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. doi: 10.3879/j.issn.1000-0887.2010.12.007
 Citation: 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.

# Sensitivity Analysis of Composite Laminated Plates With Bonding Imperfection in Hamilton System

##### doi: 10.3879/j.issn.1000-0887.2010.12.007
• Rev Recd Date: 2010-11-09
• Publish Date: 2010-12-15
• The sensitivity analysis of composite laminated plates with bonding interfacial imperfection was investigated based on the radial point interpolation method (RPMI) in Hamilton system.A hybrid governing equations of the response and sensitivity quantities was reduced by the spring-layer model and modified Hellinger-Reissner (H-R) variational principle.The analy ticalmethod (AM),semi-analy ticalmethod (SA) and the finite difference method (FD) were given for the sensitivity analysis approach which is based on this reduced hybrid governing-equation.One of the main advantages of the hybrid governing equation is that the convoluted algorithm is avoided in sensitivity analysis.In addition,the sensitivity analysis method using this hybrid governing equation not only obtains the response values and the sensitivity coefficients smiultaneity,butalso accounts for the bonding interfacial imperfections of composite laminated plates.
•  [1] Arora J S, Haug E J. Methods of design sensitivity analysis in structural optimization[J]. AIAA J， 1979, 17(9): 970-974. doi: 10.2514/3.61260 [2] Choi K K, Santos J L T, Frederick M C. Implementation of design sensitivity analysis with existing finite element codes[J]. ASME Journal of Mechanisms, Transmissions, and Automation in Design, 1987, 109(3): 385-391. [3] Haftka R T. Sensitivity calculations for iteratively solved problems[J]. International Journal for Numerical Methods in Engineering, 1985, 21(8): 1535-1546. [4] Haftka R T, Barthelemy B. On the accuracy of shape sensitivity[J]. Structural and Multidisciplinary Optimization, 1991, 3(1): 1-6. [5] Choi K K, Chang K H. A study of design velocity field computation for shape optimal design[J]. Finite Elements in Analysis and Design, 1994, 15(4): 317-341. [6] 顾元宪，赵红兵，陈飚松，亢战. 热-应力耦合结构灵敏度分析方法[J]. 力学学报，2001，33(5): 685-691. [7] 郭旭，顾元宪，赵康. 广义变分原理的结构形状优化伴随法灵敏度分析[J]. 力学学报，2004，36(3): 288-295. [8] Barthelemy B, Haftka R T. Accuracy analysis of the semi-analytical method for shape sensitivity calculation[J]. Mechanics Based Design of Structures and Machines, 1990, 18(3): 407-432. [9] Olhoff N, Rasmussen J, Lund E. Exact numerical differentiation for error elimination in finite element based semi-analytical shape sensitivity analysis[J]. Mech Struct Mach, 1993, 21(1): 1-66. [10] 钱令希，程耿东，隋允康， 钟万勰，林家浩. 结构优化设计理论与方法的某些进展[J] . 自然科学进展，1995，5(1): 64-69. [11] Cheng Z Q, Kennedy D, Williams F W. Effect of interfacial imperfection on buckling and bending behavior of composite laminates[J]. AIAA Journal, 1996, 34(12): 2590-2595. doi: 10.2514/3.13443 [12] Cheng Z Q, Jemah A K, Williams F W. Theory for multi-layered anisotropic plates with weakened interfaces[J]. Journal of Applied Mechanics, 1996, 63(4): 1019-1026. [13] Cheng Z Q, He L H, Kitipornchai S. Influence of imperfect interfaces on bending and vibration of laminated composite shell[J]. International Journal of Solids and Structures, 2000, 37(15): 2127-2150. [14] Chen W Q, Cai J B, Ye G R. Exact solution of cross-ply laminates with bonding interfacial imperfections[J]. AIAA Journal, 2003, 41(11): 2244-2250. doi: 10.2514/2.6817 [15] 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): 239-337. [16] Chen W Q, Cai J B, Ye G R, Wang Y F. Exact three-dimensional solutions of laminated orthotropic piezoelectric rectangular plates featuring interlaminar bonding imperfections modeled by a general spring layer[J]. International Journal of Solids and Structures, 2004, 41(18/19): 5247-5263. [17] Zhou Y Y, Chen W Q, Lu C F. Semi-analytical solution for orthotropic piezoelectric laminates in cylindrical bending with interfacial imperfections[J]. Composite Structures, 2010, 92(4): 1009-1018. [18] 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. [19] 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: 182-187. [20] 钟万勰. 应用力学对偶体系[M]. 北京: 科学出版社, 2003: 22-44. [21] 卿光辉, 邱家俊, 塔娜. 压电材料修正后的H-R混合变分原理及其层合板的精确法[J]. 工程力学, 2005, 22(5): 43-47. [22] 陈新锋, 徐建新, 卿光辉. 层合板固有频率分析的B样条小波元法[J]. 动力学与控制学报, 2009, 7(1): 50-54. [23] QING Guang-hui, QIU Jia-jun, LIU Yan-hong. Free vibration analysis of stiffened laminated plates[J]. International Journal of Solids and Structures, 2006, 43(6): 1357-1371. [24] Liu G R, Gu Y T. An Introduction to Meshfree Methods and Their Programming[M]. Netherlands: Springer, 2005.

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