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运用变分原理,推导了考虑初始荷载效应情况下板的屈曲控制微分方程。以微分方程为基础,运用伽辽金法解得了简支矩形板考虑初始荷载效应的屈曲临界荷载系数近似解;同时,提出了考虑初始荷载效应情况下板的稳定有限元公式。对比验证了考虑初始荷载效应情况下,简支矩形板的屈曲临界荷载系数近似解和稳定有限元公式的正确性。并通过本文建立的有限元公式深入分析了考虑初始荷载效应情况下,初始荷载、板的厚度对板稳定性的影响,得到了如下结论:初始荷载效应提高了板的屈曲临界荷载;初始荷载越大,或板的厚度越薄,或边界约束越弱,初始荷载效应对板的屈曲临界荷载提高越明显。
By using the principle of variational principle, the buckling control differential equation of the plate under the initial load effect is deduced. Based on the differential equation, the approximate solution of the critical buckling load factor considering the initial load effect was obtained by using the Galerkin method. At the same time, a stable finite element formula of the plate under the initial load effect was proposed. The correctness of the approximate solution to the buckling critical load factor and the stability of the finite element formula for the simply supported rectangular plate are verified by comparison with the initial load effect. Through the finite element formula established in this paper, the influence of the initial load and the thickness of the plate on the plate stability under the initial load effect is analyzed in depth. The conclusions are drawn as follows: The initial load effect increases the buckling critical load of the plate; Large, or the thinner the plate thickness, or the weaker the boundary constraints, the more pronounced the initial load effect on the critical buckling load of the plate.