弹性基底非加载边弹性转动约束矩形板线性受压屈曲分析

Buckling analysis of rectangular plate on elastic base with elastic rotation constraint under linear compression

为了研究基于弹性基底非加载边转动约束面内线性受压下薄板的屈曲问题,采用Rayleigh-Ritz法建立了满足上述边界条件板的弹性屈曲计算理论,进一步分析了弹性基底刚度K、边界转动约束刚度ξ、长宽比γ、压力梯度λ、厚度t对临界屈曲系数κ的影响。研究结果表明:在简单边界条件下,依据弹性屈曲计算理论所得临界屈曲系数κ值与经典弹性稳定理论值具有较好的一致性,该计算理论有广泛的适用性。

In order to study the buckling problem of thin plates under linear compression with non-loaded edge rotation constraint based on elastic base, Rayleigh Ritz method is used to establish the elastic buckling calculation theory of plates under the above boundary conditions.Furthermore, the effects of elastic base stiffness, boundary rotation constraint stiffness, length to width ratio, pressure gradient and thickness on the critical buckling coefficient are analyzed.The results show that the results of elastic buckling calculation theory are in good consistency with those of the classical elastic stability theory under the simple boundary conditions. And the elastic buckling calculation theory has a wide applicability.