Design Process

Obtain applied loads

Obtain material properties

Come up with a structural configuration

Analyze structural configuration to

meet loads without failure (static and fatigue)

minimize weight

minimize cost

optimize other quantities (frequency, radar signature, etc.)

Iterate

check if

concept is

manufacturable

verify analysis

by tests

Design Process

Applied

loads

Material

properties

Design

Reqts

Structural

configuration

Analysis of

Structural

configuration

Meet loads

and design

reqts?

Design has

desirable

attributes?

N

Y

N

Y Done

Taxi, take-off,

flight, land,

crash

Fit, form, function;

No failure under

load;

Strength,

Stiffness,

Density

Preliminary

design

Producibility

trialsTest

More than 50% and, sometimes, as much as

70% of the cost is locked in during preliminary design!!

Applied Loads and Usage

Different users perform the same maneuver differently resulting in different loads

95th percentile (or some other high percentile) of max load occurring in maneuver simulation) to cover most cases

Load

TimeEntry Exit

max load during one simulation

nominally same maneuver

simulated many times

Peak

loads

95th

percentile

Load

Material

Variability (scatter)

raw material

manufacturing

etc.

Environmental effects

Effect of damage

A,B-Basis

values

mean

Material scatterTypical Uni-directional Gr/E (0 deg)

TensionCompression

B-Basis

A-Basis

Material scatter

B-Basis (10th percentile): 90% of the strength tests will have higher failure load

A-Basis (1 percentile): 99% of the strength tests will have higher failure load

typically, A-Basis is used for single-load path primary structure and B-Basis is used for multiple-load path primary

or secondary structure (failure does not lead to loss of

vehicle)

Effect of environment

knockdown due to environment (=separation between red horizontal lines): 5-30% depending on property

Typical Uni-directional Gr/E

0

200

400

600

800

1000

1200

1400

1600

1800

2000

-70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80

Temperature (deg C)

Strength

(MPa)

CT RT ET

ambient

wettension

compression

Effect of damage

(1) Whitehead, R.S., Lessons Learned for Composite Structures, Proc First NASA Advanced Composites Technology Conference, Seattle WA, 1990, pp 399-415

00.10.20.30.40.50.60.70.80.91

0 10 20 30 40 50 60 70

Damage diameter (mm) or void content (%)

Undam/damaged

compr strength

Flawed hole

Porosity

Delamination

Impact

mm

%

0 0.5 1.0 1.5 2.0 2.5

Compression loading(1)

damaged/undam

Effect of Damage (contd)

Design structure to take ultimate load in presence of Threshold Of Detectability or Barely Visible

Impact Damage

Design structure to take limit load in presence of (some) Visible Damage (VD) (e.g. 6 mm dia hole)

If TODload capability / VDload capability

Design value

Strength

mean RTA

undamaged

mean with worst

environmental

effects undamaged

mean with worst

environmental effects

and worst damage

B-Basis

design value

A-Basis

design value

5-20%

Depending on

material and

property

10-35% depending on

material and

propertydesign values

Combine worst effects for material scatter, environment, and damage

Cutoff strains (or stresses)

Worst

Knockdown

source

Knockdown

fraction

Environment

(ETW compr or

shear)

0.8

Damage (BVID) 0.65

Material scatter

(CV~11%)

0.8

Mean undamaged failure strain (compression)

~ 11000 microstrain (0.011)

Cutoff strain value=

11000 x 0.8 x 0.65 x

0.8 =4576 microstrain

(=0.0045 mm/mm)

Independent of loading

case, environment, layup,

etc.=> conservative

(CV=std. dev/mean x 100)

Weight comparison: Al versus

compositesAluminum (7075-

T6)

Quasi-Isotropic

Gr/Epoxy

Gr/E layup

used in compr*

Density (kg/m^3) 2777 1611 1611

Youngs modulus (GPa)

68.9 48.2 71.7

Compr. (yield)

failure strain (s)5700 4576 ~4500

Compr. failure

stress (MPa)

392.7 220.8 ~322.6

Aluminum is, typically, stronger than Gr/E but also has higher density

* [45/-45/02/90]s including knockdowns for material

scatter, environment and damage

Weight comparison: Al versus

composites

)(

,

)(,

Areaw

FW

w

Ft

wt

F

failureat

AreatWWeight

fail

a

fail

aa

fail

Alfail

Grfail

Al

Gr

W

W

QI/Al [45/-45/02/90]s/Al

1.03 0.706

Al

Gr

W

W

black Aluminum! 29.4% savings!

Some added considerations of the

design process

Material capability

(strength, stiffness)

Configuration

performance (different

failure modes)

Conservative(1)

analysis to

determine stresses

and strains

Failure criteria

Cutoff values

(1) Reasonably conservative, reasonably accurate and fast tends to be preferable to very accurate

but computationally very expensive methods

eccentricity

driven

out-of-plane

failure

local (bay)

buckling

Some added considerations of the

design process

Material capability

(strength, stiffness)

Configuration

performance (different

failure modes)

Conservative(1)

analysis to

determine stresses

and strains

Failure criteria

Cutoff values

(1) Reasonably conservative, reasonably accurate and fast tends to be preferable to very accurate

but computationally very expensive methods

Discuss failure modes briefly and how some of

them are difficult to pick-up in analysis

Discuss problems with failure criteria

Segway into cutoff values

eccentricity

driven

out-of-plane

failure

local (bay)

buckling

Related issues/considerations

Being able to obtain accurate stresses and/or strains is not enough to quantify failure correctly and thus not enough to generate a good design

Need to know the failure mode in advance Design to specific failure mode(s) and not on the basis of

highest stress in a model e.g. buckling vs crippling analysis Buckling of bays vs buckling of plate (isogrid) Interlaminar stresses require much higher mesh density in FE

model so a model could be good from every other respect but if you did not know the possibility of delamination you would not capture the critical failure mode (e.g. skin-stiffener separation, stiffener termination)

Modelling issues (e.g. fasteners, BCs between ss and clamped, etc)

Multiplicity and interaction of failure

modes (lugs)

Net section

failure

Bearing, (hole elongates and

material ahead of pin fails) and

net section failure combined

Shearout, (shear failure ahead of

pin hole along loading plane) and

net section failure combined

Delamination

Even for a simple detail like a lug, the multiplicity

of failure modes can

make failure prediction

extremely difficult. FE

cannot help much.

Multiplicity and interaction of failure

modes (sandwich structure)

Wavy shape of facesheet can lead to:

material failure of the facesheet (bending combined with compression)-A

material failure of the adhesive (tension, compression, shear)- A, B

material failure of the core (tension, compression, shear)

Stability driven/related failure of the facesheet

facesheet buckling (plate on elastic foundation)

wrinkling

intra-cellular buckling

etc.

AB sandwich under

compression at

failure

Governing Equations - Linear(Cartesian coordinates)

Equilibrium (no body forces)

5.2.2

0

0

0

zyx

zyx

zyx

zyzxz

yzyxy

xzxyx

or in terms of force and moment resultants:

0

0

0

y

Q

x

Q

y

N

x

N

y

N

x

N

yx

yxy

xyx

y

M

x

MQ

y

M

x

MQ

yxy

y

xyxx

Governing Equations (contd) Stress-strain equations (e.g. per ply)

xy

xz

yz

z

y

x

66362616

5545

4544

36332313

26232212

16131211

00

0000

0000

00

00

00

EEEE

EE

EE

EEEE

EEEE

EEEE

xy

xz

yz

z

y

x

or, in terms of force and moment resultants

xy

y

x

xy

y

x

M

M

M

N

N

N

662616662616

262212262212

161211161211

662616662616

262212262212

161211161211

DDDBBB

DDDBBB

DDDBBB

BBBAAA

BBBAAA

BBBAAA

xy

y

x

o

xy

o

y

o

x

x,1

y,2

z,3

x

z

MxMx

y

z

Mxy

Mxy MyMy

(e.g. per laminate)

Governing Equations (contd)

Strain-displacement equations

x

v

y

u

y

v

x

u

o

xy

o

y

o

x

yx

w

y

w

x

w

xy

y

x

2

2

2

2

2

2

xy

o

xyxy

y

o

yy

x

o

xx

y

z

17 eqns in the 17 unknowns: u, v, w, Nx, Ny, Nxy, Mx, My, Mxy, Qx, Qy, x, y, xy, x, y, xy

Governing Equations (contd) eliminating strains and forces and moments (e.g. Jones section

5.2.2):

0)2(3

)(2

3

3

262

3

66122

3

163

3

11

2

2

26

2

66122

2

162

2

66

2

162

2

11

y

wB

yx

wBB

yx

wB

x

wB

y

vA

yx

vAA

x

vA

y

uA

yx

uA

x

uA

03)2(

)2(3

4)2(24

3

3

222

3

262

3

66123

3

16

3

3

262

3

66122

3

163

3

114

4

22

3

4

2622

4

66123

4

164

4

11

y

vB

yx

vB

yx

vBB

x

vB

y

uB

yx

uBB

yx

uB

x

uB

y

wD

yx

wD

yx

wDD

yx

wD

x

wD

(no body force)

03)2(

2)(

3

3

222

3

262

3

66123

3

16

2

2

22

2

262

2

662

2

26

2

66122

2

16

y

wB

yx

wB

yx

wBB

x

wB

y

vA

yx

vA

x

vA

y

uA

yx

uAA

x

uA

Governing Equations (contd) if in-plane forces Nx, Ny, Nxy 0, additional terms from Fz=0

Nyx

pz

Nx

z

x

dxx

QQ xx

dxx

NN xx

Qx

px

y

wp

x

wp

yx

wN

y

wN

x

wNp

y

wD

yx

wDD

x

wD

yx

xyyxz

2

2

2

2

2

4

4

2222

4

66124

4

11 2)2(2

LHSpy

wp

x

wp

y

wN

yx

wN

x

wN

y

Q

x

Q

zyx

yxy

x

yx

2

22

2

2

2

Governing Equations (contd)

to see how additional terms are derived, consider Fzforce at two ends

pz

z

x

px

Fz

dyy

wNdx

x

wNdx

y

wNdxQdyQdy

x

wNF xyxyyyxxz

dxx

FF zz

Nx NyQyQx

NxyNxypx py

pz

Example:

Composite plate under localized in-plane load

Motivation: Stiffener termination

Simplified

problem to

be solved

x

y

1h

b

a

o

Stiffened

panel

Transitioning

into flat panel

F

Objectives determine the stresses in the plate so they can be used in

some form of failure criterion to predict failure

determine the length and width w of the region where stresses exceed significantly their far-field values (near the

point of load application) to get an idea of the geometry of

the region that needs reinforcement (doubler)

design transition region for load introduction into the plate to be used in further analysis

Stresses do not vary appreciably

from far-field stresses

Stresses vary appreciably from

far-field stresses

w

Concentrated load acting on composite

plate solution(1)

Assumptions

Homogeneous orthotropic plate

Layup is symmetric (B matrix=0)

Layup is balanced (no stretching/shearing coupling=> A16=A26=0)

There is no twisting/bending coupling (D16=D26=0)

Plate is sufficiently long and wide so solution is not affected by boundary proximity

(1) Kassapoglou, C., and Bauer, G., Composite Plates Under Concentrated Load on One Edge and Uniform Load on the Opposite Edge, Mechanics of Advanced Materials and Structures, 17, 2010 pp 196-203

Derive governing PDE

stress-strain eqns

xy

yx

yx

ANxy

AANy

AANx

66

2212

1211

averaged over plate thickness H

xyxy

yxy

yxx

H

A

H

A

H

A

H

A

H

A

66

2212

1211

x

y

1h

b

a

o

Governing PDE (contd)

No dependence on out-of-plane coordinate z:

out-of-plane stresses xz= yz= z=0

equilibrium eqns have the form:

0

z

0

0

yx

yx

yxy

xyx

Governing PDE (contd)

Solving for the strains

2

2

2

22

xyyx

yxxy

Eliminating the displacements from the strain-displacement equations gives the strain compatibility:

Substituting for the strains in the strain compatibility eqn:

2

2

122

2

112

2

122

2

22

2

66

2

122211

xA

xA

yA

yA

yxA

AAA xyyxxy

x

y

1h

b

a

o

2

122211

1211

2

122211

1222

AAA

HAHA

AAA

HAHA

xy

y

yx

x

66AH

xy

xy

Governing PDE (contd)

Use stress equilibrium equations and successive differentiations to substitute in the above equation

02

4

4

11

22

22

4

11

12

6611

2

122211

4

4

yA

A

yxA

A

AA

AAA

x

xxx

or:

0

4

4

22

4

4

4

yyxx

xxx

x

y

1h

b

a

o

Boundary Conditions

x

y

1h

b

a

o

0)()0()()0(

0)()0(

)(

22)0(

2200)0(

1

byyaxx

byy

bH

Fax

hby

hbfor

Hh

Fx

byhb

andhb

yx

xyxyxyxy

yy

ox

x

x

reaction

applied

load

Stress-free

condition

Solution of PDE

Assume solution of the form (fn unknown)

b

ynxfnx

cos)(

Substituting, fn is found to satisfy the eqn:

0

4

2

22

4

4

n

nn fb

n

dx

fd

b

n

dx

fd

from which, fn=Cex with

4

2

1 2

b

n

combining, the final form of the solution is

1

cos21

n

x

n

x

nxb

yneCeAKo

Fourier cosine series at

any given x!

Solution of PDE (contd)

only the two solutions with negative real parts are used (decaying exponentials) provided the plate is long enough; otherwise, all four solutions must be used

a constant Ko is introduced to get the most general form of the solution

Determination of all stresses

using equilibrium equations and boundary conditions (except at x=0) the stresses are found

to be:

b

yneeA

n

b

b

yneeA

n

b

b

yneeAKo

xx

n

n

xy

xx

n

n

y

n

xx

nx

2sin

2

2cos1

2

2cos

21

21

21

1

1

211

2

1

1 2

1

only even terms contribute to the solution

Ko and An are still unknown

x

y

1h

b

a

ox

y

1h

b

a

o

Boundary condition at x=0

Ko and An are determined as Fourier cosine series coefficients:

bH

FKo average of x at any x

location

dyb

yq

b

yneeAKdy

b

yqx

b

x

xx

no

b

x

2cos

2cos

2cos)0(

0 02

1

0

21

b

hnn

nhH

FAn

sincos

2

12

2

y

x(x=0)

F/(Hh)

2

hb

2

hb y=b