Unstiffened plates in structures are usually welded or fastened to supporting members, providing rotational restraint stiffness to the plate. Previous studies have shown that neglect of rotational restraint stiffness at the edges of a plate in a structure can introduce deviations in the analysis of dynamic elastic buckling. In this study, the in-plane impact-induced dynamic elastic buckling responses of isotropic imperfect unstiffened plates with four elastically restrained edges are analytically investigated, based on the large-deflection theory of thin plate. The evolution of the peak deflection predicted by the proposed analytical method is found to be consistent with the responses available from the literature. Then the method is further used to estimate the deformation map of an unstiffened plate with four elastically restrained edges, and the effects of rotational restraint stiffness, initial geometric imperfection and shock duration on the dynamic buckling response of the plate are examined. The results show that the critical dynamic buckling load and the maximum deflection response of the plates are significantly influenced by the rotational restraint stiffness as well as the first-order initial geometric imperfection, and thus cannot be neglected in the analysis of dynamic buckling.

中文翻译：

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一种估计平面内冲击下沿所有边缘弹性约束的未加筋板的动态屈曲响应的方法

结构中的未加劲板通常焊接或固定在支撑构件上，为板提供旋转约束刚度。先前的研究表明，忽略结构中板边缘的旋转约束刚度会导致动态弹性屈曲分析出现偏差。本研究基于薄板大挠度理论，分析研究了具有四个弹性约束边的各向同性不完美无筋板的面内冲击诱发动态弹性屈曲响应。发现通过所提出的分析方法预测的峰值挠度的演变与文献中可用的响应一致。然后将该方法进一步用于估计具有四个弹性约束边的无加强板的变形图，并研究了旋转约束刚度、初始几何缺陷和冲击持续时间对板的动态屈曲响应的影响。结果表明，板的临界动态屈曲载荷和最大挠度响应受旋转约束刚度和一阶初始几何缺陷的显着影响，因此在动态屈曲分析中不可忽视。