浸透层对层合梁力学性能的影响分析

复合材料科学与工程 ›› 2014, Vol. 0 ›› Issue (1): 43-47.

浸透层对层合梁力学性能的影响分析

赵凯, 周叮^*, 刘伟庆, 方海

南京工业大学土木工程学院,南京211816

收稿日期:2013-05-14 出版日期:2014-01-28 发布日期:2021-09-17
通讯作者: 周叮(1957-),男,教授,博导,主要从事结构动力学和复合材料力学研究,dingzhou57@yahoo.com。
作者简介:赵凯(1987-),男,硕士,主要从事新型复合结构材料研究。
基金资助:
国家重点基础研究发展计划(2012CB026205)

MECHANICAL PROPERTIES ANALYSIS OF SIMPLE-SUPPORTED SANDWICH COMPOSITE BEAM WITH IMBUE LAYERS

ZHAO Kai, ZHOU Ding, LIU Wei-qing, FANG Hai

College of Civil Engineering, Nanjing University of Technology, Nanjing 211816, China

Received:2013-05-14 Online:2014-01-28 Published:2021-09-17

摘要/Abstract

摘要： 将层合梁粘结层形成的浸透层考虑为功能梯度层,并假设弹性模量在浸透层内沿厚度指数变化,泊松比为常数,利用平面应力弹性力学问题的基本方程,导出满足控制微分方程和两端简支边界条件的位移函数的一般解,然后根据层合梁上下表面的边界条件确定待定系数,带回递推公式得到整个层合梁的应力和位移分布。对三明治梁进行了精细化分析,结果显示浸透层的存在对减小界面层的应力突变和梁的整体位移有一定的积极作用,浸透层的厚度越大,效果越明显。

关键词: 复合材料, 梁, 浸透层, 功能梯度, 弹性力学解

Abstract: In this paper, the imbue layers caused by the banding layer of the composite material are considered as the functionally graded materials, and the Young’s modulus is graded through the thickness following the exponential-law and the Poisson’s ratio keeps constant. According to the governing equations of plane stress problems, the general expressions of displacements, which exactly satisfy the governing differential equations and the simply-supposed boundary conditions at two ends of the beam are deduced. Afterwards, the unknown coefficients are determined by using the upper surface and lower surface conditions of the laminated beam. Finally, the displacements and stresses in the beam are given by substituting the unknown coefficients back to the recurrent formulae. Detailed analysis compared with sandwich beams, results show that the existence of imbue layer has a certain positive role to reduce the stress of the interface layer mutation and the overall displacement of beam, and the imbue layer is thicker, the effect is more obviously.

Key words: composite material, beam, imbue layer, functionally graded, elasticity solutions

中图分类号:

TB332
TQ11

赵凯, 周叮, 刘伟庆, 方海. 浸透层对层合梁力学性能的影响分析[J]. 复合材料科学与工程, 2014, 0(1): 43-47.

ZHAO Kai, ZHOU Ding, LIU Wei-qing, FANG Hai. MECHANICAL PROPERTIES ANALYSIS OF SIMPLE-SUPPORTED SANDWICH COMPOSITE BEAM WITH IMBUE LAYERS[J]. COMPOSITES SCIENCE AND ENGINEERING, 2014, 0(1): 43-47.

参考文献

[1] Kirchhoff G J. Uber das gleichgewicht und die bewegung einer elastischen schreitbe[J]. Reine Angew Math,1850,40:51-58.
[2] Reissner E. Reflection on the theory of elastic plates[J]. J Appl Mech,1945,38:1453-1464.
[3] Mlindlin R D. Influence of rotary inertia and shear on flexural motions of isotropic elastic plates[J]. J Appl Mech, 1951, 18:31-38.
[4] 马满珍. 日本功能材料的发展[J]. 玻璃钢/复合材料,1992,(1):52-53.
[5] Hirai T, Chen L. Recent and prospective devel -opment of functionally graded materials in Japan[J]. Materials Science Forum,1999,308:509-514.
[6] 仲政,吴林志,陈伟球. 功能梯度材料与结构的若干力学问题研究进展[J]. 力学进展,2010,40( 5): 528-540.
[7] Sankar B V. An elastic solution for functionally graded beams[J]. Composite Science and Technology,2001,61(5):689-696.
[8] 仲政,于涛. 功能梯度悬臂梁弯曲问题的解析解[J]. 同济大学学报:自然科学版,2006,34(4):443-447.
[9] 于涛, 仲政. 均布荷载作用下功能梯度悬臂梁弯曲问题的解析解[J]. 固体力学学报,2006,27(1):15-20.
[10] 黄德进,丁皓江,陈伟球.线性分布荷载作用下功能梯度各向异性悬臂梁的解析解[J].应用数学和力学,2007,28(7):763-768.
[11] 黄德进,丁皓江,陈伟球. 任意荷载作用下各向异性功能梯度悬臂梁的解析解和半解析解[J]. 中国科学G辑:物理学,2009,39(6):830-842.
[12] 王明禄,马文蕾,魏高峰. 热荷载下功能梯度材料梁的热弹性弯曲[J]. 玻璃钢/复合材料,2009,(1):7-9.
[13] 黄立新,姚琪,张晓磊. 基于分层法的功能梯度材料有限元分析[J]. 玻璃钢/复合材料,2013,(2):43-48.
[14] 程红梅,曹志远. 功能梯度材料单参数反演分析[J]. 玻璃钢/复合材料,2009,(3):16-22.
[15] 徐芝纶. 弹性力学[M]. 北京:高等教育出版社,1990.
[16] Lee W J et al.Thermal Fatigue Cracking and Extension Behaviorsof Squeeze Infiltrated Al₁₈B₄O₃₃/Mg Functionally Graded Materials[J]. Materials Transactions,2009,50(4):864-871.