基于无网格方法的复合材料层合板固有频率及特征值灵敏度分析  

Natural frequency analysis and eigenvalues sensitivity analysis of composite laminates based on meshless method

作　　者：钱若力[1] 陈兴华[2] 卿光辉[1] 

机构地区：[1]中国民航大学航空工程学院,天津300300 [2]中国商用飞机有限责任公司上海飞机设计研究院,上海200436

出　　处：《船舶力学》2012年第7期820-828,共9页Journal of Ship Mechanics

基　　金：国家自然科学基金民航联合研究基金(编号:60979001);中国民航大学校级重大项目(编号:CAUA2009ZD0101)资助

摘　　要：文章基于无网格法和弹性力学Hamilton正则方程,研究了复合材料层合板固有频率和特征值灵敏度分析问题。首先,结合径向基插值函数和修正后的H-R变分原理,推导了Hamilton正则方程的无网格列式。然后,以Multiquadric(MQ)、Gaussian(EXP)和薄板样条(TPS)为基函数,计算了复合材料层合板的固有频率及其特征值的灵敏度系数。文中的工作使得无网格法的优越性与弹性力学Hamilton正则方程的半解析法得到了有机的结合,为Hamilton正则方程提出了一种新的特征值灵敏度分析方法。Abstract：Based on meshless method and Hamilton canonical equation, the problem of natural frequency and eigenvalues sensitivity analysis was investigated for composite laminates. Firstly, meshless formulation of Hamilton canonical equation was derived by combining the modified Hellinger-Reissner variational princi- ple and the radial interpolation functions. And then, based on the shape functions of Multiquadric （MQ）, Gaussian （EXP） and thin plane spine （TPS）, the natural frequencies of the single laminated plates were ob- tained by the meshless formulation of Hamilton canonical equation. This study introduced the advantages of meshless method into semi-analytic solution of Hamilton canonical equation, and a new eigenvalues sensi- tivity analysis method was presented for Hamilton canonical equation.

关 键 词：固有频率 灵敏度分析 无网格法 HAMILTON正则方程 径向基插值函数(RPIM) H-R变分原理 

分 类 号：TB332[一般工业技术—材料科学与工程]