利用小波有限元法的优越性可方便地求解压电材料与复合材料混合层合板的某些静力学问题.根据层合结构的特点,将区间B样条尺度函数作为插值函数离散结构的平面域,应用压电材料修正后的H-R(Hellinger-Reissner)变分原理推导了压电材料的Hamilton正则方程的区间B样条小波(BSWI)元列式.该BSWI元的主要特点之一是厚度方向是解析解形式的.针对具体问题的求解,为了保证各层之间力学量和电学量的连续性,进一步应用了状态转移矩阵技术.数值算例表明所提出的区间B样条小波单元是成功的.采用推导压电材料BSWI元的方法可建立磁电弹性材料类似的BSWI元.
参考文献
| [1] | Lee J S,Jiang L Z.Exact electroelastic analysis of piezoelectric laminate via state space approach[J].International Journal Solids and Structures,1996,33(7):977-990. |
| [2] | Heyliger P R,Brooks P R.Exact solutions for simply supported laminated piezoelectric plates[J].Journal of Applied Mechanics,1997,64(2):299-306. |
| [3] | Ding H J,Chen W Q,Xu R Q.New state space formulations for transversely isotropic piezoelectricity with application[J].Mechanics Research Communications,2000,27(3):319-326. |
| [4] | 卿光辉,邱家俊,刘艳红.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.Qing Guanghui,Qiu Jiajun,Liu Yanhong.Modified H-R mixed variational principle for piezoelectric material and exact solution of piezoelectric laminates[J].Engineering Mechanics,2005,22(5):43-47. |
| [5] | Qing Guanghui,Qiu Jiajun,Liu Yanhong.A semi-analytical solution for dynamic analysis of plate with piezoelectric patches[J].International Journal of Solids and Structures,2006,43(6):1388-1403. |
| [6] | 代海涛,程伟.压电复合材料层合结构中的SH波[J].复合材料学报,2007,24(1),179-184.Dai Haitao,Cheng Wei.SH wave in piezoelectric composite layered structure[J].Acta Materiae Compositae Sinica,2007,24(1):179-184. |
| [7] | 韩旭,龚双.机电耦合载荷下的压电层合板瞬态响应分析[J].复合材料学报,2007,24(6):160-165.Han Xu,Gong Shuang.Analysis of transient responses in piezoelectric laminates excited by coupled electro-mechanical loads[J].Acta Materiae Compositae Sinica,2007,24(6):160-165. |
| [8] | Allik H,Hughes T J R.Finite element method for piezoelectric vibration[J].Int J Numerical Method in Engineering,1970,2(2):151-157. |
| [9] | Kim J S,Varadan V V,Varadan V K.Finite element modeling of structures including piezoelectric active devices[J].International Journal for Numerical Methods in Engineering,1997,40(5):817-832. |
| [10] | Sze K Y,Pan Y S.Hybrid finite element models for piezoelectric materials[J].Journal of Sound and Vibration,1999,226(3):519-547. |
| [11] | 林西强,任钧国.含压电片层合壳的有限元分析与控制仿真[J].计算力学学报,1998,15(3):329-337.Lin Xiqiang,Ren Junguo.Finite element analysis and control simulation of laminate shell containing piezoelectric patches[J].Chinese Journal of Computational Mechanics,1998,15(3):329-337. |
| [12] | 丁皓江,池毓蔚,国凤林.压电材料轴对称有限元分析[J].计算力学学报,2000,17(1):1-7.Ding Haojiang,Chi Yuwei,Guo Fenglin.Axisymmetric finite element analysis of piezoelectric media[J].Chinese Journal of Computational Mechanics,2000,17(1):1-7. |
| [13] | 何正嘉,陈雪峰,李兵,等.小波有限元理论及其工程应用[M].北京,科学出版社,2006:1-227. |
| [14] | Shen Pengcheng,Wang jianguo.Vibration analysis of cylinder shells by using B-spline functions[J].Computers & Structures,1987,25(1):1-10. |
| [15] | 龙驭球.新型有限元[M].北京:科学出版社,2004:482-497. |
| [16] | 徐长发,冯勇.B小波有限元方法数值稳定性分析[J].华中理工大学学报,1996,24(6):109-112.Xu Changfa,Feng Yong.The numerical stability of the Bwavelet FE method in solving partial differential equations[J].Journal of Huazhong University of Science and Technology,1996,24(6),109-112. |
| [17] | Xiang Jiawei,Chen Xuefeng,He Yumin,He Zhengjia.The construction of plane elastomechanics and Mindlin plate elements of B-spline wavelet on the interval[J].Finite Elements in Analysis and Design,2006,42(14/15),1269-1280. |
| [18] | Xiang Jiawei,Chen Xuefeng,He Yumin,He Zhengjia.A new wavelet-based thin plate element using B-spline wavelet on the interval[J].Computational Mechanics,2008,41(2):243-255. |
| [19] | 唐立民.弹性力学的混合方程和Hamilton正则方程[J].计算结构力学及其应用,1991,8(4):343-349.Tang Limin.Mixed formulation and Hamilton canonical equations of theory of elasticity[J].Computational Structural Mechanics and Application,1991,8(4),343-349. |
| [20] | 钟万勰.弹性力学求解新体系[M].大连,大连理工大学出版社,1995:38-41. |
| [21] | 钟万勰.应用力学对偶体系[M].北京:科学出版社,2003:472-484. |
| [22] | 陈浩然,杨正林,唐立民.复合材料层合板固化过程的数值模拟[J].应用力学学报,1998,15(3):30-36.Chen Haoran,Yang Zhenglin,Tang Limin.Solidification numerical simulation of composite laminate[J].Chinese Journal of Applied Mechanics,1998,15(3):30-36. |
| [23] | 范家让.强厚叠层板壳的精确理论[M].北京:科学出版社,1996:131-191. |
| [24] | Qing Guanghui,Qiu Jiajun,Liu Yanhong.Modified H-R variational principle for magnetoelectroelastic bodies and statevector equation[J].Applied Mathematics and Mechanics,2005,26(6),722-728. |
上一张
下一张
上一张
下一张
计量
- 下载量()
- 访问量()
文章评分
- 您的评分：
-
10%
-
20%
-
30%
-
40%
-
50%