objects and many of the attendant advantages of this
invention will become more readily appreciated as the same becomes
better understood from the following detailed description when
taken in conjunction with the accompanying drawings, wherein:
FIG. 1 is a perspective view of a minimal surface element of a
tubule layer defined by a rectangular parallelopiped;
FIG. 2 is a perspective view of a portion of a tubule layer formed
of minimal surface elements of the type illustrated in FIG. 1;
FIG. 3 is a top view of a honeycomb core periodic tubule layer
formed of an array of tubule layer portions of the type illustrated
in FIG. 2;
FIG. 4 is a side view of a honeycomb core panel including a single
tubule layer of the type illustrated in FIG. 3;
FIG. 5 is a side view of a honeycomb core panel including two
tubule layers of the type illustrated in FIG. 3;
FIG. 6 is a side view of a honeycomb core panel including three
tubule layers of the type illustrated in FIG. 3;
FIG. 7 is a perspective view of a minimal surface element of a
tubule layer defined by an equilateral triangular prism;
FIG. 8 is a perspective view of a portion of a tubule layer formed
of minimal surface elements of the type illustrated in FIG. 7;
and,
FIG. 9 is a top view of a periodic tubule layer formed of an array
of tubule layer portions of the type illustrated in FIG. 8.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Prior to describing the preferred embodiments of the invention,
reference is made to a co-pending U. S. Pat. application Ser. No.
57,253 entitled, "Honeycomb Core Structures Formed of Minimal
Surface Tubule Sections", by Alan H. Schoen, filed July 22, 1970 .
That patent application describes in greater detail than this
application the structure and formation of honeycomb core
structures utilized to form the panels of this invention. As will
be better understood from the referenced co-pending patent
application, the minimal surface elements that form honeycomb core
structures can be defined inside of a group of seven kaleidoscopic
cells which are fundamental regions of discrete groups generated by
reflections. When thusly defined minimal surface elements are
formed in an appropriate manner, they form honeycomb core
structures which can be utilized to form the honeycomb core panels
of this invention.
Turning now to a description of the drawings which illustrate
preferred embodiments of the invention, FIG. 1 illustrates a
minimal surface element 11 defined inside of a rectangular
parallelopiped 13, one of the seven discrete kaleidoscopic
geometrical figures which can be used to define the edges of a
minimal surface element. The minimal surface element illustrated in
FIG. 1 has six curved edges 15, 17, 19, 21, 23, and 25. Each of the
curved edges intersects one of the faces of the rectangular
parallelopiped 13 orthogonally. Moreover, the minimal surface
element 11 has a mean curvature at all points that is equal to zero
(i.e., a minimal value) and it is not a plane.
While the exact size and nature of the minimal surface element 11
illustrated in FIG. 1 can be mathematically determined and
described, a considerably less complicated and time-consuming
method of determining the exact surface configuration can be used.
More specifically, a kaleidoscopic cell of the type described is
constructed out of plastic or some other transparent material. A
soap film is constructed inside of the transparent kaleidoscopic
cell and varied in position until the desired configuration is
formed. The correct configuration is obtained by blowing and
sucking air through a metal tube inserted into the transparent
kaleidoscopic cell through a suitable hole cut out of a corner (or
corners) of the cell. The configuration of the soap film is
determined to be that of the desired minimal surface by observing
when the film reaches the so-called stationary state, i.e., the
state of unstable mechanical equilibrium. Because of the frictional
drag between the soap film and the bounding faces of the enclosed
transparent kaleidoscopic cell, the soap film remains stationary in
this equilibrium position long enough for detailed measurements to
be made of the configuration of the soap film. These measurements
may be made using various optical techniques, such as the sighting,
along orthogonal axes, of a reflected laser beam.
Whenever the symmetry of the minimal surface element implies that
one or more straight line segments are contained in the surface of
the element, tightly stretched fine filaments are placed in the
positions of these line segments. This operation transforms the
unstable equilibrium of the soap film into a stable equilibrium and
the film then remains absolutely stationary indefinitely. This
situation is illustrated in FIG. 1. More specifically, when the
enclosing rectangular parallelopiped 11 is a cube, the six-edged
minimal surface element is in its most symmetrical form. At this
point, all three pairs of diagonally opposite vertices of the
minimal surface element 13 may be joined by straight line segments,
all of which lie in the surface of the minimal surface element. By
placing fine filaments along these lines, the minimal surface
element remains absolutely stationary indefinitely.
As an alternate method and, in fact, preferred method for deriving
the detailed configuration of a minimal surface element of the type
considered herein, the following technique can be employed. In
accordance with this technique, a closed polygonal boundary,
composed of straight line segments which are orthogonal,
respectively, to the planes containing the successive (curved)
edges of the minimal surface, is constructed from fine stretched
filaments. This polygonal boundary is dipped into a stable soap
solution to form a stable equilibrium minimal surface spanning the
boundary. A laser beam is directed onto the film at a large nuber
of points very near the polygonal boundary, around the entire
boundary of the soap film. Measurements are made of the orientation
of a line normal to the film at all points. Then, by making use of
the classical theory of Bonnet of the bending of simply connected
minimal surfaces, a good approximation of the detailed shape of all
of the curved edges of the desired minimal surface element is
derived. When a final model of this derived boundary for the
desired minimal surface element is constructed and dipped into a
suitable soap solution, a stable equilibrium model of the desired
minimal surface itself is obtained. From this point on, detailed
optical measurements using sightings along orthogonal axes of
laser-illuminated spots on the surface are employed, as described
above, to determine the configuration of the desired minimal
surface element.
The direct construction of a model of a given minimal surface
element in the form of a soap film orthogonally bounded by the
interior faces of an appropriate kaleidoscopic cell leads -- in the
cases described herein -- to a detailed determination of the
configuration of the minimal surface which does not depart
significantly from the true mathematical form of the surface.
Hence, for all intents and purposes, this form can be used to
obtain an approximately minimal surface element. However, as stated
above, the alternate method provides an independent means of
determining the configuration of each minimal surface element and
works for all of the minimal elements described herein.
FIG. 2 illustrates four minimal surface elements 11 of the type
illustrated in FIG. 1 joined in such a manner that a portion of a
minimal surface tubule layer having no internal discontinuities is
provided. The minimal surface tubule layer portion 27 illustrated
in FIG. 2 can further be defined inside of a rectangular
parallelopiped 29. The top and bottom of the rectangular
parallelopiped 29 illustrated in FIG. 2 are squares and the sides
are rectangles. By joining a plurality of tubule layer portions 27
of the type illustrated in FIG. 2 along their rectangular sides in
an image-like manner (i.e., the two opposing tubule layer portions
are mirror images of one another) an array or tubule layer is
created. FIG. 3 is a top view of such a tubule layer 31. While the
tubule layer 31 illustrated in FIG. 3 is, broadly, essentially
infinite, FIG. 3 does include side panels 33 and 37, and an end
panel 35 to illustrate the termination of the tubule layer.
FIG. 4 is a side view of a honeycomb core panel formed of a single
tubule layer 31 of the type illustrated in FIG. 3, parallel
boundary surfaces 39 and 41, and end panel 35. FIGS. 5 and 6 are
side views of honeycomb core panels formed of tubule layers of the
type illustrated in FIG. 3. The minimal surface periodic tubule
layers are stacked in an image-like (mirror) manner to double and
triple, respectively, the distance between the parallel outer
surfaces 39 and 41. The planes between layers are illustrated in
FIGS. 5 and 6 as dash-dot centerlines. It will be appreciated that
stacking tubule layers in an image-like (mirror) manner as
illustrated in FIGS. 5 and 6 results in a relatively thick
honeycomb core panel that lacks internal discontinuities.
From viewing FIGS. 3-6, it will be appreciated that the invention
provides a honeycomb core panel wherein the core is formed of
minimal surface periodic tubule layers. The tubule layers have no
internal discontinunities per se. Moreover, the layers intersect
one another in an image-like (mirror) manner whereby no
discontinuities are created at the planes of intersection. While
discontinunities do exist where the tubule layers intersect the
outer parallel surfaces as well as the end and side panels, because
these approximately circular intersections are orthogonal, optimum
discontinuity strength is provided at these points. Moreover,
because minimal surface forms are used by the invention, optimum
strength-to-weight ratio is provided. That is, the thickness of the
material forming the tubule layers can be decreased to a minimum
value while maximum strength is retained because the tubule layers
tend to distribute boundary panel forces in a multitude of
directions on account of the membrane action which derives from the
doubly curved character of the core structure. Because of this
force distribution, the likelihood of panel rupture is
lessened.
It will be appreciated that the minimal surface periodic tubule
layers 31 heretofor described can be formed in a unitary manner in
many different ways of many different materials. For example, the
information concerning the detailed surface configurations
previously derived can be utilized to create dies for compression
forming the layers from metal, plastic, or pressed paper. In
addition, injection molding techniques can be utilized with
suitable dies to form the layers from plastics. Other suitable
techniques will be apparent to those skilled in the art.
FIG. 7 illustrates an alternate embodiment of a minimal surface
element 43 formed inside of an equilateral triangular prism 45. As
with the rectangular parallelopiped, an equilateral triangular
prism falls within the seven kaleidoscopic cells described in more
detail in the referenced co-pending patent application. By suitably
mounting, in a composite or other manner, six minimal surface
elements 43 of the type illustrated in FIG. 7, a portion of a
tubule layer 47 of the type illustrated in FIG. 8 is obtained. And,
by suitably arraying a plurality of tubule layer portions of the
type illustrated in FIG. 8, a honeycomb core periodic tubule layer
of the type illustrated in FIG. 9 is obtained. More specifically,
FIG. 9 is a top view of an alternate embodiment of a honeycomb core
periodic tubule layer formed of minimal surface tubule layer
portions of the type illustrated in FIG. 8. The minimal surface
periodic tubule layer illustrated in FIG. 9 can be mounted between
surfaces in the manner illustrated in FIGS. 3-6 to form an
alternate embodiment of a honeycomb core panel. Again, the minimal
surface periodic tubule layers can be formed in a composite unitary
manner by different methods utilizing different materials.
It will be appreciated by those skilled in the art and others from
the foregoing description of preferred embodiments of the invention
and the referenced co-pending patent application that only two of a
multitude of panels having different types of minimal surface
periodic tubule layers have been described. It will also be
understood, however, that other types of panels utilizing tubule
cores of the general type described in the referenced co-pending
patent application fall within the purview of this invention.
It will also be appreciated that the size of the tubules and the
thickness of the material forming the tubule layers, as well as
other parameters, will be determined by the strength, rigidity and
weight requirements of the ultimate panel. These requirements and
others will also determine the material to be used in the boundary
panels as well as the honeycomb core structure. Hence, the
invention can be practiced in many ways not specifically described
herein.
* * * * *