Equivalent Stiffness of Sinusoidal Periodic Dimpled Plates
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摘要: 针对构造正交各向异性周期性正弦凸起结构凹凸板的等效刚度问题,根据经典弹性薄板理论,基于对单胞结构力学特性分析和单胞结构在板宏观结构上周期性均匀化分布的特点,推导了正弦凸起凹凸板的等效刚度解析公式.以四边简支周期性正弦凸起结构凹凸板为例,将该文计算结果与有限元模拟结果进行对比,验证了该文等效刚度的合理性和精确性.最后,分析了正弦凸起凹凸板几何参数对等效刚度特性的影响,给出了结构几何参数与等效刚度之间的关系.结果表明:应用该文方法可以有效计算周期性正弦凸起凹凸板的等效刚度;由于凹凸板在构造上的几何结构变化,与基础平板相比其弯曲刚度和抗扭刚度都有明显的提升.该研究结果对凹凸板静力学和动力学的进一步研究以及实际工程应用具有指导意义.
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关键词:
- 周期性正弦凸起凹凸板 /
- 构造正交各向异性 /
- 单胞结构 /
- 等效刚度 /
- 有限元
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. -
[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))
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