TONG Yao, YAO Yuzhe. 20-Node Hexahedron Symplectic Elements for Stress Analysis of Composite Laminates[J]. Applied Mathematics and Mechanics, 2020, 41(5): 509-516. doi: 10.21656/1000-0887.400283
Citation: TONG Yao, YAO Yuzhe. 20-Node Hexahedron Symplectic Elements for Stress Analysis of Composite Laminates[J]. Applied Mathematics and Mechanics, 2020, 41(5): 509-516. doi: 10.21656/1000-0887.400283

20-Node Hexahedron Symplectic Elements for Stress Analysis of Composite Laminates

doi: 10.21656/1000-0887.400283
Funds:  The National Natural Science Foundation of China(11502286)
  • Received Date: 2019-09-20
  • Rev Recd Date: 2019-11-22
  • Publish Date: 2020-05-01
  • Usually, the accuracy of the stresses obtained with the conventional displacement finite element method is one-order lower than that of the displacements, and the out-of-plane stresses can hardly meet the continuity requirements. Then, combined with the minimum potential energy principle and the H-R variational principle, a 20-node hexahedral symplectic element involving displacement and out-of-plane stress variables was established. Incompatible displacement terms are needless in the element since the 2 kinds of variables are approximated with higher-order interpolation functions. Hence, the derivation process of the theory is very simple. Unlike in the partially mixed Hamiltonian element, the variables involved in the symplectic element are discretized in 3 coordinate directions without restriction of the element thickness and the structure geometry. Numerical examples show that, the 20-node symplectic elements exhibit stable convergence. Under the coarse mesh, the out-of-plane stresses obtained with the proposed element are closer to the exact solution than those by the incompatible 8-node symplectic element.
  • loading
  • [1]
    REDDY J N. A simple higher-order theory for laminated composite plates[J]. Journal of Applied Mechanics,1984,51(4): 745-746.
    [2]
    NOOR A K, BURTON W S. Assessment of shear deformation theories for multilayered composite plates[J]. Applied Mechanics Reviews,1989,〖STHZ〗42(1): 1-13.
    [3]
    PIAN T H H, WU C C. Hybrid and Incompatible Finite Element Methods [M]. Chapman and Hall CRC, 2005.
    [4]
    JING H S, LIAO M L. Partial hybrid stress element for the analysis of thick laminated composite plates[J]. Computers & Structures,1990,36(1): 57-64.
    [5]
    田宗漱, 卞学鐄. 多变量变分原理与多变量有限元方法[M]. 北京: 科学出版社, 2011.(TIAN Zhongshu, PIAN T H H. Variational Principle With Multi-Variables and Finite Element With Multi-Variables [M]. Beijing: Science Press, 2011.(in Chinese))
    [6]
    REDDY J N, ROBBINS D H. Theories and computational models for composite laminates[J]. Applied Mechanics Reviews,1994,47(6): 147-169.
    [7]
    钟万勰. 应用力学的辛数学方法[M]. 北京: 高等教育出版社, 2006.(ZHONG Wanxie. Symplectic Solution Methodology in Applied Mechanics [M]. Beijing: Higher Education Press, 2006.(in Chinese))
    [8]
    唐立民, 褚致中, 邹贵平, 等. 混合状态Hamilton元的半解析解和叠层板的计算[J]. 计算力学学报, 1992,9(4): 347-360.(TANG Limin, CHU Zhizhong, ZOU Guiping, et al. The semi-analytical solution of mixed state Hamilton element and the computation of laminated plates[J]. Chinese Journal of Computational Mechanics,1992,9(4): 347-360.(in Chinese))
    [9]
    ZOU G P, TANG L M. A semi-analytical solution for laminated composite plates in Hamilton system[J]. Computer Methods in Applied Mechanics and Engineering,1995,128(3/4): 395-404.
    [10]
    QING G H, QIU J J, LIU Y H. Free vibration analysis of stiffened laminated plates[J]. International Journal of Solids and Structures,2006,43(6): 1357-1371.
    [11]
    ATLURI S N, GALLAGHER R H, ZIENKIEWICZ O C. Hybrid and Mixed Finite Element Methods [M]. Chichester: Wiley, 1983.
    [12]
    ARNOLD D N, FALK R S, WINTHER R. Mixed finite element methods for linear elasticity with weakly imposed symmetry[J]. Mathematics of Computation,2007,76: 1699-1724.
    [13]
    LIAO C L, TSAI J S. Partial mixed 3-D element for the analysis of thick laminated composite structures[J]. International Journal For Numerical Methods in Engineering,1992,35(7): 1521-1539.
    [14]
    QING G, TIAN J. Highly accurate symplectic element based on two variational principles[J]. Acta Mechanica Sinica,2018,34(1): 151-161.
    [15]
    刘艳红, 李锐. 含参数辛元与热弹性复合材料层合板分析[J]. 复合材料学报, 2019,36(5): 1306-1312.(LIU Yanhong, LI Rui. Parametered symplectic element and analysis of thermoelastic composite laminates[J]. Acta Materiae Compositae Sinica,2019,36(5): 1306-1312.(in Chinese))
    [16]
    PAGANO N. Exact solutionsfor composite laminates in cylindrical bending[J]. Journal of Composite Materials,1969,3(3): 398-411.
    [17]
    范家让. 强厚叠层板壳的精确理论[M]. 北京: 科学出版社, 1996.(FAN Jiarang. Exact Theory of Laminated Thick Plates and Shells [M]. Beijing: Science Press, 1996.(in Chinese))
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (845) PDF downloads(372) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return