【摘要】 本文用三次B样条函数和迭代法求解圆底扁球壳在逐次加载时挠度增量和内力增量所满足的变系数非线性微分方程,从而得出均布荷载作用下周边固定圆底扁球壳轴对称弯曲问题的解答。文中计算了λ≤46的各种λ值的极值屈曲荷载,所得结果在λ≤20时与Budiansky等所得结果一致。更多还原

【Abstract】 Cubic B-spline approximations and iterative techniques have been used in computing highly nonlinear deflections of clamped shallow spherical shells under successive increments of uniformly distributed loads. We find that for the shells with the geometric pa-rameter arch chord length, R = radius of curvature, h=thickness), the slopes dP/dW. of p-W. (load-central deflection) curves may go to infinity (and become negative) before snap-through buckling loads have been attained. A special algorithm which uses alternatively the increments of central deflection and load as iterative parameters has been developed to cope with this situation. This algorithm gives fairly good convergence rates for values of λ as high as 46 and the buckling loads obtained for λ<20 are compatible with that computed by B. Budiansky and R. Archer with entirely different methods.更多还原