两相邻角点支承对边固支正交各向异性矩形薄板的弯曲解  

Bending Solution of an Orthotropic Rectangular Thin Plate Point-Supported at Two Adjacent Corners and Clamped at the Opposite Edge

作　　者：张春玲 额布日力吐[1] 阿拉坦仓[2] ZHANG Chun-ling;Eburilitu;Alatancang(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China;Hohhot Minzu College,Hohhot 010051,China)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]呼和浩特民族学院,呼和浩特010051

出　　处：《内蒙古大学学报（自然科学版）》2020年第4期357-364,共8页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金项目(11862019,11761029)。

摘　　要：运用辛叠加方法研究了均布荷载下两相邻角点支承对边固支的正交各向异性矩形薄板的弯曲问题。首先将正交各向异性薄板方程转化为Hamilton系统,通过计算得到对边简支问题所对应的Hamilton算子本征值及本征函数系。基于本征函数系的辛正交性及Cauchy主值意义下的完备性,求得相应Hamilton系统的通解。然后分别得到三个子问题的解,再利用叠加方法将三个子问题的解叠加得到原弯曲问题的辛叠加解,最后将得到的辛叠加解的数值结果与已有文献的数值结果进行比较,验证了所得解析解的正确性。The bending problem of an orthotropic rectangular thin plate supported at two adjacent corner points and clamped at the opposite edge under a uniform load is studied by the symplectic superposition method.First,the bending equation of the orthotropic rectangular thin plate is transformed into the Hamiltonian system.By calculating,the eigenvalues and eigenfunctions of the Hamiltonian operators corresponding to the Hamiltonian system with two opposite edges simply supported are derived.Based on the symplectic orthogonality and completeness of the eigenfunctions,the general solution of the Hamiltonian system is derived.Then the analytical solutions of the three subproblems,which all belong to the two opposite edges simply supported problems,are obtained,respectively.And then the analytical bending solution of the original bending problem is obtained by the superposition of the analytical solutions of the above three subproblems.Furthermore,the numerical results of the obtained symplectic superposition solution are compared with the numerical results in the existing literature,and the correctness of the obtained analytical bending solution is verified.

关 键 词：正交各向异性矩形薄板 HAMILTON系统 辛叠加解 解析解 

分 类 号：O175.3[理学—数学]