Winkler地基上变厚度圆板的轴对称弯曲

本文提出了Winkler地基上变厚度圆板轴对称弯曲的传递矩阵算法。首先，根据贝塞尔函数理论获得了等厚度圆板和环板单元在任意荷载作用下轴对称弯曲的解析解，这些解均由通解和特解两部分组成。基于这些解析解，导出了等厚度圆板和环板单元的传递矩阵。然后沿径向将变厚度圆板划分成一个等厚度圆板单元和一系列等厚度环板单元，应用传递矩阵算法原理获得了变厚度圆板的整体传递矩阵。引入圆板的边界条件，给出了该板每条节线上的挠度、径向转角、径向弯矩和径向剪力。最后，讨论了受均布荷载作用的简支线性变厚度圆板的弯曲，将本文数值解与解析解进行比较，证实了本文方法的有效性，并简要地讨论了地基参数对板挠度和径向弯矩的影响。

Axi-Symmetric Bending of Circular Plates with Variable Thickness on Winkler Foundation

A transfer matrix algorithm was presented for the axi-symmetric bending of circular plates with variable thickness on Winkler foundation. Firstly, according to the theory of Bessel functions, the analytical solutions were obtained for the axi-symmetric bending of circular and annular plate elements with uniform thickness subjected to arbitrary loads. The solutions consist of a general solution and particular solution. Based on the analytical solutions, the transfer matrixes of circular and annular plate elements with uniform thickness were derived. Secondly, the circular plate with variable thickness was divided into a circular plate element and a series of annular plate ones with uniform thickness along its radial direction. The global transfer matrix was formulated by applying the principle of transfer matrix algorithm. By introducing the boundary conditions of the circular plate, the flexure displacement, radial rotation angle, radial bending moment and radial shear force on each nodal line of the plate were given. Finally, the bending of a simply supported circular plate with linearly variable thickness subjected to uniform load was discussed. The validity of the algorithm was verified by comparing the numerical solution with the analytical one. The influence of the foundation parameter on the flexure displacement and radial bending moment of the plate was briefly discussed.