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随着工程结构的轻型化、薄壁化,薄板结构稳定问题越来越受到重视,针对不同条件下薄板屈曲问题开展了大量研究。弹性支承上的薄板屈曲、边界弹性转动约束的薄板屈曲和刚性支承上边界转动约束的薄板屈曲问题已有相关文献,关于非加载边弹性转动约束、弹性支承上薄板屈曲问题的研究尚不充分。该文研究了非加载边弹性转动约束、均匀受压弹性支承矩形薄板弹性屈曲问题。由Ritz能量变分法得到了临界载荷计算公式,应用有限元分析证实了理论解的适用性。得到了屈曲半波数与板的纵横比、边界转动约束系数及支承刚度之间的关系式,支承刚度增加使屈曲半波数和屈曲系数增大。
With the engineering structure of light weight, thin-walled, more and more attention to the problem of sheet structure stability, a lot of studies have been carried out on the sheet buckling problems under different conditions. There are some related literatures about the buckling of the thin plates with the constraint of the buckling of the plate on the elastic support, the constraint of the boundary elastic rotation and the constraint on the rotation of the rigid support. The research on the buckling problem of the thin plate on the elastic support is not sufficient. In this paper, the problem of elastic buckling of rectangular thin plate under uniformly loaded compression is studied in this paper. The critical load calculation formula is obtained by Ritz energy variation method. The applicability of the theoretical solution is verified by finite element analysis. The relationship between the buckling half-wave number and the plate aspect ratio, the boundary rotation restraint coefficient and the bearing stiffness was obtained. The increase of the bearing stiffness increased the buckling half-wave number and the buckling coefficient.