应用混合变量最小势能原理求解悬臂弹性矩形板的稳定问题

Application of principle of minimum potential energy with mixed variables in stability analysis of elastic thin cantilever rectangular plates

将混合变量的最小势能原理推广到求解弹性矩形薄板的稳定问题中,求解了悬臂弹性矩形薄板的稳定问题,并给出了相应问题确定临界载荷的特征方程及计算结果,为工程中薄板的设计计算提供了有效的参考,尤其是对现代建筑和桥梁中的受压构件的稳定设计和计算提供了一个简捷有效的计算方法。计算表明,混合变量的最小势能原理适用于矩形板稳定问题的求解。

The principle of minimum potential energy with mixed variables was extend to solve the stability problem of elastic thin cantilever rectangular plates.The characteristic equation was provided with its results given out.The results give a reference to engineering design of elastic thin plates and present an efficacious,simple and convenient method to calculate the stability of pressurized structures.By calculation,it is proved that the solution is well suited to the case of cantilever rectangular plates.