应用混合变量最小势能原理求解简单边界条件弹性矩形薄板的稳定

The Application of Principle of Minimum Potential Energy with Mixed Variables in Stability of Elastic Thin Rectangular Plates with Simple Boundary Conditions

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,求解了简单边界条件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。通过文中计算表明,混合变量的最小势能原理适用于简单边界条件矩形板稳定问题的求解,从而验证了它用于薄板稳定问题的一般性和通用性。

In this paper, the principle of minimum potential energy with mixed variables is extended to solve the stability of elastic thin rectangular plates with simple boundary conditions and the characteristic equation and the result are given by it. The result can be a reference for engineering. Especially, the paper gives a efficacious, simple and convenient method to design for stability of pressure structures. By calculation, it is proved that the solution is well suited to some rectangular plates with simple boundary conditions. So, the principle of minimum potential energy with mixed variables solution is proved.