初曲矩形薄板的非线性动力屈曲研究

对两参数冲击载荷面内压缩作用下初曲矩形薄板的非线性动力屈曲问题进行了理论研究。首先采用双重余弦函数的组合确定了面内冲击矩形薄板的艾雷应力函数和中面力的分布；其次根据伽辽金法求得了初曲矩形薄板非线性动力屈曲问题的控制方程，基于巴拿赫压缩映象原理，采用逐次逼近方法求解了该控制方程。最后，应用本文发展的理论，给出了面内两参数冲击载荷作用下初曲矩形薄板动力屈曲响应的计算实例，计算结果与已有的实验结果较吻合

Nonlinear Dynamic Buckling of Imperfect Rectangular Plates

The nonlinear dynamic buckling of imperfect rectangular thin plates under two parameters impact loads in plane is investigated theoretically. Firstly, Airy stress function and the distributions of the membrane forces are determined by the combination of double cosine series. Secondly, the governing equation of the nonlinear dynamic buckling of the plates is obtained by Galerkin method. Based on Banach compression image principle, the solution of the governing equation is presented by an iteration scheme. The effectiveness of the present solution is checked by the good agreement between the theoretical and experimental results.