辛几何形态下不同边界条件的薄板解析解

利用平面弹性与板弯曲的相似性理论,用直接法研究辛几何形态下的薄板弯曲问题。当薄板对边边界条件形式不同时,将其进行降阶形成对偶方程组,再利用分离变量法把问题转化为本征值问题求解。通过本征函数、辛正交关系、展开求解等手段得到了薄板的解析解。算例表明辛求解的有效性与快速收敛性。

Analytical solutions of thin plate with different boundaries under symplectic geometry form

Based on the analogies between plane elasticity and thin plate bending problem,the thin plate bending under symplectic geometry form was solved by direct method.For thin plate with different boundaries,first the order of the governing equations was decreased to form a dual equation set,then the variable separation method was used,so the problem was transformed into an eigen-value problem.The following methods such as eigen-function,symplectic orthogonal relationship and symplectic expansion method were usded to obtain the analytical solutions of the thin plate.The numerical example shows that the method is effective and converges fast.