正交异性极扁薄壳的几何非线性分析

本文用最小二乘配置法求解正交异性极扁薄壳承受横向载荷作用下几何非线性弯曲问题。由于所设之应力函数和位移函数均能满足边界条件,且具有正交性,故而使大挠度极扁薄壳的控制方程组化为一组包含待定常数的非线性代数方程组,通过逐步接近的方法,求出待定常数,从而求得壳体的挠度、中曲面的应力、力矩等值。其代表点挠度与实验结果基本吻合。

Geometrically Nonlinear Analysis of Very Flat and Thin Orthotropic Shell

This paper solves problems of geometrically nonlinear bending of very flat and thin orthotropic shell under transverse load with least square method of collocation. Because the trial functions of transverse deflection and stree function satisfy all required boundary conditions and possess orthogonal properties, the governing nonlinear partial differential equations for the very flate shell with greater deflection are reduced to a set of nonlinear algeraic equations with their constant coefficients to be determined in the trial functions. By using progressive replacement, the authors obtian all coefficients, thus the transverse deflection, stress in medium curved surface and moment of forces. The calculated deflection at the representative point coincides with the measured one.