分步迭代加权残值法

本文提出一种分步迭代的加权残值方法,并从理论上证明了分步迭代的最小二乘法用于求解线性问题时的收敛性。文中应用所提出的方法计算了方形固支板的位移,方形杆的扭转刚度及柔性圆板的大挠度位移和应力。结果表明了文中的方法可逐步提高计算精度。     

厚壳理论及其在圆柱壳中的应用

本文从Hellinger-Reissner广义变分原理出发,以位移和应力的假设为基础,建立了厚壳理论.文中把壳体的位移展开为其厚度方向的幂级数,对平行和垂直于中面的位移分别保留其级数的前四项和前三项.并假定壳体的法向挤压和横向剪切应力沿壳厚为三次曲线,使其满足上下壳面上的应力条件,利用变分原理推导出分析厚壳所需的物理方程,平衡方程和边界条件.文中对圆柱壳的情况作了实例计算,并作了光弹性实验,结果表明理论和实验符合良好.     

拋物旋转扁壳的轴对称弯曲

本文首先对扁壳的基本方程作了新的改进,将它表达为一般正交曲线坐标的普遍形式,同时还包括有势的切向表面载荷的情况。文中结合旋转扁壳,建立了这类壳体的简化复数微分方程。根据这一简化理论,对抛物旋转扁壳的轴对称弯曲问题作了研究,并给出以Thomson函数形式表示的普遍解。它将适用于所有类型的抛物旋转扁壳。文中还针对各类壳体的具体情况作了比较深入的分析,使设计者便于在给定载荷的情况下进行壳体最佳线型的选择。最后作者以简单法向均布载荷为例,示范其设计方法。通过数值计算的比较表明,球面扁壳乃是在这类载荷形式之下具有最佳承载性能的壳体。     

THEORY OF THICK-WALLED SHELLS AND ITS APPLICATION IN CYLINDRICAL SHELL

In this paper, a theory of thick-walled shells is established by means of Hellinger-Reissner's variational principle, with displacement and stress assumptions. The displacements are expanded into power series of the thickness coordinate. Only the first four and the first three terms are used for the displacements parallel and normal to the middle surface respectively. The normal extruding and transverse shear stresses are assumed to bt, cubic polynomials and to satLyfy the boundary stress conditions on the outer and inner surfaces of the shell. The governing equations and boundary conditions are derived by means of variational principle. As an example, a thick-walled cylindrical.shell is disscussed with the theory proposed. Furthermore, a photoelastic experiment has been carried out, and the results are in fair agreement with the computations.