Strength optimization of ultralight corrugated-channel-core sandwich panels

ZhenYu ZHAO; Lang LI; Xin WANG; QianCheng ZHANG; Bin HAN; TianJian LU

doi:10.1007/s11431-018-9356-8

SCIENCE CHINA Technological Sciences

Download PDF

SCIENCE CHINA Technological Sciences, Volume 62 , Issue 8 : 1467-1477(2019) https://doi.org/10.1007/s11431-018-9356-8

Strength optimization of ultralight corrugated-channel-core sandwich panels

ZhenYu ZHAO ^1,2, Lang LI ^1,2, Xin WANG ^1,2, QianCheng ZHANG ^1,2,*, Bin HAN ^2,3, TianJian LU ^1,2,4,*

More info

Affiliations：

1. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, China;

2. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;

3. Nanjing Center for Multifunctional Lightweight Materials and Structures (MLMS), Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;

4. School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China

* Corresponding authors (email: zqc111999@mail.xjtu.edu.cn; tjlu@mail.xjtu.edu.cn)

ReceivedMay 29, 2018
AcceptedSep 11, 2018
PublishedDec 26, 2018

Previous Table of Contents Next

Rating

Abstract

Novel ultralight sandwich panels, which are comprised of corrugated channel cores and are faced with two identical solid sheets, subjected to generalized bending are optimally designed for minimum mass. A combined analytical and numerical (finite element) investigation is carried out. Relevant failure mechanisms such as face yielding, face buckling, core yielding and core buckling are identified, the load for each failure mode derived, and the corresponding failure mechanism maps constructed. The analytically predicted failure loads and failure modes are validated against direct finite element simulations, with good agreement achieved. The optimized corrugated channel core is compared with competing topologies for sandwich construction including corrugations, honeycombs and lattice trusses, and the superiority of the proposed structure is demonstrated. Corrugated-channel-core sandwich panels hold great potential for multifunctional applications, i.e., simultaneous load bearing and active cooling.

Funded by

the National Natural Science Foundation of China(Grant,Nos.,11472209,11472208)

the China Postdoctoral Science Foundation(Grant,No.,2016M600782)

the Postdoctoral Scientific Research Project of Shaanxi Province(Grant,No.,2016BSHYDZZ18)

the Fundamental Research Funds for Xian Jiaotong University(Grant,No.,xjj2015102)

and the Jiangsu Province Key Laboratory of High-end Structural Materials(Grant,No.,hsm1305)

Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11472209, 11472208), the China Postdoctoral Science Foundation (Grant No. 2016M600782), the Postdoctoral Scientific Research Project of Shaanxi Province (Grant No. 2016BSHYDZZ18), the Fundamental Research Funds for Xi’an Jiaotong University (Grant No. xjj2015102), and the Jiangsu Province Key Laboratory of High-end Structural Materials (Grant No. hsm1305). ZHAO ZhenYu wishes to thank Zhang Zhi-jia for insightful discussion.

Supplement

Appendix: Indentation model

For the indentation failure mode, local loading is transmitted to the corrugated channel core through deformation of the face sheet by a loading platen with width a. In general, indentation failure is accompanied by the formation of plastic hinges and compressive collapse of the underlying core [31]. Correspondingly, the collapse load of indentation is

$\begin{array}{lr} V = 2 t_{f} \sqrt{σ_{ys} Σ_{I}} + a Σ_{I}, & (a1) \end{array}$

where $Σ_{I}$ is the compressive strength of the core, given by [4]

$\begin{array}{lr} Σ_{I} = {\begin{matrix} \frac{6.74 π^{2} E_{s}}{12 (1 - ν_{s}^{2})} {(\frac{t_{c}}{s})}^{2} \bar{ρ}, & core buckling, \\ σ_{ys} \bar{ρ}, & core yielding, \end{matrix} & (a2) \end{array}$

where $\bar{ρ} = \frac{t_{c}}{d \cos θ}$ . The non-dimensional form of eq. (a1) is

$\begin{array}{lr} \frac{V^{2}}{E_{s} M} = 2 {\bar{t}}_{f} \sqrt{\frac{σ_{ys}}{E_{s}} \frac{Σ_{I}}{E_{s}}} + \bar{a} \frac{Σ_{I}}{E_{s}}, & (a3) \end{array}$

where $\bar{a} = a / χ$ is the normalized width of loading platen. Upon substituting $h / s = 1$ , $d / h = n$ and eq. (a2) into eq. (a3), the non-dimensional form of indentation failure criteria become

$\begin{array}{lr} \frac{V^{2}}{E_{s} M} = {\begin{cases} 2 {\bar{t}}_{f} \sqrt{ε_{ys} \frac{6.74 π^{2}}{12 (1 - ν_{s}^{2})} {(\frac{{\bar{t}}_{c}}{\bar{h}})}^{3} \frac{1}{n \cos θ}} \\ + \bar{a} \frac{6.74 π^{2}}{12 (1 - ν_{s}^{2})} {(\frac{{\bar{t}}_{c}}{\bar{h}})}^{3} \frac{1}{n \cos θ}, \\ core buckling, \\ 2 {\bar{t}}_{f} \sqrt{ε_{ys} ε_{ys} \frac{{\bar{t}}_{c}}{\bar{h}} \frac{1}{n \cos θ}} + \bar{a} ε_{ys} \frac{{\bar{t}}_{c}}{\bar{h}} \frac{1}{n \cos θ}, \\ core yielding . \end{cases} & (a4) \end{array}$

Upon adding eq. (a4) into eq. (9), the minimum weight design of 3CSP subject to simultaneous generalized bending and indentation is performed using the SQP algorithm coded in MATLAB.

References

[1] Lu T, Valdevit L, Evans A. Active cooling by metallic sandwich structures with periodic cores. Prog Mater Sci, 2005, 50: 789-815 CrossRef Google Scholar

[2] Han B, Zhang Z J, Zhang Q C, et al. Recent advances in hybrid lattice-cored sandwiches for enhanced multifunctional performance. Extreme Mech Lett, 2017, 10: 58-69 CrossRef Google Scholar

[3] Zhang Q, Yang X, Li P, et al. Bioinspired engineering of honeycomb structure—Using nature to inspire human innovation. Prog Mater Sci, 2015, 74: 332-400 CrossRef Google Scholar

[4] Zhao Z, Han B, Wang X, et al. Out-of-plane compression of Ti-6Al-4V sandwich panels with corrugated channel cores. Mater Des, 2018, 137: 463-472 CrossRef Google Scholar

[5] Kim T, Zhao C Y, Lu T J, et al. Convective heat dissipation with lattice-frame materials. Mech Mater, 2004, 36: 767-780 CrossRef Google Scholar

[6] Kim T, Hodson H P, Lu T J. Fluid-flow and endwall heat-transfer characteristics of an ultralight lattice-frame material. Int J Heat Mass Transfer, 2004, 47: 1129-1140 CrossRef Google Scholar

[7] Yan H B, Zhang Q C, Lu T J. An X-type lattice cored ventilated brake disc with enhanced cooling performance. Int J Heat Mass Transfer, 2015, 80: 458-468 CrossRef Google Scholar

[8] Yan H B, Zhang Q C, Lu T J. Heat transfer enhancement by X-type lattice in ventilated brake disc. Int J Thermal Sci, 2016, 107: 39-55 CrossRef Google Scholar

[9] Guo R, Zhang Q C, Zhou H, et al. Progress in manufacturing lightweight corrugated sandwich structures and their multifunctional applications. Mech Eng, 2017, 39: 226–239. Google Scholar

[10] Valdevit L, Hutchinson J W, Evans A G. Structurally optimized sandwich panels with prismatic cores. Int J Solids Struct, 2004, 41: 5105-5124 CrossRef Google Scholar

[11] Valdevit L, Wei Z, Mercer C, et al. Structural performance of near-optimal sandwich panels with corrugated cores. Int J Solids Struct, 2006, 43: 4888-4905 CrossRef Google Scholar

[12] Côté F, Deshpande V S, Fleck N A, et al. The compressive and shear responses of corrugated and diamond lattice materials. Int J Solids Struct, 2006, 43: 6220-6242 CrossRef Google Scholar

[13] Tian Y S, Lu T J. Optimal design of compression corrugated panels. Thin-Walled Struct, 2005, 43: 477-498 CrossRef Google Scholar

[14] Lu T J. Heat transfer efficiency of metal honeycombs. Int J Heat Mass Transfer, 1999, 42: 2031-2040 CrossRef Google Scholar

[15] Gu S, Lu T J, Evans A G. On the design of two-dimensional cellular metals for combined heat dissipation and structural load capacity. Int J Heat Mass Transfer, 2001, 44: 2163-2175 CrossRef Google Scholar

[16] Valdevit L, Pantano A, Stone H A, et al. Optimal active cooling performance of metallic sandwich panels with prismatic cores. Int J Heat Mass Transfer, 2006, 49: 3819-3830 CrossRef Google Scholar

[17] Wen T, Xu F, Lu T J. Structural optimization of two-dimensional cellular metals cooled by forced convection. Int J Heat Mass Transfer, 2007, 50: 2590-2604 CrossRef Google Scholar

[18] Liu T, Deng Z C, Lu T J. Minimum weights of pressurized hollow sandwich cylinders with ultralight cellular cores. Int J Solids Struct, 2007, 44: 3231-3266 CrossRef Google Scholar

[19] Liu T, Deng Z C, Lu T J. Bi-functional optimization of actively cooled, pressurized hollow sandwich cylinders with prismatic cores. J Mech Phys Solids, 2007, 55: 2565-2602 CrossRef ADS Google Scholar

[20] Tan X H, Soh A K. Multi-objective optimization of the sandwich panels with prismatic cores using genetic algorithms. Int J Solids Struct, 2007, 44: 5466-5480 CrossRef Google Scholar

[21] Rathbun H J, Zok F W, Evans A G. Strength optimization of metallic sandwich panels subject to bending. Int J Solids Struct, 2005, 42: 6643-6661 CrossRef Google Scholar

[22] Ali M M, Ramadhyani S. Experiments on convective heat transfer in corrugated channels. Exp Heat Transfer, 1992, 5: 175-193 CrossRef Google Scholar

[23] Hassanein M F, Kharoob O F. Shear buckling behavior of tapered bridge girders with steel corrugated webs. Eng Struct, 2014, 74: 157-169 CrossRef Google Scholar

[24] Driver R G, Abbas H H, Sause R. Shear behavior of corrugated web bridge girders. J Struct Eng, 2006, 132: 195-203 CrossRef Google Scholar

[25] Wicks N, Hutchinson J W. Optimal truss plates. Int J Solids Struct, 2001, 38: 5165-5183 CrossRef Google Scholar

[26] Chen J. Stability Theory and Design of Steel Structure. Beijing: Science Press, 2014. Google Scholar

[27] Timoshenko S P, Gere J M, Prager W. Theory of Elastic Stability. 2nd ed. New York: McGraw-Hill Book Co, 1961. Google Scholar

[28] Han B, Qin K K, Yu B, et al. Design optimization of foam-reinforced corrugated sandwich beams. Composite Struct, 2015, 130: 51-62 CrossRef Google Scholar

[29] Zok F W, Rathbun H J, Wei Z, et al. Design of metallic textile core sandwich panels. Int J Solids Struct, 2003, 40: 5707-5722 CrossRef Google Scholar

[30] Zok F W, Rathbun H, He M, et al. Structural performance of metallic sandwich panels with square honeycomb cores. Philos Mag, 2005, 85: 3207-3234 CrossRef Google Scholar

[31] Ashby M F, Evans A, Fleck N A, et al. Metal Foams: A Design Guide. Oxford: Butterworth-Heinemann, 2000. Google Scholar

Click to view Download high-quality image

Figure 1
(Color online) (a) Schematic of sandwich panel with triangular corrugated channel core subjected to generalized bending; (b) top view of corrugated channel core.
Click to view Download high-quality image

Figure 2
Effect of $n = d / h$ on the optimization of 3CSP subjected to longitudinal bending. Results are presented for titanium alloy ( $ε_{ys} = 0.007$ , $ν_{s} = 0.34$ ) and fixed inclination angle $θ =$ 45°. (a) Minimum weight; (b) optimal face thickness; (c) optimal core web thickness; (d) optimal core web height.
Click to view Download high-quality image

Figure 3
Influence of failure criteria on optimal design of 3CSP for: (a) $n = 1$ ; (b) $n = 2$ ; (c) $n = 3$ ; (d) $n = 4$ .
Click to view Download high-quality image

Figure 4
Effect of inclination angle $θ$ on minimum weight of 3CSP subjected to generalized bending.
Click to view Download high-quality image

Figure 5
Effect of yield strain on optimal design on 3CSP subjected to generalized bending.
Click to view Download high-quality image

Figure 6
(Color online) Failure mechanism map for 3CSPs ( $n = 1$ , $θ =$ 45°) made from Ti-6Al-4V alloy ( $ε_{ys} = 0.007$ , $ν_{s} = 0.34$ ). (a) Weight index $ψ = 0.01$ ; (b) weight index $ψ = 0.02$ ; (c) weight index $ψ = 0.04$ .
Click to view Download high-quality image

Figure 7
(Color online) Effect of loading platen width on optimal design on 3CSP subjected to generalized bending and indentation.
Click to view Download high-quality image

Figure 8
(Color online) Finite element model of 3CSP under longitudinal four-point bending.
Click to view Download high-quality image

Figure 9
Typical failure modes of 3CSPs under longitudinal four-point bending captured by FE calculations: (a) face buckling for specimen A1; (b) face yielding for specimen B1; (c) core buckling for specimen C1; (d) core yielding for specimen D1.
Click to view Download high-quality image

Figure 10
(Color online) Initial failure contours of face yielding and core yielding under longitudinal four-point bending captured by FE calculations: (a) face yielding for specimen B1; (b) core yielding for specimen D1.
Click to view Download high-quality image

Figure 11
Comparison of minimum weight for different types of lightweight sandwich panel: 3CSP and corrugated panel loaded in longitudinal bending, corrugated panel loaded in transverse bending, hexagonal and square honeycomb panels, and truss core panels. The base material for all the panels is Ti-6Al-4V with $ε_{ys} = 0.007$ .

Table 1 Geometric details of 3CSP specimens used in FE simulation

Specimen label	L^b (mm)	L^p (mm)	B (mm)	χ (mm)	t^f (mm)	t^c (mm)	h (mm)	d (mm)	s (mm)	θ (°)
A1	339	113	40	113	0.2	1	20	20	20	45
A2	339	113	40	113	0.4	1	20	20	20	45
B1	339	113	40	113	2	1	20	20	20	45
B2	339	113	40	113	2	0.8	20	20	20	45
C1	339	113	40	113	2	0.2	20	20	20	45
C2	339	113	40	113	2	0.3	20	20	20	45
D1	339	113	40	113	2	0.5	20	20	20	45
D2	339	113	40	113	2	0.4	20	20	20	45

Table 2 Comparison between FE simulations and analytical predictions for 3CSPs under longitudinal four-point bending

Specimen label	Non-dimensionalweight ψ	Failure mode		Non-dimensional load V²/E_sM
Specimen label	Non-dimensionalweight ψ	Anal.	FE	Anal.	FE	Error
A1	0.0160	FB	FB	2.05×10⁻⁷	2.15×10⁻⁷	5%
A2	0.0196	FB	FB	1.65×10⁻⁶	1.61×10⁻⁶	−3%
B1	0.0479	FY	FY	2.43×10⁻⁵	2.48×10⁻⁵	2%
B2	0.0454	FY	FY	2.43×10⁻⁵	2.46×10⁻⁵	1%
C1	0.0379	CB	CB	2.42×10⁻⁶	2.44×10⁻⁶	1%
C2	0.0391	CB	CB	8.16×10⁻⁶	8.16×10⁻⁶	0%
D1	0.0416	CY	CY	1.80×10⁻⁵	1.81×10⁻⁵	1%
D2	0.0404	CY	CY	1.44×10⁻⁵	1.49×10⁻⁵	3%

2

Citations
0

Altmetric
Article metrics

Email
Export

Strength optimization of ultralight corrugated-channel-core sandwich panels

Abstract

Funded by

Acknowledgment

Supplement

References

2

0

Interesting search

Top 5Related Articles