Equivalent Stiffness of Sinusoidal Periodic Dimpled Plates

FENG Yan; DU Guojun; SHEN Zhenxing; WANG Mixiao

doi:10.21656/1000-0887.390160

Volume 40 Issue 5

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2019 > 40(5): 490-497

FENG Yan, DU Guojun, SHEN Zhenxing, WANG Mixiao. Equivalent Stiffness of Sinusoidal Periodic Dimpled Plates[J]. Applied Mathematics and Mechanics, 2019, 40(5): 490-497. doi: 10.21656/1000-0887.390160

Citation:

FENG Yan, DU Guojun, SHEN Zhenxing, WANG Mixiao. Equivalent Stiffness of Sinusoidal Periodic Dimpled Plates[J]. Applied Mathematics and Mechanics, 2019, 40(5): 490-497. doi: 10.21656/1000-0887.390160

Citation:

FENG Yan, DU Guojun, SHEN Zhenxing, WANG Mixiao. Equivalent Stiffness of Sinusoidal Periodic Dimpled Plates[J]. Applied Mathematics and Mechanics, 2019, 40(5): 490-497. doi: 10.21656/1000-0887.390160

PDF( 2281 KB)

Equivalent Stiffness of Sinusoidal Periodic Dimpled Plates

doi: 10.21656/1000-0887.390160

Key Laboratory of Mechanics Reliability for Heavy Equipment and Large Structure of Hebei Province, Yanshan University, Qinhuangdao, Hebei 066004, P.R.China

Funds: The National Natural Science Foundation of China(11702241)

Received Date: 2018-06-13
Rev Recd Date: 2018-09-18
Publish Date: 2019-05-01

Abstract

Abstract

The equivalent stiffness of sinusoidal periodic dimpled plates was derived according to the classical elastic thin plate theory, in view of the analysis of the mechanical properties of the unit cell structure and the homogeneous distribution of unit cells over the plate. The sinusoidal periodic dimpled plate with 4 sides simply supported under a concentrated load was taken as an example, the analytical results were compared with those of the finite element method (FEM), and the rationality and accuracy of the analytical equivalent stiffness were verified. Finally, the effects of some structural parameters on the equivalent stiffness of the dimpled plate were analyzed. The results show that, the presented method can effectively calculate the equivalent stiffness of the sinusoidal periodic dimpled plate. The bending stiffness and torsional stiffness of the dimpled plate are obviously higher than those of the basic plate, for the geometric change of the dimpled plate. The work has important meanings for the research on statics and dynamics of dimpled plates and the engineering application.
- sinusoidal periodic dimpled plate,
- structure of orthogonal anisotropy,
- unit cell,
- equivalent stiffness,
- finite element

FullText(HTML)

References(22)

References

[1]	TOKURA S, HAGIWARA I. A study for the influence of work hardening on bending stiffness of truss core panel[J]. Journal of Applied Mechanics,2010,77(3): 448-452.
[2]	NGUYEN V B, WANG C J, MYNORS D, et al. Mechanical properties and structural behaviour of cold-roll formed dimpled steel[C]// The 〖STBX〗10th International Conference on Technology of Plasticity, ICTP . Aachen, Germany, 2011: 1072-1077.
[3]	XIA Z Z, ZHAO X L, HAGIWARA I. A simulation approach to improve forming limitation of truss core panel[J]. Applied Mechanics & Materials,2011,121/126: 2471-2475.
[4]	TOKURA S, HAGIWARA I. Forming process simulation of truss core panel[J]. Journal of Computational Science and Technology,2010,4(1): 25-35.
[5]	YOO S H, CHANG S H, SUTCLIFFE M P F. Compressive characteristics of foam-filled composite egg-box sandwich panels as energy absorbing structures[J]. Composites Part A: Applied Science and Manufacturing,2010,41(3): 427-434.
[6]	HALDAR A K, ZHOU J, GUAN Z. Energy absorbing characteristics of the composite contoured-core sandwich panels[J]. Materials Today Communications,2016,8: 156-164.
[7]	赵伟东, 高士武, 马宏伟. 扁球壳在热-机械荷载作用下的稳定性分析[J]. 应用数学和力学, 2017,38(10): 1146-1154.(ZHAO Weidong, GAO Shiwu, MA Hongwei. Thermomechanical stability analysis of shallow spherical shells[J]. Applied Mathematics and Mechanics,2017,38(10): 1146-1154.(in Chinese))
[8]	DESHPANDE V S, FLECK N A. Energy absorption of an egg-box material[J]. Journal of the Mechanics & Physics of Solids,2003,51(1): 187-208.
[9]	KALAMKAROV A L, SAHA G C, GEORGIADES A V. General micromechanical modeling of smart composite shells with application to smart honeycomb sandwich structures[J]. Composite Structures,2007,79(1): 18-33.
[10]	KALAMKAROV A L, GEORGIADES A V, ROKKAM S K, et al. Analytical and numerical techniques to predict carbon nanotubes properties[J]. International Journal of Solids & Structures,2006,43(22/23): 6832-6854.
[11]	CHALLAGULLA K S, GEORGIADES A V, KALAMKAROV A L. Asymptotic homogenization modeling of smart compositegenerally orthotropic grid-reinforced shells, part I: theory[J]. European Journal of Mechanics: A/Solids,2010,29(4): 530-540.
[12]	LEE C Y, YU W. Homogenization and dimensional reduction of composite plates with in-plane heterogeneity[J]. International Journal of Solids & Structures,2011,48(10): 1474-1484.
[13]	NGUYEN V B,WANG C J,MYNORS D J, et al. Finite element simulation on mechanical and structural properties of cold-formed dimpled steel[J]. Thin-Walled Structures,2013,64: 13-22.
[14]	NGUYEN V B, WANG C J, MYNORS D J, et al. Dimpling process in cold roll metal forming by finite element modelling and experimental validation[J]. Journal of Manufacturing Processes,2014,16(3): 363-372.
[15]	SASHIKUMAR S, CHIRWA E C, MYLER P, et al. Numerical investigation into the collapse behaviour of an aluminium egg-box under quasi-static loading[J]. International Journal of Crashworthiness,2012,17(6): 582-590.
[16]	MARCUZZI A, MORASSI A. Dynamic identification of a concrete bridge with orthotropic plate-type deck[J]. Journal of Structural Engineering,2010,136(5): 586-602.
[17]	胡肇滋, 钱寅泉. 正交构造异性板刚度计算的探讨[J]. 土木工程学报, 1987,20(4): 49-61.(HU Zhaozi, QIAN Yinquan. Research on the calculation of structurally orthotropic plate rigidity[J]. China Civil Engineering Journal,1987,20(4): 49-61.(in Chinese))
[18]	程远兵, 程文瀼, 党纪. 均布荷载下四边简支蜂窝式空心板的解析解[J]. 工程力学, 2009,26(8): 34-38.(CHENG Yuanbing, CHENG Wenrang, DANG Ji. Analytical solution of cellular hollow plates simply supported subjected to uniformly distributed loads[J]. Engineering Mechanics,2009,26(8): 34-38.(in Chinese))
[19]	SUQUET P. Elements of homogenization forinelastic solid mechanics[C]//Homogenization Techniques for Composite Media. Berlin, Germany, 1987.
[20]	SMIT R J M,BREKELMANS W A M,MEIJER H E H. Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling[J]. Computer Methods in Applied Mechanics & Engineering,1998, 1〖STHZ〗55(1/2): 181-192.
[21]	张福范. 弹性薄板[M]. 北京: 科学出版社, 1984.(ZHANG Fufan. Elastic Thin Plate [M]. Beijing: Science Press, 1984.(in Chinese))
[22]	常福清, 袁帅. 正弦波纹板第二主刚度的补正[J]. 机械强度,2010,〖STHZ〗32(2): 152-155.(CHANG Fuqing, YUAN Shuai. Emendations of secondly main stiffen formula for the sine corrugated plate[J]. Journal of Mechanical Strength,2010,32(2): 152-155.(in Chinese))