## 留言板

 引用本文: 姚伟岸, 聂臆瞩, 肖峰. 基于辛对偶体系的层合板自由边缘效应的分析解[J]. 应用数学和力学, 2011, 32(9): 1021-1029.
YAO Wei-an, NIE Yi-zhu, XIAO Feng. Analytical Solutions to Edge Effect of Composite Laminates Based on Symplectic Dual System[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1021-1029. doi: 10.3879/j.issn.1000-0887.2011.09.001
 Citation: YAO Wei-an, NIE Yi-zhu, XIAO Feng. Analytical Solutions to Edge Effect of Composite Laminates Based on Symplectic Dual System[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1021-1029.

• 中图分类号: O343

## Analytical Solutions to Edge Effect of Composite Laminates Based on Symplectic Dual System

• 摘要: 在原变量——位移和其对偶变量——应力组成的辛几何空间，建立了Pipes-Pagano模型的复合材料层合板问题的辛对偶求解体系．与传统的单类变量不同，辛对偶变量有利于同时描述层间位移连续性条件和应力平衡条件．进入辛对偶体系以后，就可以应用辛对偶体系的统一解析求解方法，如分离变量和辛本征展开的方法对层合板问题进行解析分析和求解．对层合板自由边缘效应的分析求解，验证了辛对偶体系的方法对层合板问题的分析求解是十分有效的．
•  [1] Pipes R B, Pagano N J. Interlaminar stresses in composite laminates under uniform axial extension[J]. J Comp Mater, 1970, 4(10): 538-548. [2] Pipes R B, Pagano N J. Interlaminar stresses in composite Laminates—an approximate elasticity solution[J]. J Appl Mech Trans ASME, 1974, 41(9): 668-672. [3] Hsu P W, Herakovick C T. Edge effects in angle-ply composite laminates[J]. J Comp Mater, 1977, 11(4): 422-438. [4] Bar-Yoseph P, Pian T H H. Calculation of interlaminar stress concentration in composite laminates[J]. J Comp Mater, 1981, 15(5): 225-239. [5] Tang S. A boundary layer theory—part Ⅰ: laminated composites in plane stress[J]. J Comp Mater, 1975, 9(1): 33-41. [6] Wang S S, Choi I. Boundary-layer effects in composite laminates: part Ⅰ—free-edge stress singularities[J]. J Appl Mech Trans ASME, 1982, 49(9): 541-548. [7] Mittelstedt C, Becker W. Free-edge effects in composite laminates[J]. Applied Mechanics Reviews, 2007, 60(5): 217-245. [8] Timoshenko S P, Goodier J N. Theory of Elasticity[M]. 3rd ed. New York: McGraw-Hill, 1970. [9] 钟万勰.弹性力学求解新体系[M].大连: 大连理工大学出版社, 1995.(ZHONG Wan-xie. A New Systematic Methodology for Theory of Elasticity[M]. Dalian: Dalian University of Technology Press, 1995.(in Chinese)) [10] Zhong W X, Yao W A. The Saint Venant solutions of multi-layered composite plates[J]. Advances in Strunctural Engineering, 1997, 1(2): 127-133. [11] Yao W A, Yang H T. Hamiltonian system based Saint Venant solutions for multi-layered composite plane anisotropic plates[J]. I J Solids & Structures, 2001, 38(32): 5807-5817. [12] Yao W A, Zhong W X, Lim C W. Symplectic Elasticity[M]. Singapore: World Scientific, 2009.

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##### 出版历程
• 收稿日期:  2011-04-02
• 修回日期:  2011-07-01
• 刊出日期:  2011-09-15

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