薄板的几何非线性求积元分析

针对薄板非线性迭代计算量很大的问题,依据von Kárman薄板非线性理论构造能量泛函,并用数值积分和数值微分进行离散,得到非线性方程组,从而利用求积元法(Quadrature Element Method,QEM)求解薄板的中等挠度的弯曲和非线性屈曲问题,得到可信的结果.算例表明:在处理薄板几何非线性问题上,QEM计算效率很高,应用潜力很大.

Geometrical nonlinear quadrature element analysis on thin plate

As to the issue that the amount of nonlinear computation of thin plate is very large, according to the von Kárman nonlinear thin plate theory, the energy functional is built and discretized using numerical integration and numerical differentiation to obtain nonlinear equations; the moderate deflection and nonlinear buckling problems of thin plate are solved by Quadrature Element Method(QEM) and the convincible results are obtained. The examples indicate that the calculation efficiency is high and the application potential is great for QEM to solve geometrical nonlinear problem of thin plate.