正交各向异性矩形薄板稳定问题的直接解法

用分离变量法求解了正交异性矩形薄板的稳定问题,得到了3种边界条件下的解析解,结果与相关文献完全相同,求解方法比传统的半逆法要简单.分析了力边界条件给实施分离变量法带来的困难.给出了不产生泊松效应并能消除板刚体位移的方法.将叠层材料板等效为正交各向异性板,用解析方法求解了面内单向压曲问题,结果与有限元分析结果吻合很好,证明了分离变量方法的正确性和实用性.

Separation of variables solutions of stability problems of orthotropic rectangular thin plates

The stability problems of orthotropic rectangular thin plates were solved by using separation of variables, and the analytic solutions were obtained for three boundary conditions, which are the same with the results in literature. The present solution method is much simpler than traditional semi-inverse method.The effects of the force boundary conditions on the implementation of separation of variables were also investigated. The basic method without causing Poisson-s effect and rigid displacement has also been presented. The laminated plate was reckoned to be the orthotropic rectangular thin plate whose buckling problems were solved with present method for the plate subjected to in-plane unidirectional distributed compressive force, the results agree well with those of finite element method, which validate the correctness and practicability of present method.