Post on 19-Aug-2020
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