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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.
Solving the problem of stability of orthotropic rectangular thin plate by using the method of separate variables, the analytic solutions of the three kinds of boundary conditions are obtained, and the results are the same as those of the related literatures. The solving method is simpler than the traditional semi-inverse method. The method of separating variable method is given.The method of generating no Poisson effect and eliminating the rigid body displacement is given.The laminated plate is equivalent to an orthotropic plate and the in-plane unidirectional pressure The results are in good agreement with the finite element analysis, which proves the correctness and practicability of the method of separating variables.