Application of Composite Laminated Plates With Bonding Imperfection in Hamilton System
-
摘要: 层合板的层间粘接模型对整个层合板的结构有重要影响.运用Hamilton正则方程对层合板层间的不同类型的粘接模型进行了分析.结合弹性材料修正后的HellingerReissner变分原理和插值函数,构建了直角坐标系下8节点层合板的每一层的线性方程;考虑到脱层板的连接界面处应力和位移的关系,改进了现有的常用弱粘接模型,建立不同粘接模型的控制方程;最后通过求解整个板的控制方程,得到层合板的层间应力和位移.数值算例验证了该模型的正确性,并研究了层间界面为线性和非线性时的问题.结果表明:应用改进后的弱粘接模型,能够更好地模拟层合板的弱界面失效过程.
-
关键词:
- 层合板 /
- 层间模型 /
- Hamilton正则方程 /
- 半解析法 /
- 8节点
Abstract: The weak interfacial bonding seriously affected the mechanical behavior of laminated plates. Different imperfect bonding models of laminated plates were discussed in Hamilton canonical equation. By combining the modified HR variational principle for elastic material with the quadratic interpolation functions, the linear formulation of laminated plates with 8node for Hamilton canonical equation in the Cartesian coordinate was derived. The relationship between stress and displacement on the interface between layers was considered to improve the normal bonding model, and the state equation with delamination situation was established. The stress and displacement were obtained by solving the overall model. Numerical examples showed that the methods presented were correct, and this paper studied the linear and nonlinear bonding models of the laminated plate respectively. The last results show that the application of improved models can simulate the process of fail better.-
Key words:
- laminated plates /
- bonding model /
- Hamilton canonical equation /
- semi-analytical solution /
- 8-nodes
-
[1] 沈观林, 胡更开. 复合材料力学[M]. 北京:清华大学出版社, 2006.(SHEN Guanlin, HU Gengkai. Mechanics of Composite Materials[M].Beijing: Tsinghua Press, 2006. (in Chinese)). [2] Pagano N J. Exact solutions for composite laminates in cylindrical bending[J]. Journal of Composite Materials,1969,3(3): 398-411. [3] Srinivas S, Rao A K. Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates[J].International Journal of Solids and Structures,1970,6(5): 1463-1481. [4] Fan J R, Ye J Q. An exact solution for the static and dynamics of laminated thick plate with orthotropic[J].International Journal of Solids and Structures,1990,26(5):655-662. [5] Fan J R, Ye J Q. A series solution of the exact equation for thick orthotropic plate[J].International Journal of Solids and Structures,1990,26(7): 773-778. [6] Zou G P, Tang L M. A semi-analytical solution for thermal stress analysis of laminated composite plate in the Hamiltonian system[J]. Composite Sturcture,1995,55(1):113-118. [7] Williams T O, Addessio F L.A general theory for laminated plates with delaminations[J].International Journal of Solids and Structures,1997,34(7):2003-2024. [8] Williams T O. Efficiency and accuracy considerations in a unified plate theory with delamination[J]. Composite Structures,2001,52(1):27-40. [9] Chen W Q, Cai J B, Ye G R. Exact solution of crossply laminates with bonding interfacial imperfections[J]. AIAA Journal,2003,41(11):2244-2250. [10] Chen W Q, Lee K Y.Exact solution of angle-ply piezoelectric laminates in cylindrical bending with interfacial imperfections [J].Composite Structures,2004,65(3/4): 329-337. [11] Chen W Q, Cai J B, Ye G R, Wang Y F. Exact threedimensional solutions of laminated orthotropic piezoelectric rectangular plates featuring inter-laminar bonding imperfections modeled by a general spring layer[J].International Journal of Solids and Structures,2004,41(18/19):5247-5263. [12] Geun W K, Kang Y L.Influence of weak interfaces on buckling of orthotropic rectangular laminates[J].Composite Structures,2007,81(6):427-431. [13] Iannucci L, Willows M L. An energy based damage mechanics approach to modeling impact onto woven composite material—part-1: numerical models[J].Composites, Part A: Applied Science and Manufacturing, 2006, 37(1): 2041-2056.[14]Elder D J, Rodney S T, Minh Q N, Murray L S. Review of delamination predictive methods for low speed impact of composite laminates[J]. Composite Structures,2004,66(2): 677-683. [14] Achenbach J D, Zhu H. Effect of interfacial zone on mechanical behavior and failure of fiberreinforced composites[J].Journal of the Mechanics and Physics of Solids,1989,37(3):381-393. [15] Levy A J.The effective dilatational response of fiberreinforced composites with nonlinear interface[J].Journal of Applied Mechanics, 1996, 63(2): 357364. [16] 孙志刚, 宋迎东, 廉英琦. 弱界面粘结对复合材料有效能的影响[J]. 航空动力学报, 2005, 20(6): 915919.(SUN Zhigang, SONG Ying-dong, LIAN Ying-qi. Composite Mechanical Behavior with Weak Interfacial Bonding[J]. Journal of Aerospace Power, 2005, 20(6): 915-919. (in Chinese)) [17] 高希光, 孙志刚, 廉英琦. 弱界面黏结通用单胞模型理论及应用[J]. 航空动力学报, 2009, 24 (8): 1684-1690.(GAO Xi-guang, SUN Zhi-gang, LIAN Yin-qi. Generalized method of cell with weak interfacial bonding[J].Journal of Aerospace Power,2009,24(8): 1684-1690. (in Chinese)) [18] 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: 1-187.(ZHONG Wan-xie. A New Systematic Methodology for Theory of Elasticity[M]. Dalian: Dalian University of Technology Press, 1995: 1-187. (in Chinese)) [19] Zou G P, Tang L M. A semi-analytical solution for thermal stress analysis of laminated composite plate in the Hamiltonian system[J]. Computer&Structure, 1995,55(1): 113-118. [20] 范家让. 强厚叠层板壳的精确理论[M]. 北京: 科学出版社, 1996: 111-385.(FAN Jia-rang. Exact Theory of Laminated Thick Plates and Shells[M]. Beijing: Science Press, 1996: 111-385. (in Chinese)) [21] 钟万勰. 应用力学对偶体系[M]. 北京: 科学出版社, 2002:22-44.(ZHONG Wan-xie.Symplectic System of Applied Mechanics[M]. Beijing: Science Press, 2002: 22-44. (in Chinese)) [22] Qing G H, Liu Y H, Qiu J J. A semi-analytical method for the free vibration analysis of thick doubleshell systems[J]. Finite Elements in Analysis and Design, 2006, 42(10): 837-845. [23] Qing G H, Qiu J J, Liu Y H. A semianalytical solution for dynamic analysis of plate with piezoelectric patches[J]. International Journal of Solids and Structures, 2006, 43(6): 1388-1403. [24] Qing G H, Wang F X, Liu Y H. Statespace approach for energy release rate analysis of delaminated laminates with stiffeners[J]. AIAA Journal, 2011, 49(10): 2123-2129. [25] Qing G H, Liu Y H, Li D H. A semi-analytical model for the energy release rate analyses of composite laminates with a delamination[J]. Finite Elements in Analysis and Design, 2011, 47(9): 1017-1024. [26] 但敏, 卿光辉.脱层板固有频率的有限元方法分析[J].动力学与控制学报, 2011, 9(1): 7-11.(DAN Min, QING Guanghui. Natural frequencies analysis of delamination planes with finite element method[J]. Journal of Dynamics and Control, 2011, 9(1): 7-11. (in Chinese)) [27] Majumdar B S, Newaz G M. Inelastic deformation of metal matrix composites: plasticity and damage mechanisms[J] . Philosophical Magazine A, 1992, 66(2): 187-121. [28] Lars F, Walter L, Fabrizio V. Ageneralized higherorder theory for multi-layered, shear-deformable composite plates[J] .Acta Mechanica,2010, 209(1/2): 85-98.
点击查看大图
计量
- 文章访问数: 1419
- HTML全文浏览量: 90
- PDF下载量: 1098
- 被引次数: 0