环形薄板轴对称非线性屈曲的样条函数解法

环形薄板的大挠度计算因为边界条件复杂,仅有少数特殊情形的数值解答。均布边缘径向力作用下环形薄板非线性屈曲迄今尚未有研究成果。作者以三次B样条函数为试函数,用配点法计算环形薄板的大挠度。在12种不同的边界条件下,首次计算了环形薄板的压曲临界荷载及超临界荷载作用的变形。在所有的算例中均取得了收敛的数值结果。结果表明样条配点法具有收敛范围大、精度高和计算时间少的优点。

Spline solution of nonlinear axisymmetrical buckling of an annular thin plate

The problem of the large deflection of an annular plate had only a few special numerical solutions because of the complication about boundary conditions.So far there is no investigation for nonlinear buckling of an annular plate subjected to uniformly radial thrust.Cubic B-splines taken as trial functions, the large deflection of an annular plate was calculated by the method of point collection.For the first time,critical loads of annular plates and buckling beyond the critical thrust were calculated by nonlinear theory.Under 12 different boundary conditions,the figures of the radial ratio of inside edge to outside edge-buckling load(including single outside edge thrust,single inside edge thrust or the same thrusts subjected to outside edge and inside edge) were drawn.These figures can be applied in engineering design.In general,if the floatpoint numbers have 16 significant digits,the relative error of buckling is less than 0.0001,when the number of point collocation n=100 or 200.Different n is used to solve the same problem.Their results are compared.Conclusions can be drawn on the accuracy and convergence region of solutions.It shows the advantages of the spline collection method are wide convergence region(the thrust is 13 times than those by the power series method),high precision and little amount of computing time.