Research on Reissner Plate With an Inclusion or Flaw

JIANG Quan; WEI Hai-e; ZHOU Zhi-dong

doi:10.3879/j.issn.1000-0887.2013.11.009

Volume 34 Issue 11

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2013 > 34(11): 1197-1208

JIANG Quan, WEI Hai-e, ZHOU Zhi-dong. Research on Reissner Plate With an Inclusion or Flaw[J]. Applied Mathematics and Mechanics, 2013, 34(11): 1197-1208. doi: 10.3879/j.issn.1000-0887.2013.11.009

Citation:

JIANG Quan, WEI Hai-e, ZHOU Zhi-dong. Research on Reissner Plate With an Inclusion or Flaw[J]. Applied Mathematics and Mechanics, 2013, 34(11): 1197-1208. doi: 10.3879/j.issn.1000-0887.2013.11.009

Citation:

JIANG Quan, WEI Hai-e, ZHOU Zhi-dong. Research on Reissner Plate With an Inclusion or Flaw[J]. Applied Mathematics and Mechanics, 2013, 34(11): 1197-1208. doi: 10.3879/j.issn.1000-0887.2013.11.009

PDF( 1063 KB)

Research on Reissner Plate With an Inclusion or Flaw

doi: 10.3879/j.issn.1000-0887.2013.11.009

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）

Received Date: 2013-04-25
Rev Recd Date: 2013-06-27
Publish Date: 2013-11-15

Abstract

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

FullText(HTML)

References(26)

References

[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.