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

摘要

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 principle 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 obtained 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 sensitivity analysis method was presented for Hamilton canonical equation.%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.