双参数弹性地基板计算新方法

A New Method for Bending Problem of Plates on Two Parameter Elastic Foundation

弹性地基板的弯曲问题,尤其是自由边板,一直是学者和工程师们所十分关切的问题。本文用无单元法研究了双参数弹性地基板的弯曲问题,由最小二乘法和变分原理导出了双参数弹性地基板的无单元法刚度矩阵,编制相应的无单元法计算程序,并给出计算实例。结果表明本文方法精度良好,可求出任意荷载作用下板中任一点的挠度、转角、弯矩和扭矩,且有广泛的工程应用前景。

For scholars and engineers, it has ever been a concerned problem that the analysis of bending plates with free edges on elastic foundation. In this paper, the bending problem of the plates on two - parameter elastic foundation are solved by use of the Element - free method. The corresponding formulae of the plates are derived by using the vari-ational principles and moving - squares method. The computer program are also developed. Numerical examples show that the method is feasible, the displacement, rotation, bending moment and torsion at any point in the plate subjected to any load, can be obtained and has a promising prospect in engineering application.