基于可分型Hamilton正则方程的复合材料层合板自由边缘效应研究

RESEARCH OF FREE-EDGE EFFECT OF COMPOSITE LAMINATES BASED ON SEPARABLE HAMILTON CANONICAL EQUATION

提出一种可分型Hamilton正则方程与有限元法相结合的半解析法理论,研究辛体系下正交异性复合材料层合板自由边缘效应问题。首先根据修正后的H-R变分原理,推导可分型Hamilton正则方程,应用有限元法建立沿厚度方向的状态方程。然后,实例计算分析复合材料层合板层间应力。通过数值算例验证了方法的有效性。

A semi-analytical solution theory is presented by combining the separable Hamilton canonical equation and finite element method.The problem of free-edge effect of orthotropic laminates is studied in symplectic system.First,the separable Hamilton canonical equations are established with modified Hellinger-Reissner variational principle.And the state equations are established with finite element method.Then,an example analysis of the distribution of interlaminar stresses in composite laminates is calculated.The numerical results show the efficiency of the proposed method.