Minimum-weight design of compressively loaded stiffened panels for postbuckling response

About: The article was published on 1995-04-10 and is currently open access. It has received 4 citations till now. The article focuses on the topics: Minimum weight.

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MINIMUM-WEIGHT
DESIGN
OF
COMPRESSIVELY
LOADED
STIFFENED
PANELS
FOR
POSTBUCKLING
RESPONSE
by
Christine
Ann
Perry
Thesis
submitted
to
the
Faculty
of
the
Virginia
Polytechnic
Institute
and
State
University
in
partial
fulfillment
of
the
requirements
for
the
degree
of
MASTER
OF
SCIENCE
in
Engineering
Mechanics
APPROVED:
.
i/
-Z.
Giirdal,
Chairman
Yi
b
A
toa
Ak
.
Hyer
E.R.
Johnson
V
L.T.
Watson
March,
1995
Blacksburg,
Virginia
Key
Words:
Buckling,
Composite
Design,
Imperfection
Sensitivity,
Postbuckling,
Stiffened
Panels

ub
LD
VeEs
14s
PAT]
Care.

MINIMUM-WEIGHT
DESIGN
OF
COMPRESSIVELY
LOADED
STIFFENED
PANELS
FOR
POSTBUCKLING
RESPONSE
by
Christine
Ann
Perry
Committee
Chair:
Dr.
Zafer
Giirdal
Engineering
Mechanics
(ABSTRACT)
A
computationally
efficient
procedure,
NLPANOPT,
is
developed
for
the
preliminary
design
of
minimum-weight
thin-walled
stiffened
composite
panels
loaded
in
uniaxial
compression
based
on
a
geometrically
nonlinear
analysis.
An
approximate,
semi-analyti-
cal
nonlinear
analysis
code,
NLPAN,
which
requires
buckling
eigenfunction
information
from
the
buckling
analysis
code,
VIPASA,
is
linked
with
the
optimization
code
ADS.
A
blade-stiffened
and
T-stiffened
panel
are
designed
for
specified
loads
using
NLPANOPT
for
postbuckling
response
and
PASCO
for
buckling-critical
response.
Comparisons
of
panel
weight
and
imperfection
sensitivity
between
the
NLPANOPT
designs
and
PASCO
designs
are
presented.
In
general,
the
designs
obtained
with
NLPANOPT
are
lighter
and
less
imperfection
sensitive
than
the
designs
obtained
with
PASCO.
The nonlinear
analysis
allows
for
a
more
accurate
prediction
of
the
true
strength
of
the
stiffened
structure,
by
accounting
for
postbuckling
strength
and
modal
interaction.
The
effect
of
laminate
stack-
ing
sequence
is
also
investigated.
The
current
design
procedure
requires
the
stacking
sequence
to
be
prescribed,
proving
to
be
a
limitation
in
the
design
procedure.

Acknowledgements
This
material
is
based
upon
work
supported
under
a
National
Science
Foundation
Gradu-
ate
Fellowship.
Any
opinions,
findings,
conclusions
or
recommendations
expressed
in
this
publication
are
those
of
the
author
and
do
not
necessarily
reflect
the
views
of
the
National
Science
Foundation.
This
study
was
also
supported
by
the
NASA-Virginia
Tech
Compos-
ites
Program
under
NASA
Grant
NAG-1-643.
The
author
would
like
to
thank
Dr.
Giirdal
and
Dr.
James
H.
Starnes,
Jr.
for
their
advice
and
direction
throughout
this
work,
along
with
Dr.
Hyer,
Dr.
Johnson,
and
Dr.
Watson
for
their
time
and
interest.
The
work
of
Dr.
Frederick
Stoll
on
the
nonlinear
analysis
method
used
in
this
design
procedure
and
his
continuous
support
is
greatly
appreciated.
Thanks
are
also
due
to
Nagendra
Somanath,
Scott
Ragon,
and
Brian
Tatting
for
their
input
and
assistance.
Finally,
the
author
would
like
to
thank
her
family
for
their
support
from
the
very
beginning.
Acknowledgements
iii

Table
of
Contents
1.0
Introduction
and
Literature
Review
..............cccccccssscssssscscscccscccccscsooee
I
LL
Imtroduction
en...
ceeccscceesssecesssseceesssneecesesueeesscseeecssnseesesesseseecesueacecesseaaaeecesseenaees
1
1.2
Literature
REVICW........c
ce
eesccssssesssnscesssscesssecessesessssecesseeceseeecssaeesessaeeeeseassesessneeeess
5
2.0
ANALYSIS
......ccccccccccssscsscccssssssseccssssssscrssssssscssssssssscsscssssssssscsessssssscccrscscoee
LL
2.1
Nonlinear
Panel
Analysis
(NLPAN)...........c:::cccssseccesssecceessecescecssnseesecssessseeeeeeas
11
2.1.1
Nonlinear
Plate
Theory
............cccccccccccessssnneeecessessneeeeeeeeseseseeeeseeeseeseeneatas
12
2.1.2
Linked-Plate
Geometry
.00.....
ccc
eesccccesseeeeceeeesnesseeneceeaaecenseaeeetseneeeeseeatens
17
2.1.3
Expansions
of
Displacement
FUNCTIONS
.............ccesscceceessssessseceeeeeeeeeeeeenees
21
2.1.4
Solution
of
Equations...
ceccesesscecsseeeeeseeeesseceeseeeeeecesessaeeetesseeeeseneees
27
2.2
Mode
Selection
.........cccccccccccccsesssssssssseceeeececcesensesnesaeaeeseeseeseeseseseseesesessessneaneaes
28
2.3 Imitial
Imperfections...
ec
eeecceeseeeceseecsnceeeeseesesaeeeesseeecesaeeesssacesesaeerseeaeees
44
3.0
Design
Formulation
..............cccsssssssssscsccsssssscscssesssssssessscsess
seccssssseeseee
F/
3.1
Program
Organization
........
eee
eeeecesseeeesseceesaseessccesesceesseecessteeceseeesssereesesaeeseees
47
3.2
Optimization
Program
-
ADS
ooo...
eee
ceeseeeeseeceeseeseeeneeessneecesaceesesaseseeeaceseneaeeees
49
3.3
Statement
of
Minimization
Problem..................ccccccccccccceseeeesesssessssenescsssnaceeeeeeeees
49
3.4
NLPAN
Refinements
.............ccccccccecccssecnccceceececeeeeeceececeeceseeeceeseeseseaasaeesssesceeeceees
51
3.4.1
Material
Failure
Constraint
.............ccccccccccsssetecceeceseeeeseteeseessesessesseensneneaes
51
3.4.2
Gradient
Calculations..............cccccccccccesessccceeesessececceesesesteeeececesenssneseseeeeeens
52
4.0
Design
Study
..............cccssssesssssccssssccscssssssssscccssccssscscscsccscccoscccsosesesssssses
DO
4.1
Design
of
Blade-Stiffened
Panel
for
Four
Levels
of
Axial
Compressive
Loads
55
4.1.1
Case
1:
100
Ib/in
Design
L0ad.......
eee
eeceeeeceneesesanasaeceneaeeacenseeeseees
57
4.1.2
Case
2:
1000
Ib/in
Design
Lad...
cccceceessseseetettaaceeeeeeeneeeeeseeeeeseees
58
4.1.3
Case
3:
5000
Ib/in
Design
Load...
cece
ccceeeeeessesneeeeeeeeseceaneeeeeeeeesseseeaee
70
4.1.4
Case
4:
10000
Ib/in
Design
Load...
eee
cccenennnceeceeeeeeeececeeeeeeeeeeeenenes
86
4.2
Effect
of
Skin
Laminate
Stacking
Sequence...
eee
ceeeeeeeeeneceeceeetenseseeneees
90
4.3
Design
of
Blade-Stiffened
Panel
with
Flanges
2.00...
eeeneeeeeeeeeeeeeeneeee
98
4.3.1
1000
Ib/in
Design
Load...
eee
ceeeceesennceeeteeeessaneceteeeesessneeeeeeseeeserees
100
Table
of
Contents
iv