Reissner板中的夹杂和缺陷问题研究

蒋泉; 魏海娥; 周志东

doi:10.3879/j.issn.1000-0887.2013.11.009

Reissner板中的夹杂和缺陷问题研究

doi: 10.3879/j.issn.1000-0887.2013.11.009

¹南通大学建筑工程学院, 江苏南通 226019;²南通大学理学院, 江苏南通 226019;
厦门大学材料学院, 福建厦门 361005

基金项目: 国家自然科学基金资助项目(10902055;11172252）

详细信息

作者简介:
蒋泉(1974—),男,江苏南通人,博士,副教授,硕士生导师(通讯作者. Tel:+86513-85012659; E-mail: jiang.q@ntu.edu.cn).

中图分类号: O343.7
计量
- 文章访问数: 1029
- HTML全文浏览量: 53
- PDF下载量: 1293
- 被引次数: 0
出版历程
- 收稿日期: 2013-04-25
- 修回日期: 2013-06-27
- 刊出日期: 2013-11-15

Research on Reissner Plate With an Inclusion or Flaw

¹School of Architecture Engineering, Nantong University, Nantong, Jiangshu 226019, P.R.China;²School of Science, Nantong University, Nantong, Jiangshu 226019, P.R.China;³College of Materials, Xiamen University, Xiamen, Fujian 361005, P.R.China

Funds: The National Natural Science Foundation of China(10902055;11172252）

摘要

摘要: 基于保角变换技术和Faber级数展开，研究了含任意形状夹杂或缺陷的无限大Reissner板弯曲问题．将变换域中单位圆内、外解析函数分别展开成Faber级数，并将波动函数展开成第一类和第二类修正的n阶Bessel函数；利用边界位移、剪力和弯矩连续性条件得到问题的高阶线性方程组．以含椭圆形夹杂和缺陷的无限大Reissner板柱面弯曲为例，进一步给出了数值算例和理论分析．结果表明，对于软夹杂，板内力矩随夹杂与板厚尺寸比a/h变化非常敏感；在含硬夹杂条件下，板内力矩随夹杂尺寸变化相对不敏感．
- 弯曲问题 /
- Reissner板 /
- 夹杂 /
- 缺陷 /
- Faber级数
Abstract: The bending problems for the Reissner plate with arbitrarily shaped inclusion or flaw were solved with the conformal transformation method and Faber series expanding. The analytical functions were expanded with Faber series, and the wave functions were expressed by n-order first-kind and second-kind modified Bessel functions in/out the unit circle in the transform domain. The linear equations were obtained under the continuous displacement, shear force and bending moment conditions along the interface of the unit circle. The numerical examples and the theoretical analysis were presented for the Reissner plate with an elliptic inclusion or flaw under cylindrical bending. It is concluded that, the inner torques in the plate are sensitive to the ratio a/h for the soft inclusion, and are insensitive for the stiff one.
- bending-problem /
- Reissner-plate /
- inclusion /
- flaw /
- Faber-series

HTML全文

参考文献(26)

[1]	Sayin G N. Stress Concentration Round Holes [M]. London: Pergamon Press, 1961.
[2]	何福保, 沈亚鹏. 板壳理论[M]. 西安: 西安交通大学出版社, 1993.(HE Fu-bao, SHEN Ya-peng. Theory of Plates and Shells [M]. Xi’an Jiaotong University Press, 1993.(in Chinese))
[3]	Redwood R G. The bending of a plate loaded through a rigid rectangular inclusion[J]. International Journal of Mechanical Sciences,1965, 7(6): 421-430.
[4]	贺鹏飞. 弯曲外载作用下夹杂角点的应力奇异性[J]. 同济大学学报(自然科学版), 1996, 24(4): 405-410.(HE Peng-fei. Stress singularity at corner point of an inclusion under moment[J]. Journal of Tongji Univesity(Natural Science),1996, 24(4): 405-410.(in Chinese))
[5]	Cheng Z Q, Reddy J N. Laminated anisotropic thin plate with an elliptic inhomogeneity[J]. Mechanics of Materials,2004, 36(7): 647-657.
[6]	董春迎. 基于边界元法的非均质薄板弯曲问题的解[J]. 计算力学学报, 2011, 28(1): 25-28. (DONG Chun-ying. BEM-based solution of heterogeneous thin plate bending problems[J]. Chinese Journal of Computational Mechanics,2011, 28(1): 25-28.(in Chinese))
[7]	Rudoy E M. The Griffith formula and CherepanovRice integral for a plate with a rigid inclusion and a crack[J]. J Math Sci,2012, 186(3): 511-529.
[8]	毛春见, 许希武, 郭树祥. 含椭圆孔有限大薄板弯曲应力分析[J]. 固体力学学报, 2012, 31(1): 80-85.(MAO Chun-jian, XU Xi-wu, GUO Shu-xiang. Stress analysis of a finite anisotropic thin plate with an elliptical hole[J]. Chinese Journal of Solid Mechanics,2012, 31(1): 8085.(in Chinese))
[9]	许希武, 章怡宁, 杨旭. 含孔有限大各向异性板的应力集中[J]. 航空学报, 1995, 16(3): 370-375.(XU Xi-wu, ZHANG Yi-ning, YANG Xu. Stress concentration of finite anisotropic plate with elliptical hole[J]. Acta Aeronautica et Astronautica Sinica,1995, 16(3): 370-375.(in Chinese))
[10]	Hsieh M C, Hwu C. Anisotropic elastic plates with holes/cracks/inclusions subjected to out-of-plane bending moments[J].International Journal of Solids and Structures,2002, 39(19): 4905-4925.
[11]	Hwu C, Tan C J. In-plane/out-of-plane concentrated forces and moments on composite laminates with elliptical elastic inclusions[J]. International Journal of Solids and Structures,2007, 44(20): 6584-6606.
[12]	Gao L M, Wang J, Zhong Z, Du J K. An analysis of surface acoustic wave propagation in functionally graded plates with homotopy analysis method[J].Acta Mech,2009, 208(3): 249-258.
[13]	Liu D Y, Wang C Y, Chen W Q. Free vibration of FGM plates with inplane material inhomogeneity[J].Composite Structures,2010, 92(5): 1047-1051.
[14]	Kunets Y I, Matus V V. Modelling of flexural vibrations of a Kirchhoff plate with a thin-walled elastic inclusion of weak contrast[J].J Math Sci,2012, 187(5): 667-674.
[15]	Palermo L. The tangential differential operator applied to a stress boundary integral equation for plate bending including the shear deformation effect[J].Engineering Analysis With Boundary Elements,2012, 36(8): 1213-1225.
[16]	Sladek J, Sladek V, Krahulec S, Pan E. Analyses of functionally graded plates with a magnetoelectroelastic layer[J].Smart Materials and Structures,2013, 22(3): 35003-35019.
[17]	Zhong Y F, Chen L, Yu W B, Zhang L L. Asymptotical construction of a fully coupled, Reissner-Mindlin model for piezoelectric and piezomagnetic laminates[J]. Composite Structures,2012, 94(12): 3583-3591.
[18]	吕品, 黄茂光. Reissner板弯曲的复变函数分析方法[J]. 力学学报, 1990, 22(6): 689-699. (Lü Pin, HUANG Mao-guang. Complex variable analytic method for solving Reissner plate bending problem[J]. Acta Mechanica Sinica,1990, 22(6): 689-699.(in Chinese))
[19]	杨丽敏, 柳春图, 曾晓辉. 含圆孔压电板弯曲问题[J]. 机械强度, 2005, 27(1): 85-94.(YANG Li-min, LIU Chun-tu, ZENG Xiao-hui. Bending problem of piezoelectric plate with a circular hole[J]. Journal of Mechanical Strength, 2005, 27(1): 85-94.(in Chinese))
[20]	Opanasovych V K, Yatsyk I M, Sulym H T. Bending of Reissner’s plate containing a through-the-thickness crack by concentrated moments taking into account the width of a contact zone of its faces[J]. J Math Sci, 2012, 187(5): 620-634.
[21]	王子昆, 李丽娟. 含球形空腔或刚性夹杂的中厚圆板在弯曲变形时的弹性场[J]. 应用力学学报, 1989, 6(2): 51-60.(WANG Zikun, LI Li-juan. The elastic field of middle thick circular plate with a spherical cavern or a rigid inclusion undergoing bending load[J].Chinese Journal of Applied Mechanics, 1989, 6(2): 51-60.(in Chinese))
[22]	Muskhelishvili N I. Some Basic Problems of the Mathematical Theory of Elasticity [M]. Groningen: Noordhoff, 1975.
[23]	Mazurak L P, Berezhnyts’kyi L T, Kachur P S. A method for the determination of the elastic equilibrium of isotropic bodies with curvilinear inclusions—part 1: mathematical foundations[J]. Mater Sci,1998,34(6): 760-772.
[24]	Curtiss J H. Faber polynomials and the Faber series[J].Am Math Mon,1971, 78(6): 577-596.
[25]	Luo J C, Gao C F. Faber series method for plane problems of an arbitrarily shaped inclusion[J].Acta Mech, 2009,208(3): 133-145.
[26]	Luo J C, Gao C F. Stress field of a coated arbitrary shape inclusion[J]. Meccanica, 2011, 46(5): 1055-1071.