摘要
借助于圆薄板和圆底扁球壳的几何非线性积分方程组,本文严格证明了求解轴对称板壳几何非线性方程的修正迭代法的收敛性,并给出了适宜于计算机求解高阶解的通式,其有关力学量均可表征为迭代参数的解析表达式,这可使求高阶迭代解的计算量大为减少。
By means of the integral equations of the axisymmetric deformationof circular thin plates and spherical thin shells with circular edge, a strictproof of convergence is given for the modified-iterative method in solvingthe geometrically nonlinear equations of the plates and the shells. At thesame time, a programme of calculation of the high-order solutions of theiteration method, which is able to be carried out by computers, is alsogained. All mechanical quantities can be formulated by the analyticalfunctions of the iterative parameter so that the calculation of solvinghigh-order solutions of the iteration can be reduced.
出处
《兰州大学学报（自然科学版）》
CAS
CSCD
北大核心
1991年第1期14-20,共7页
Journal of Lanzhou University(Natural Sciences)
基金
国家自然科学基金
关键词
修正迭代法
收敛性
薄板
壳体
圆形
circular thin plates
spherical thin shells with circular edge
large defletion problem
geometrically nonlinear equations
modified-iterative method
convergence
