用样条加权残值法分析具有初始几何缺陷的壳体结构

导出了具有任意初始几何缺陷的壳体在曲线坐标中的小应变和大挠度情形下的基本方程,并给出了柱壳的控制方程。对该方程用加权残值法求解,采用最小二乘配点法解决了壳体的静力计算,计算中,对位移和应力函数沿子午向选取了5次B样条,环向选三角级数,以两者的组合函数作为试函数,其初始几何缺陷则根据给定的离散值进行拟合。文中给出了算例,计算结果与已有文献吻合较好。

Analysis of Shell Construction With Arbitrary Initial Imperfection by the Spline Weighted Residual Method

The basic equations of small strains and large deflection in arbitrary shells with arbitrary initial inperfections in curve coordinates and also the control equa- tions of cylindrical shells are deduced by the spline weighted residual method and ap- plying the least square collocation method to the static calculation of shells. In calcula- tion the fifth order B spline is chosen along meridional direction and the trigonometric se- ries along circumferential direction for both displacement and stress functions, and the trigonometric series is used as a trial function. All the initial geometric impertections are fitted in terms of the given discrete values. Several calculating examples given by the pa- per are found to be in accord with the literatures now available.