基于高阶变形理论的硬夹芯夹层板横向载荷条件下的弯曲

郝加琼; 李明成; 邓宗白

doi:10.3879/j.issn.1000-0887.2014.08.005

基于高阶变形理论的硬夹芯夹层板横向载荷条件下的弯曲

doi: 10.3879/j.issn.1000-0887.2014.08.005

南京航空航天大学航空宇航学院,南京 210016

基金项目: 江苏省优势学科建设平台资助项目

详细信息

作者简介:
郝加琼（1986—），男，安徽安庆人，中级工程师，硕士(通讯作者. E-mail:HJQ_2014@163.com).

中图分类号: V214.8;O342
计量
- 文章访问数: 994
- HTML全文浏览量: 60
- PDF下载量: 741
- 被引次数: 0
出版历程
- 收稿日期: 2013-12-03
- 修回日期: 2014-05-04
- 刊出日期: 2014-08-15

Bending of Sandwich Plates With Hard Cores Under Transverse Loading Based on the HighOrder Deformation Theory

College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R.China

摘要

摘要: 考虑面板和夹芯的面内刚度及抗弯刚度，基于高阶变形理论考虑各层的横向抗剪刚度，并根据横向剪应变分布情况给出应力函数，基于广义虚位移原理推导了夹层板的基本方程.详细研究了四边简支受横向载荷条件下的夹层板的弯曲，对比计算了面板与芯层厚度变化对计算结果的影响，并与一阶变形理论计算结果进行对比.研究了厚度方向的剪应变分布情况以及中面法线变形后的形态，给出了横向剪应变引起的附加转角在面内的分布情况.
- 高阶变形理论 /
- 夹层板 /
- 硬夹芯 /
- 横向剪切 /
- 广义虚位移原理 /
- 基本方程
Abstract: Based on the high-order deformation theory, the in-plane stiffness and bending stiffness of both surface layer and core layer of the sandwich plate were considered to derive the transverse shearing stiffnesses of all the layers. The transverse stress function was given according to the transverse strain distribution, and the differential equations for the sandwich plate were deduced with the generalized principle of virtual displacement. The bending deformation of simply supported rectangular sandwich plates with different core-to-surface thickness ratios were detailedly studied under transverse loading, and the calculation results were compared with those from the 1st-order deformation theory to give a bigger relative deformation difference at a smaller thickness ratio. The distribution of transverse strain along the thickness direction makes a half sine curve, and the center-plane normal line distortion culminates at the surface height.
- high-order deformation theory /
- sandwich plate /
- hard core /
- transverse shear /
- generalized principle of virtual displacement /
- basic equation

HTML全文

参考文献(26)

[1]	Reissner E. Finite deflections of sandwich plates[J]. Journal of the Aeronautical Science,1948,15(7): 435-440.
[2]	Reissner E. Small bending and stretching of sandwich-type shells[R]. NACA/TN-975. Washington: NASA, 1950.
[3]	Hoff N J. Bending and buckling of rectangular sandwich plates[R]. NACA/TN-2225. Washington: NASA, 1950.
[4]	杜庆华. 三合板的一般弹性理论[J]. 物理学报, 1954,10(4): 395-412.(TU Ching-hua. General equations of sandwich plates under transverse loads and edgewise shears and compressions[J]. Acta Physica Sinica,1954,10(4): 395-412.(in Chinese))
[5]	胡海昌. 各向同性夹层板反对称小挠度的若干问题[J]. 力学学报, 1963,6(1): 53-59.（HU Hai-chang. On some problems of the antisymetrical small deflection of isotropic sandwich plates[J]. Acta Mechanica Sinica,1963,6(1): 53-59.(in Chinese))
[6]	周际平, 薛大为. 具有不等厚表层的硬夹心双曲夹层扁壳问题[J]. 北京工业学院学报, 1988,8(4):32-45.（ZHOU Ji-ping, XUE Da-wei. On the problems of a shallow double curved sandwich shell with hard core and face layers of unequal thickness[J]. Journal of Beijing Institute of Technology,1988,8(4):32-45.(in Chinese))
[7]	周际平. 考虑各层抗弯刚度和夹心横向弹性的夹层板问题[J]. 北京理工大学学报, 1993,13(1): 101-107.(ZHOU Ji-ping. Problems involving plates of sandwich construction when considering the bending rigidity of each layers and transverse elasticity of the core[J]. Journal of Beijing University of Technology,1993,13(1): 101-107.(in Chinese))
[8]	胡宁宁, 张永发. 变厚度智能硬夹心板振动分析[J]. 动力学与控制学报, 2003,1(1): 70-73.（HU Ning-ning, ZHANG Yong-fa.Vibration analysis of smart changed hard-sandwich plate[J].Journal of Dynamics and Control,2003,1(1): 70-73.(in Chinese))
[9]	马超, 邓宗白. 四边简支硬夹芯夹层板的弯曲问题研究[J]. 应用力学学报, 2013,2(30): 196-200.(MA Chao, DENG Zong-bai. Research on bending of simply supported rectangular sandwich plates with hardened cores[J]. Chinese Journal of Applied Mechanics,2013,2(30): 196-200.(in Chinese))
[10]	杨贺, 邓宗白. 硬夹心矩形夹层板的整体稳定性分析[J]. 固体力学学报, 2013,34(3): 251-258.(YANG He, DENG Zong-bai. The overall buckling analysis of rectangular sandwich plates with hard core[J]. Acta Mechanica Solida Sinica,2013,34(3): 251-258.(in Chinese))
[11]	Reddy J N. A simple higher-order theory for laminated composite plates[J]. Journal of Applied Mechanics,1984,51(4): 745-752.
[12]	Reddy J N. A refined nonlinear theory of plates with transverse shear deformation[J]. International Journal of Solids and Structures,1984,20(9): 881-896.
[13]	Hassis H. A ‘warping’theory of plate deformation[J]. European Journal of Mechanics-A/Solids,1998,17(5): 843-853.
[14]	Hassis H. A “warping-Kirchhoff” and a “warping-Mindlin” theory of shell deformation[J]. Journal of Sound and Vibration,1999,225(4): 633-653.
[15]	Hassis H. A higher order theory for static-dynamic analysis of laminated plates using a warping model[J]. Journal of Sound and Vibration,2000,235(2): 247-260.
[16]	Ferreira A J M, Roque C M C, Jorge R M N, Kansa E J. Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and multiquadrics discretizations[J]. Engineering Analysis With Boundary Elements,2005,29(12): 1104-1114.
[17]	Swaminathan K, Patil S S, Nataraja M S, Mahabaleswara K S. Bending of sandwich plates with anti-symmetric angle-ply face sheets-analytical evaluation of higher order refined computational models[J]. Composite Structures,2006,75(1): 114-120.
[18]	Aydogdu M. A new shear deformation theory for laminated composite plates[J]. Composite Structures,2009, 89(1): 94-101.
[19]	Berdichevsky V L. An asymptotic theory of sandwich plates[J]. International Journal of Engineering Science,2010,48(3): 383-404.
[20]	Ferreira A J M, Roque C M C, Neves A M A, Jorge R M N, Soares C M M, Reddy J N. Buckling analysis of isotropic and laminated plates by radial basis functions according to a higher-order shear deformation theory[J]. Thin-Walled Structures,2011,49(7): 804-811.
[21]	Kheirikhah M M, Khalili S M R, Malekzadeh F K. Biaxial buckling analysis of soft-core composite sandwich plates using improved high-order theory[J]. European Journal of Mechanics-A/Solids,2012,31(1): 54-66.
[22]	Grover N, Maiti D K, Singh B N. A new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates[J]. Composite Structures,2013,95: 667-675.
[23]	Sahoo R, Singh B N. A new inverse hyperbolic zigzag theory for the static analysis of laminated composite and sandwich plates[J]. Composite Structures,2013,105: 385-397.
[24]	Tounsi A, Houari M S A, Benyoucef S, Bedia El A A. A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates[J].Aerospace Science and Technology,2013,24（1）: 209-220.
[25]	Timoshenko S, Woinowsky-Krieger S. Theory of Plates and Shells [M]. New York: McGraw-Hill, 1959.
[26]	尹思明, 阮圣磺. 变厚度矩形薄板的线性和非线性理论的弹性平衡问题的Navier解[J]. 应用数学和力学, 1985,6(6): 519-530.(YIN Si-ming, RUAN Sheng-huang. Navier solution for the elastic equilibrium problems of rectangular thin plates with variable thickness in linear and nonlinear theories[J]. Applied Mathematics and Mechanics,1985,6(6): 519-530.(in Chinese))