弹性地基上变厚度环板分析的传递矩阵法

讨论了弹性地基上变厚度环板轴对称弯曲的传递矩阵法.首先,简单地介绍了开尔文函数及其基本性质.其次,基于开尔文函数理论导出了文克勒地基上等厚度环板单元的正确传递矩阵,并证明了当地基参数趋近于零时,该传递矩阵退化为一般等厚度环板的传递矩阵.然后,沿径向将变厚度环板划分成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环板的整体传递矩阵.最后,给出了一些数值结果,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弯矩的影响.

Transfer matrix method for the analysis of annular plates with variable thickness on an elastic foundation

A transfer matrix method for the axi-symmetric bending of annular plates with variable thickness on an elastic foundation is presented in this paper. Firstly, by applying the theory of Kelvin functions, the exact transfer matrix of an annular plate element with uniform thickness is derived. Secondly, the annular plate with variable thickness is divided into a series of annular plate elements with uniform thickness along its radial direction. The global transfer matrix of the annular plate with variable thickness is formulated by applying the principle of transfer matrix method. Finally, some numerical results are given to verify the effectiveness of the method presented in this paper. The influence of the foundation parameter on the flexure and bending moment of the plate is discussed in brief.