功能梯度板的柱面弯曲弹性力学解

杨云芳; 杨博; 陈伟球; 丁皓江

doi:10.3879/j.issn.1000-0887.2015.12.004

功能梯度板的柱面弯曲弹性力学解

doi: 10.3879/j.issn.1000-0887.2015.12.004

¹浙江理工大学建筑工程学院土木工程系, 杭州 310018;²浙江大学航空航天学院工程力学系, 杭州 310027;³浙江大学建筑工程学院土木工程系, 杭州 310027

基金项目: 国家自然科学基金(11202188；11172263)

详细信息

作者简介:
杨云芳(1957—), 女, 浙江金华人, 教授, 硕士生导师(E-mail: yyfzist@163.com)；杨博(1979—), 男, 宁夏灵武人, 副教授, 博士, 硕士生导师(通讯作者. Tel: +86-571-86843376; E-mail: bo.young@163.com);陈伟球(1969—), 男, 江苏吴江人, 教授, 博士, 博士生导师(E-mail: chenwq@zju.edu.cn);丁皓江(1934—2015), 男, 江苏常州人, 教授, 博士生导师(E-mail: dinghj@zju.edu.cn).

中图分类号: O343.1
计量
- 文章访问数: 1289
- HTML全文浏览量: 118
- PDF下载量: 649
- 被引次数: 0
出版历程
- 收稿日期: 2015-09-17
- 修回日期: 2015-10-19
- 刊出日期: 2015-12-15

Elasticity Solutions for Cylindrical Bending of Functionally Graded Plates

¹Department of Civil Engineering, School of Civil Engineering and Architecture, Zhejiang Sci-Tech University, Hangzhou 310018, P.R.China;²Department of Engineering Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, P.R.China;³Department of Civil Engineering, College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310027, P.R.China

Funds: The National Natural Science Foundation of China(11202188；11172263)

摘要

摘要: 在推广后的England-Spencer功能梯度板理论基础上,研究了功能梯度板在不同荷载作用下的柱面弯曲问题.采用该理论中的位移展开公式,并且材料参数沿板厚方向可以任意连续变化,并将材料由各向同性推广到正交各向异性.假设板在y方向无限长,最终建立了一个从弹性力学理论出发的正交各向异性功能梯度板在横向分布荷载作用下柱面弯曲问题的板理论.通过算例分析,讨论了边界条件、材料梯度及板厚跨比等因素对功能梯度板静力响应的影响.
- 功能梯度板 /
- 柱面弯曲 /
- 弹性力学解
Abstract: The cylindrical bending of functionally graded rectangular plates under different loads was studied based on a generalization of the England-Spencer theory. The expansion formulae for displacements and the assumption that the material parameters can vary along the thickness direction in an arbitrary fashion were adopted. The elasticity solutions were obtained for an orthotropic functionally graded plate in cylindrical bending with an infinite length in y-direction. The effects of the boundary conditions, the material gradient and the thickness-to-span ratio on the static responses of the functionally graded plates were investigated through a numerical example. The proposed solutions are useful for the validation of various numerical methods or approximate plate theories.
- functionally graded plate /
- cylindrical bending /
- elasticity solution

HTML全文

参考文献(13)

[1]	Li X Y, Ding H J, Chen W Q. Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qr^k[J].International Journal of Solids and Structures,2008,45(1): 191-210.
[2]	Woodward B, Kashtalyan M. Three-dimensional elasticity solution for bending of transversely isotropic functionally graded plates[J].European Journal of Mechanics—A/Solids,2011,30(5): 705-718.
[3]	WANG Yu, XU Rong-qiao, DING Hao-jiang. Three-dimensional solution of axisymmetric bending of functionally graded circular plates[J]. Composite Structures,2010,92(7): 1683-1693.
[4]	Birman V, Byrd L W. Modeling and analysis of functionally graded materials and structures[J].ASME Applied Mechanics Reviews,2007,60(5): 195-216.
[5]	Timoshenko S P, Woinowsky-Krieger S. Theory of Plates and Shells [M]. 2nd ed. New York: McGraw-Hill, 1959.
[6]	Bian Z G, Chen W Q, Lim C W, Zhang N. Analytical solutions for single- and multi-span functionally graded plates in cylindrical bending[J].International Journal of Solids and Structures,2005,42(24/25): 6433-6456.
[7]	Navazi H M, Haddadpour H, Rasekh M. An analytical solution for nonlinear cylindrical bending of functionally graded plates[J].Thin-Walled Structures,2006,44(11): 1129-1137.
[8]	Kaci A, Bakhti K, Hebali H, Tounsi A. Mathematical solution for nonlinear cylindrical bending of sigmoid functionally graded plates[J]. Journal of Applied Mechanics and Technical Physics,2013,54(1): 124-131.
[9]	Mian M A, Spencer A J M. Exact solutions for functionally graded and laminated elastic materials[J].Journal of the Mechanics and Physics of Solids,1998,46(12): 2283-2295.
[10]	杨博, 丁皓江, 陈伟球. 功能梯度板柱面弯曲的弹性力学解[J]. 应用数学和力学, 2008,29(8): 905-910.(YANG Bo, DING Hao-jiang, CHEN Wei-qiu. Elasticity solutions for functionally graded plates in cylindrical bending[J].Applied Mathematics and Mechanics,2008,29(8): 905-910.(in Chinese))
[11]	England A H. Bending solutions for inhomogeneous and laminated elastic plates[J]. Journal of Elasticity,2006,82(2): 129-173.
[12]	Yang B, Ding H J, Chen W Q. Elasticity solutions for functionally graded rectangular plates with two opposite edges simply supported[J].Applied Mathematical Modelling,2012,36(1): 488-503.
[13]	Yang B, Chen W Q, Ding H J. Elasticity solutions for functionally graded annular plates subject to biharmonic loads[J]. Archive of Applied Mechanics,2014,84(1): 51-65.