ZHANG Ying, MEI Jing, CHEN Ding, YANG Bo. Elasticity Solutions for Functionally Graded Circular and Annular Plates Subjected to Boundary Forces and Moments[J]. Applied Mathematics and Mechanics, 2018, 39(5): 538-547. doi: 10.21656/1000-0887.380275
Citation: ZHANG Ying, MEI Jing, CHEN Ding, YANG Bo. Elasticity Solutions for Functionally Graded Circular and Annular Plates Subjected to Boundary Forces and Moments[J]. Applied Mathematics and Mechanics, 2018, 39(5): 538-547. doi: 10.21656/1000-0887.380275

Elasticity Solutions for Functionally Graded Circular and Annular Plates Subjected to Boundary Forces and Moments

doi: 10.21656/1000-0887.380275
Funds:  The National Natural Science Foundation of China(11202188)
  • Received Date: 2017-07-14
  • Rev Recd Date: 2018-01-09
  • Publish Date: 2018-05-15
  • On the basis of the generalized England-Spencer plate theory, the 3D elastic fields of functionally graded circular and annular plates subjected to boundary forces were studied. The elastic constants of the material can be arbitrarily continuously variable along the thickness direction. Expressions of 4 complex potentials for solving the problem were given with the complex variable function method in which the undetermined constants were solved from the cylindrical boundary conditions of the plate. When the inner radius of the annular plate approaches zero, solutions of the annular plate reach to those of the corresponding circular plate. Numerical examples conducted show the effects of the material gradient, the load type and the thickness to radius ratio on the static responses of functionally graded plates.
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  • [1]
    赵劲彪, 郑香伟, 冯蕴雯, 等. 飞机起落架应急放机构可靠性分析[J]. 机械设计与制造, 2014,8: 31-33.(ZHAO Jinbiao, ZHENG Xiangwei, FENG Yunwen, et al. Reliability analysis of landing gear mechanism during emergency extending[J]. Machinery Design & Manufacture,2014,8: 31-33.(in Chinese))
    [2]
    武晓全, 薛军. 民机结构疲劳损伤可靠性分析[J]. 装备制造技术, 2014,10: 201-203.(WU Xiaoquan, XUE Jun. Structural reliability analysis of fatigue damage of civil aircraft[J]. Equipment Manufacturing Technology,2014,10: 201-203.(in Chinese))
    [3]
    YOO D, LEE I, CHO H. Probabilistic sensitivity analysis for novel second-order reliability method(SORM) using generalized chi-squared distribution[J]. Structural and Multidisciplinary Optimization, 2014,50(5): 787-797.
    [4]
    LI Gang, ZHANG Kai. A combined reliability analysis approach with dimension reduction method and maximum entropy method[J]. Structural and Multidisciplinary Optimization,2011,43(1): 121-134.
    [5]
    EZZATI G, MAMMADOV M, KULKARNI S. A new reliability analysis method based on the conjugate gradient direction[J]. Structural and Multidisciplinary Optimization,2015,51(1): 89-98.
    [6]
    MARTINO L, ELVIRA V, LUENGO D, et al. Layered adaptive importance sampling[J]. Statistics and Computing,2017,27(3): 599-623.
    [7]
    FAN Haijian, LIANG R. Importance sampling based algorithm for efficient reliability analysis of axially loaded piles[J]. Computers and Geotechnics,2015,65: 278-284.
    [8]
    DUBOURG V, SUDRET B, BOURINET J-M. Reliability-based design optimization using Kriging surrogates and subset simulation[J]. Structural and Multidisciplinary Optimization, 2011,44(5): 673-690.
    [9]
    LI Hongshuang, MA Yuanzhuo, CAO Zijun. A generalized subset simulation approach for estimating small failure probabilities of multiple stochastic responses[J]. Computers & Structures,2015,153: 239-251.
    [10]
    RAMU P, KIM N H, HAFTKA R T. Multiple tail median approach for high reliability estimation[J]. Structural Safety,2010,32(2): 124-137.
    [11]
    TANG Zhangchun, LU Zhenzhou, PAN Wang, et al. A mean extrapolation technique for high reliability analysis[J]. Applied Mathematics and Computation,2013,222: 82-93.
    [12]
    PICKANDS J. Statistical-inference using extreme order statistics[J]. The Annals of Statistics,1975,3(1): 119-131.
    [13]
    TORII A J, LOPEZ R H, MIGUEL L F F. A general RBDO decoupling approach for different reliability analysis methods[J].Structural and Multidisciplinary Optimization,2016,54(2): 317-332.
    [14]
    JEONG S, MURAYAMA M, YAMAMOTO K. Efficient optimization design method using Kriging model[J]. Journal of Aircraft,2005,42(2):413-420.
    [15]
    谢延敏, 于沪平, 陈军, 等. 基于Kriging模型的可靠度计算[J]. 上海交通大学学报, 2007,41(2): 177-180.(XIE Yanmin, YU Huping, CHEN Jun, et al. The reliability estimation based on Kriging model[J].Journal of Shanghai Jiaotong University,2007,41(2): 177-180.(in Chinese))
    [16]
    BALESDENT M, MORIO J, MARZAT J. Kriging-based adaptive importance sampling algorithms for rare event estimation[J].Structural Safety,2013,44: 1-10.
    [17]
    SANTOS S R, MATIOLI L C, BECK A T. New optimization algorithms for structural reliability analysis[J]. Computer Modeling in Engineering and Sciences,2012,83(1): 23-55.
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