LIU Hang, DU Guojun, FENG Yan. Study on Equivalent Stiffnesses of Orthotropic Hemi-Spherical Convex Plates[J]. Applied Mathematics and Mechanics, 2020, 41(1): 70-80. doi: 10.21656/1000-0887.400181
Citation: LIU Hang, DU Guojun, FENG Yan. Study on Equivalent Stiffnesses of Orthotropic Hemi-Spherical Convex Plates[J]. Applied Mathematics and Mechanics, 2020, 41(1): 70-80. doi: 10.21656/1000-0887.400181

Study on Equivalent Stiffnesses of Orthotropic Hemi-Spherical Convex Plates

doi: 10.21656/1000-0887.400181
  • Received Date: 2019-06-04
  • Rev Recd Date: 2019-07-01
  • Publish Date: 2020-01-01
  • The hemispherical convex plate was periodically divided into representative unit structures. Firstly, the stiffness characteristics of representative units were studied, and the equivalent stiffness of the hemispherical convex plate was obtained by means of the deformation equivalence principle, the homogenization procedure and the stiffness combination method. Then the 3 principal stiffnesses were brought into the theoretical solution of the 4-side simple plate to solve the plate center deflection. The finite element numerical simulation solution and the theoretical solution were compared and analyzed to verify the accuracy of the theoretical principal stiffnesses. The effect of the material dimensions of the representative units on the equivalent stiffness was then discussed. As the ratio of the length of the representative unit to the convex radius increases, the accuracy of the theoretical results will improve, and the equivalent stiffness formula is applicable to hemispherical convex plates of different thicknesses. Finally, a relatively simple engineering application formula was given with the approximate range of the convex radius based on several examples.
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  • [1]
    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))
    LIAO Y, ZHAO X, ISHIDA S, et al. 〖STBX〗3D Origami Structure Design and Simulation by Parametric Origami Module [M]. Berlin: Springer, 2012.
    YANG Y, XIA Z, ZHAO X, et al. Comprehensive Optimization for Raised Floor Structure Using Origami Engineering [M]. Berlin: Springer, 2012.
    郑宇宁, 邱志平, 苑凯华. 复合材料波纹板在剪切载荷下的屈曲特性分析与可靠性优化[J]. 振动与冲击, 2016,35(20): 7-14.(ZHENG Yuning, QIU Zhiping, YUAN Kaihua. Buckling performance analysis and reliability optimization of composite corrugated plates under shear loading[J]. Journal of Vibration and Shock,2016,35(20): 7-14.(in Chinese))
    TOKURA S, HAGIWARA I. Forming process simulation of truss core panel[J]. Journal of Computational Science & Technology,2010,4(4): 25-35.
    XIA Z Z, ZHAO X L, HAGIWARA I. A simulation approach to improve forming limitation of truss core panel[J]. Applied Mechanics and Materials,2011,121/126: 2471-2475.
    王光辉, 王定标, 彭旭, 等. 凹凸板的传热流阻特性及其多目标优化[J]. 工程热物理学报, 2019,40(1): 143-149.(WANG Guanghui, WANG Dingbiao, PENG Xu, et al. Heat transfer and resistance of plant heat exchanger with dimples and protrusions and optimization[J]. Journal of Engineering Thermophysics,2019,40(1): 143-149.(in Chinese))
    BURGESS N K, LIGRANI P M. Effects of dimple depth on channel nusselt numbers and friction factors[J]. Journal of Heat Transfer,2005,127(8): 839-847.
    王晓霞. 酒窝板换热特性的实验研究[D]. 硕士学位论文. 西安: 西安科技大学, 2008.(WANG Xiaoxia. Experimental study on heat transfer characteristics of dimple plates[D]. Master Thesis. Xi’an: Xi’an University of Science and Technology, 2008.(in Chinese))
    STROUD W J. Elastic constants for bending and twisting of corrugation stiffened panels[R]. 1963.
    BRIASSOULIS D. Equivalent orthotropic properties of corrugated sheets[J]. Computers & Structures,1986,23(2): 129-138.
    MCFARLAND D E. An investigation of the static stability of corrugated rectangular plates loaded in pure shear[D]. PhD Thesis. Kansas: University of Kansas, 1967.
    WINKLER M, KRESS G. Deformation limits for corrugated cross-ply laminates[J]. Composite Structures,2010,〖STHZ〗 92(6): 1458-1468.
    LIEW K M, PENG L X, KITIPORNCHAI S. Buckling analysis of corrugated plates using a mesh-free Galerkin method based on the first-order shear deformation theory[J]. Computational Mechanics,2006,38(1): 61-75.
    XIA Y, FRISWELL M I, FLORES E I S. Equivalent models of corrugated panels[J]. International Journal of Solids and Structures,2012,49(13): 1453-1462.
    冯岩, 杜国君, 沈振兴, 等. 周期性正弦凸起凹凸板等效刚度的研究[J]. 应用数学和力学, 2019,40(5): 490-497.(FENG Yan, DU Guojun, SHEN Zhenxing, et al. Equivalent stiffness of sinusoidal periodic dimpled plates[J]. Applied Mathematics and Mechanics,2019,40(5): 490-497.(in Chinese))
    冯岩, 杜国君, 赵卫东. 构造上正交各向异性凹凸板等效刚度的研究[J]. 应用力学学报, 2018,35(4): 900-905.(FENG Yan, DU Guojun, ZHAO Weidong. Equivalent stiffness research of the construction orthogonal anisotropy truss core panel[J]. Chinese Journal of Applied Mechanics,2018,35(4): 900-905.(in Chinese))
    徐芝纶. 弹性力学(下册)[M]. 北京: 高等教育出版社, 2006.(XU Zhilun. Elastic Mechanics [M]. Beijing: Higher Education Press, 2006.(in Chinese))
    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(4): 51-63.(HU Zhaozi, QIAN Yinquan. Research on the calculation of structurally orthotropic plate rigidity[J]. China Civil Engineering Journal,1987(4): 51-63.(in Chinese))
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      沈阳化工大学材料科学与工程学院 沈阳 110142

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