弹性支承上弹性转动约束矩形薄板线性荷载压屈分析

Pressure buckling analysis of rotationally restrained elastic rectangular plates onelastic base under linear compression

为探讨边界约束下不同刚度对受线性压力作用矩形板稳定性的影响,研究了弹性支承上弹性转动约束的矩形薄板线性压屈问题。采用基于能量变分原理的Ritz能量法,根据屈曲形变提出合适的挠曲面函数,由其能量变分推得临界屈曲荷载理论解。通过有限元分析得到此类矩形板压屈荷载数值解,结果表明:荷载梯度较小时误差不超过2.8%;荷载梯度较大时,通过回归得到修正系数,误差不超过4.7%。同时建立临界纵横比、荷载梯度与板的边界转动约束刚度和支承刚度之间的关系式,根据计算结果分析,边界转动约束刚度为0.8~100时对薄板受压稳定性影响显著。

In order to investigate the influence of lateral and boundary constraint stiffness on the stability of rectangular plates,the problem of local buckling of thin plates under linear pressure with elastic support and elastic rotational restraint was studied in this paper.By using Ritz method based on energy principle,a proper flexure surface function was proposed according to the buckling deformation,and the critical buckling load explicit solution was derived from its energy variation.The finite element method was used to obtain the numerical solution of compressive buckling load of this kind of rectangular plate.The results showed that the error between the theoretical solution and the finite element solution in this paper was less than 2.8%when the load gradient is low,while the error was not more than 4.7%when fixing the buckling coefficient by regression fitting at a high level of load gradient.The relationship between the critical aspect ratio,the load gradient and the boundary rotational restraint stiffness and the support stiffness was established.According to the results of calculation and analysis,the stability of the thin plate was significantly affected by the boundary rotational constraint stiffness in the range of 0.8~100.