功能梯度圆板和环板受周边力作用的弹性力学解

张莹; 梅靖; 陈鼎; 杨博

doi:10.21656/1000-0887.380275

功能梯度圆板和环板受周边力作用的弹性力学解

doi: 10.21656/1000-0887.380275

浙江理工大学土木工程系, 杭州 310018

基金项目: 国家自然科学基金(11202188)；浙江省自然科学基金(LY18A020009)

详细信息

作者简介:
张莹(1993—), 女, 硕士生(E-mail: 1013516504@qq.com);梅靖(1994—), 男, 硕士生(E-mail: 958801857@qq.com);陈鼎(1993—), 男, 硕士生(E-mail: 267402159@qq.com);杨博(1979—), 男, 副教授, 硕士生导师(通讯作者. Tel: 0571-86843376；E-mail: youngbo@zstu.edu.cn).

中图分类号: O343.1
计量
- 文章访问数: 1070
- HTML全文浏览量: 147
- PDF下载量: 463
- 被引次数: 0
出版历程
- 收稿日期: 2017-07-14
- 修回日期: 2018-01-09
- 刊出日期: 2018-05-15

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

Department of Civil Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, P.R.China

Funds: The National Natural Science Foundation of China(11202188)

摘要

摘要: 在推广后的England-Spencer板理论基础上, 研究了功能梯度圆板和环板受周边力作用的三维弹性场.材料参数沿板厚方向可以任意连续变化, 利用复变函数理论给出了求解该问题所需要的4个复势表达式, 其中含有的待定常数利用板的柱面边界条件确定.当功能梯度环板的内径趋向于零时便退化到圆板问题的解答.通过算例分析, 讨论了材料梯度、荷载类型及板厚跨比等因素对功能梯度圆环板静力响应的影响.
- 功能梯度材料 /
- 圆环板 /
- 边界力 /
- 弹性力学解
Abstract: 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.
- functionally graded material /
- annular plate /
- boundary force /
- elasticity solution

HTML全文

参考文献(17)

[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.