METNET SEMINAR 2011 IN AARHUS

Transcription

1 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

2 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.

3 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.

4 PREVIOUS PUBLISHED RESEARCH Hassinen [1991] suggested a method starting with the elastic critical stress for the panel. 2 E f crt K (1 f )( b / t f ) K 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.

5 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.

6 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.

7 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

8 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.

9 MULTIPLE HALF WAVE MODEL Nonlinear ultimate loads were obtained for 1, 3, and 5 half sine waves. 2.5a Metal face p b b/2 p x y a a a a a z Core The results (Table 3 in paper) showed that for more slender panels, using at least 5 half sine waves gave convergent results.

10 MULTIPLE HALF WAVE MODEL Table 3 Failure load (MPa) Different number of half waves b/t f The results show that for more slender panels, using at least 5 half sine waves gives convergent results.

11 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.

12 VALIDATION Table 1 Ultimate Failure load (MPa) Grade 250 Steel b/t f FEA Test The results show that, allowing for experimental uncertainties, the FEA analysis gives satisfactory results.

13 DERIVATION OF DESIGN FORMULA Previous studies aimed at deriving design formulae resulted in recommendation for effective widths. The concept used is: b eff b Ultimate strength Yield stress Where the ultimate strength is obtained either from experimental results or from some analysis or from finite element calculations.

14 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)

15 beff/b ASSESSMENT OF EXISTING FORMULAE Davies ECCS Pokharel and Mahendran 2002 Pokharel and Mahendran 2005 FEA b/t f ratio

16 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.

17 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.

18 INFLUENCE OF YIELD STRENGTH

19 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.

20 NEW DESIGN FORMULA A new formula is proposed as follows, which directly gives the ultimate strength without defining the effective width. Ultimate Strength b Yield Strength t 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.

21 NEW DESIGN FORMULA

22 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.

23 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.

24 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.

25 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.

26 THANK YOU