圆薄板非对称的非线性问题

本文首先用Fourier复级数将非线性问题化为线性问题,从而得到各级近似的边值问题,进而提出圆薄板非轴对称大变形问题的修正迭代法,讨论了圆薄板非轴对称的非线性问题。作为算例,在均变荷载、周边可移夹紧、位移在平面内不受约束的条件下对圆薄板非轴对称的非线性问题进行了求解,并绘出了特征曲线。本文的结果与相应的线性问题进行了比较,证明本文提出的理论和方法是正确的。

Non-symmetrical Nonlinear Problem of Circular Plates

In this paper, by using the complex form of Fourier series to change nonlinear problem into linear one, all orders of approximation of the boundary value problem are obtained and then a modified iteration method is given for the non-symmetrical large deflection problem and the non-symmetrical nonlinear problem of circular plates is discussed. As an example, under the movable clamped edge boundary condition, the non-symmetrical nonlinear problem of circular plate, which is subjected to uniformly varying loads and the displacements in the plane of which are not restricted, is solved. The characteristic curves are also plotted. By comparing the results given in this paper with those of the corresponding linear problem, the theory and the method presented in this paper are proved to be correct.