一角点支撑对面两边固支正交各向异性矩形薄板弯曲问题的辛叠加解  

Symplectic Superposition Solution for Bending Problem of an Orthotropic Rectangular Thin Plate with Two Adjacent Edges Clamped and Its Opposite Point-Supported at a Corner

作　　者：寇天娇 额布日力吐[1] KOU Tianjiao;Eburilitu(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China)

机构地区：[1]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《应用数学》2020年第3期550-562,共13页Mathematica Applicata

基　　金：国家自然科学基金项目(11862019,11362011,11761052)。

摘　　要：研究均匀荷载下一角点支撑对面两边固支条件下的正交各向异性矩形薄板的弯曲问题,并获得该问题的解析解.首先得到对边简支边界条件下原方程所对应的Hamilton算子的本征值及相应的本征函数系,再根据本征函数系的辛正交性和完备性,计算出对边简支问题所对应的Hamilton正则方程的通解,继而运用叠加方法求出原问题的辛叠加解.最后通过辛叠加解计算的数值结果与已有文献的数值结果进行对比,验证了本文所得解析解的正确性.In this paper, the bending problem of a uniformly loaded orthotropic rectangular thin plate with two adjacent edges clamped and its opposite point-supported at a corner is studied, and the analytical bending solution of the problem is obtained. First, we obtain the eigenvalues and eigenfunctions of the Hamiltonian operator corresponding to the original equation with two opposite sides simply supported. Then, according to the symplectic orthogonality and completeness of the eigenfunctions, the general solution of the Hamiltonian canonical equation with two opposite sides simply supported is calculated, and the analytical bending solution of the original problem is obtained by the superposition method. Finally,the numerical results calculated by the symplectic superposition solution are compared with the numerical results of the existing literature, and the correctness of the analytical bending solution is verified.

关 键 词：正交各向异性矩形薄板 HAMILTON算子 完备性 解析解 

分 类 号：O302[理学—力学]