任意厚度具有自由边叠层板的精确解析解

王德才; 关群; 范家让

doi:10.3879/j.issn.1000-0887.2013.07.002

任意厚度具有自由边叠层板的精确解析解

doi: 10.3879/j.issn.1000-0887.2013.07.002

¹中国科学技术大学地球和空间科学学院,合肥 230026;²合肥工业大学土木与水利工程学院,合肥 230009

基金项目: 国家自然科学基金资助项目(51278519)

详细信息

作者简介:
王德才(1982—),男,安徽肥东人,博士(通讯作者. E-mail: wdecai@ustc.edu.cn)

中图分类号: O343
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出版历程
- 收稿日期: 2013-05-02
- 修回日期: 2013-05-25
- 刊出日期: 2013-07-15

Exact Analytic Solution for Laminated Plates With Free-Edges and Arbitrary Thickness

¹School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230026, P.R.China;²School of Civil Engineering, Hefei University of Technology, Hefei 230009, P.R.China

摘要

摘要: 自由边问题一直是三维弹性力学中的难题，通常很难满足自由边上一个正应力和两个剪应力都等于0．基于三维弹性力学基本方程和状态空间方法，引入自由边界位移函数并考虑全部弹性常数，建立了正交异性具有自由边单层和叠层板的状态方程．对状态方程中的变量以级数形式展开，通过边界条件的满足精确求解任意厚度具有自由边叠层板的位移和应力，此解满足层间应力和位移的连续条件．算例计算表明，采用引入的位移函数形式，简化了计算过程并且采用较少的级数项可以获得收敛解．与有限元方法计算结果进行了对比，可以得到较高精度的数值结果．其解可以作为其它数值方法和半解析方法的参考解．
- 叠层板 /
- 自由边界 /
- 状态方程 /
- 精确解析解
Abstract: The problem of free-edges in three-dimensional elasticity is always a difficult one. The conditions that both normal stress and shear stress on the free edges equal zero are satisfied very difficultly. Based on the three-dimensional fundamental equations of elasticity and the state space method, the state equation for orthotropic plates was established through introduction boundary displacement function and consideration of all elastic constants of the orthotropic materials. Series expansion was carried out on the variables of the state equation. An exact solution was presented for laminated plates with arbitrary thickness by satisfaction of boundary conditions which can also satisfy the continuous conditions of stresses and displacements between plies of the laminates. The results of two examples show that the calculation process is simplified and the convergent solution can be achieved with less terms of series when the displacement function of free boundary is adopted. The numerical results with high accuracy can be obtained through comparison with the results of finite element. The results can be used as reference to numerical methods and semi-analytical methods.
- laminated plate /
- free-edges /
- state equation /
- exact analytic solution

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参考文献(16)

[1]	Xu Z L.Applied Elasticity [M]. New Delhi: Wiley Eastern Limited, 1992.
[2]	Reissner E. Note on the effect of transverse shear deformation in laminated anisotropic plates[J].Comput Method Appl M,1979, 20(2): 203-209.
[3]	Reddy J N. A simple higherorder theory for laminated composite plate[J].Journal of Applied Mechanics,1984, 51(4): 745-752.
[4]	Noor A K. Mixed finite-difference scheme for analysis of simply supported thick plates[J].Comput Struct,1973, 3(5): 967-982.
[5]	Spencer A J M, Watson P. Buckling of laminated anisotropic plates under cylindrical bending[J].J Mech Phys Solids,1992, 40(7): 1621-1635.
[6]	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））
[7]	FAN Jia-rang, YE Jian-qiao. An exact solution for the statics and dynamics of laminated thick plates with orthotropic layers[J].Int J Solids Struct,1990, 26(5/6): 655-662.
[8]	FAN Jia-rang, YE Jian-qiao. Exact solutions of buckling for simply supported thick laminates[J].Compos Struct,1993, 24(1): 23-28.
[9]	FAN Jia-rang, ZHANG Ju-yong. Analytical solutions for thick, doubly curved, laminated shells[J].J Eng Mech,1992, 118(7): 1338-1356.
[10]	FAN Jia-rang, ZHANG Ju-yong. Exact solutions for thick laminated shells[J].Science in China, Ser A ,1992, 35(11): 1343-1355.
[11]	范家让, 盛宏玉. 具有固支边的强厚度叠层板的精确解[J]. 力学学报, 1992, 24(5): 574-583.（FAN Jia-rang, SHENG Hong-yu. Exact solution for thick laminate with clamped edges[J].Acta Mechanica Sinica,1992, 24(5): 574-583.（in Chinese））
[12]	范家让. 强厚度叠层板壳的精确理论[M]. 北京：科学出版社, 1998.（FAN Jia-rang.Exact Theory of Thick Laminated Plates and Shells [M]. Beijing: Science Press, 1998.（in Chinese））
[13]	丁皓江, 陈伟球, 徐荣桥. 横观各向同性层合矩形板弯曲、振动和稳定的三维情况分析[J]. 应用数学和力学, 2001, 22(1): 16-22.(DING Hao-jiang, CHEN Wei-qiu, XU Rong-qiao. On the bending, vibration and stability of laminated rectangular plates with transversely isotropic layers[J].Applied Mathematics and Mechanics,2001, 22(1):16-22.(in Chinese))
[14]	Lee J S, Jiang L Z. Exact electroelastic analysis of piezoelectric lamina via state space approach[J].Int J Solids Struct,1996, 33(7): 977-990.
[15]	Lu C F, Chen W Q, Shao J W. Semianalytical threedimensional elasticity solutions for generally laminated composite plates[J].European Journal of MechanicsA/Solids,2008, 27(5): 899-917.
[16]	Attallah K M Z, Ye J Q, Sheng H Y. Three-dimensional finite strip analysis of laminated panels[J].Comput Struct,2007, 85(23/24):1769-1781.