An Effective Meshfree Method for Bending and Vibration Analyses of Laminated Composite Plates

WANG Wei; YI Shi-chao; YAO Lin-quan

doi:10.3879/j.issn.1000-0887.2015.12.006

Volume 36 Issue 12

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2015 > 36(12): 1274-1284

WANG Wei, YI Shi-chao, YAO Lin-quan. An Effective Meshfree Method for Bending and Vibration Analyses of Laminated Composite Plates[J]. Applied Mathematics and Mechanics, 2015, 36(12): 1274-1284. doi: 10.3879/j.issn.1000-0887.2015.12.006

Citation:

PDF( 822 KB)

An Effective Meshfree Method for Bending and Vibration Analyses of Laminated Composite Plates

doi: 10.3879/j.issn.1000-0887.2015.12.006

¹School of Mathematical Sciences, Soochow University, Suzhou, Jiangsu 215006, P.R.China;²School of Mathematics and Physics, Jiangsu University of Science and Technology,Zhenjiang, Jiangsu 212003, P.R.China;³School of Urban Rail Transportation, Soochow University, Suzhou, Jiangsu 215131, P.R.China

Funds: The National Natural Science Foundation of China（11172192；11572210）

Received Date: 2015-09-23
Rev Recd Date: 2015-10-23
Publish Date: 2015-12-15

Abstract

Abstract

Numerical analysis of laminated plates’ bending and vibration problems was presented based on the high order shear and normal deformation plate theory (HOSNDPT) with the meshless method. For the usual radial point interpolation method (RPIM), the inverses of the moment matrices are required for each Gauss point or calculation point, and are limited by the radius of the domain. For the weighted node radial point interpolation method (WN-RPIM), the number of the inverses of the system matrices is equal to the number of nodes in the problem domain, which is far less than the number of Gauss points, so the WN-RPIM can greatly reduce the computation complexity of the moment matrices and overcome the limitations on the RPIM. First, the 3D plate displacement was decomposed into the product of the thickness-direction and in-plane displacements, and the orthogonal Legendre polynomials were used as basis functions in the thickness direction, the WN-RPIM was employed in plane to construct the shape functions. Then, the numerical calculation of the bending problems of laminated plates verified the accuracy and stability of the WN-RPIM. At last, the proposed method was extended to the numerical calculation of the vibration problems of laminated plates with different boundary conditions, different thickness-to-span ratios and different laying patterns. The numerical results show the applicability and effectiveness of the proposed method.

FullText(HTML)

References(16)

References

[1]	Reddy J N.Mechanics of Laminated Composite Plates and Shells: Theory and Analysis [M]. New York: CRC Press, 1997.
[2]	Soldatos K P, Watson P. Accurate stress analysis of laminated plates combing a two-dimensional theory with the exact three-dimensional solution for simply supported edges[J].Mathematics and Mechanics of Solids,1997,2(4): 459-489.
[3]	Lee P C Y, Syngellakis S, Hou J P. A two-dimensional theory for high-frequency vibrations of piezoelectric crystal plates with or without electrodes[J].Journal of Applied Physics,1987,26(4): 1249-1262.
[4]	Mindlin R C, Medlick M A. Extensional vibrations of elastic plates[J].Journal of Applied Mechanics,1959,26(2): 145-151.
[5]	Batra R C, Vidoli S. Higher-order piezoelectric plate theory derived from a three-dimensional variational principle[J].AIAA Journal,2012,40(1): 91-104.
[6]	Batra R C, Aimmanee S. Vibrations of thick isotropic plates with higher order shear and normal deformable plate theories[J].Computers & Structures,2005,83(12/13): 934-955.
[7]	Sze K Y, Yao L Q, Pian T H H. An eighteen-node hybrid-stress solid-shell for homogenous and laminated structures[J].Finite Elements in Analysis and Design,2002,38(4): 353-374.
[8]	YAO Lin-quan, Sze K Y. A hybrid-stress solid-shell element for non-linear analysis of piezoelectric structures[J].Science in China Series E: Technological Sciences,2009,52(3): 575-583.
[9]	YIN Yu, YAO Lin-quan, CAO Yang. A 3D shell-like approach using element-free Galerkin method for analysis of thin and thick plate structures[J].Acta Mechanica Sinica,2013,29(1): 85-98.
[10]	CAO Yang, YAO Lin-quan, YI Shi-chao. A weighted nodal-radial point interpolation meshless method for 2D solid problems[J].Engineering Analysis With Boundary Elements,2014,39: 88-100.
[11]	Xiao J R, Gilhooley D F, Batra R C, Gillespie J J W, McCarthye M A. Analysis of thick composite laminates using a higher-order shear and normal deformable plate theory(HOSNDPT) and a meshless method[J].Composites Part B: Engineering,2008,39(2): 414-427.
[12]	Ferreira A J M, Roque C M C, Martins P A L S. Radial basis functions and higher-order shear deformation theories in the analysis of laminated composite beams and plates[J].Composite Structures,2004,66(1/4): 287-293.
[13]	陈富军, 魏春志, 姚林泉. 基于局部移动Kriging无网格方法的层合板自由振动分析[J]. 计算力学学报, 2013,30(4): 559-564.(CHEN Fu-jun, WEI Cun-zhi, YAO Lin-quan. Free vibration analysis of laminated composite plates by local moving Kriging meshless method[J].Journal of Computational Mechanics,2013,30(4): 559-564.(in Chinese))
[14]	Bui T Q, Khosravifard A, Zhang C, Hematiyan M R, Golub M V. Dynamic analysis of sandwich beams with functionally graded core using a truly meshfree radial point interpolation method[J].Engineering Structures,2013,47: 90-104.
[15]	李顶河, 徐建新, 卿光辉. Hamilton体系下含弱粘接复合材料层合板的灵敏度分析研究[J]. 应用数学和力学, 2010,31(12): 1465-1475.(LI Ding-he, XU Jian-xin, QING Guang-hui. Sensitivity analysis of composite laminated plates with bonding imperfection in Hamilton system[J].Applied Mathematics and Mechanics,2010,31(12): 1465-1475.(in Chinese))
[16]	王勖成. 有限单元法[M]. 北京: 清华大学出版社, 2003.(WANG Xu-cheng.Finite Element Method [M]. Beijing: Tsinghua University Press, 2003.(in Chinese))