METNET SEMINAR 2011 IN AARHUS

BEHAVIOUR OF METAL FOAM SANDWICH PANELS

Hayder H. Alkhudery

College of Engineering, Basrah University, Iraq

Kuldeep S. Virdi

Aarhus School of Engineering, Aarhus University

SANDWICH PANELS

Sandwich panels use a core of a very light material

placed between a pair of metal sheets of small

thickness.

The resulting high bending stiffness coupled with light

weight and very good thermal and damping properties

make sandwich panels attractive structures for

designers.

Cost savings result from ease of transport and

assembly in all conditions.

PREVIOUS PUBLISHED RESEARCH

Only a handful of well-focused studies were found in

literature. No published results were found for tests

on full-section sandwich panels.

DAVIES AND HAKMI [1990, 1991]

- Treated core as half space linear elastic foundation

- Derived buckling formulae.

- Adjusted one of the parameters arbitrarily to obtain

better correlation with experiments.

PREVIOUS PUBLISHED RESEARCH

Hassinen [1991] suggested a method starting with the

elastic critical stress for the panel.

22

2

)/)(1(12 ff

f

crttb

EK

is the buckling coefficient. Its value depends on

another parameter which includes the geometric and

material properties of both the core and the surface.

The solution involves an iterative procedure, making it

inconvenient for rapid design calculations.

K

PREVIOUS PUBLISHED RESEARCH

MAHENDRAN et al [2002, 2003, 2004, 2005]

- Carried out experiments on single steel plates with

supporting polystyrene foam core.

- Derived effective width formulae for use in design.

- Also conducted Finite Element analysis for a

parametric study.

ASPECTS FOR FURTHER STUDY

From the literature review, it emerges that need exists

for full scale experiments to study the overall failure

as well interaction with local buckling.

Overall failure strength is influenced by imperfections,

an aspect not covered in previous studies.

An inexpensive approach is to use nonlinear finite

element analysis. Need will remain to validate such

analyses with full scale experiments.

FINITE ELEMENT ANALYSIS

Some problems facing the analyst are mentioned

below:

- Selection of suitable elements

Solid element for core, Shell element for surface

Question remains over incompatible nodal

displacements and rotations at interfaces

- Modelling of imperfections

- Modelling of buckling modes

BUCKLING MODES

Eigen value analysis can be used to determine the

critical buckling modes.

For elastic buckling of plates, it is acceptable to

consider the buckling behaviour of square plates,

since the theoretical critical load of plates of aspect

ratio 1, 2, 3, etc remains unchanged.

It is not certain that when doing material and

geometric nonlinear analysis, the same buckling

modes can be justified.

MULTIPLE HALF WAVE MODEL

Nonlinear ultimate loads were obtained for 1, 3, and 5

half sine waves.

The results (Table 3 in paper) showed that for more

slender panels, using at least 5 half sine waves gave

convergent results.

2.5a

b

b/2

p

px

y

z

a a a a a

Core

Metal face

MULTIPLE HALF WAVE MODEL

Table 3 Failure load (MPa)

Different number of half waves

b/tf 1 3 5 7

63 345 345 346 346

125 202 203 203 203

200 136 144 144 144

250 121 129 129 129

500 97 103 104 104

The results show that for more slender panels, using

at least 5 half sine waves gives convergent results.

CORE AS HALF SPACE

Using five half waves

(and symmetry), the

results confirm that, for

panels without

imperfection, analysis

based on the core as a

half space, is justified.

Work remains to be

done for imperfect

plates.

Table 1 Ultimate Failure load (MPa)

Grade 250 Steel

b/tf FEA Test

119 164 186

190 111 149

250 83 78

330 75 72

500 71 75

The results show that, allowing for experimental

uncertainties, the FEA analysis gives satisfactory

results.

VALIDATION

DERIVATION OF DESIGN FORMULA

Previous studies aimed at deriving design formulae

resulted in recommendation for effective widths. The

concept used is:

Where the ultimate strength is obtained either from

experimental results or from some analysis or from

finite element calculations.

stressYield

strengthUltimate

b

beff

ASSESSMENT OF EXISTING FORMULAE

Different sources were selected to assess the

current state regarding design formulae.

(1) Using the values suggested by Davies and

Hakmi (1990),

(2) ECCS(2000)

(3) Two formulae suggested by Pokharel and

Mahendran (2002 and 2005)

(4) These are then compared with finite element

results obtained here, based on 5 half wave

buckling models (Table 5)

ASSESSMENT OF EXISTING FORMULAE

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0 50 100 150 200 250 300 350 400 450 500 550 600

b/tf ratio

be

ff/b

Davies

ECCS

Pokharel and Mahendran 2002

Pokharel and Mahendran 2005

FEA

ASSESSMENT OF EXISTING FORMULAE

The graph shows that Davies and Hakmi (2009) as

well as the ECCS approaches both show significant

deviation from the results obtained here using the

finite element method. The methods are too

conservative as they overestimate the effective

width, which would lead to lower design strength.

Results from Pokharel and Mahendran, especially

the 2005 publication, give good correlation with

results obtained here.

NEW ANALYSIS

Mahendran’s extensive work was limited to the two

steel grades he had used for his experimental work.

In order to assess the wider influence of the effect of

yield strength on ultimate loads, a much wider range

of yield strengths was selected for a parametric

study.

This is in the context of advances in higher strength

steels.

INFLUENCE OF YIELD STRENGTH

NEW ANALYSIS

The graph shows that at lower slenderness ratios,

the ultimate strength of sandwich panel ratio is

significantly affected by the yield stress of steel

face, while the effects become marginal for plates

with higher slenderness.

A new formula is proposed as follows, which directly

gives the ultimate strength without defining the

effective width.

Where, α, β, and g are constants.

A least squares curve fitting resulted in values of α = 37000, β = -1.25, and g = 80.

The values obtained from the curve-fitting operation

have been rounded off.

NEW DESIGN FORMULA

UltimateStrength b

Yield Strength t

NEW DESIGN FORMULA

NEW ANALYSIS

The proposed formula gives a close fit to the range

of yield strengths analysed.

This formula differs from previously proposed

formulae in that no attempt has been made to

adhere to the format for elastic critical stress.

Even for simple thin plates, the elastic critical stress

formula gives conservative results for slender plates

and non-conservative results for stocky plates.

FURTHER WORK

Mention has been made to imperfections in the

plates, especially the lack of flatness.

Further work needs to be carried out to study the

effect of imperfections on the ultimate strength of

full-scale sandwich panels.

Any parametric study will need to be validated

against matching experiments.

CONCLUSION

The finite element method has been used to study

the buckling behaviour of sandwich panels.

Good agreement between finite element results and

published test results has been obtained.

The paper considers the level of accuracy that can

be obtained by considering a single half wave

against multiple half waves. Multiple half wave

model was then used to review existing design

formulae.

CONCLUSION

It was shown that currently accepted design formula

gives acceptable results for high slenderness ratios

whereas inadequate agreement for lower

slenderness ratios was obtained.

Using a curve-fitting approach, an improved design

formula has been shown to give consistent results.

The paper also highlights topics on which further

work is needed.

THANK YOU