圆板非线性振动有限元分析的一种迭代方法

同时考虑横向振动和板平面内的运动,用3节点有限元研究均匀圆板的轴对称大振幅非线性振动,构造了一个避免发散加速收敛的平均迭代法,并将计算结果与文献的已有结果做了比较。

An Iteration Method in Finite Element Analysis of Non-linear Vibration of Circular Plates

The axisymmetric non-linear vibration is studied by using the three node annular element. In the case of finite amplitude, the transverse vibration and in-plate motion should be considered simultaneously. The motion equation is obtained by energy variational principle. As some elements of the stiffness matrix have non-linear terms, which depend on the amplitude of the plate, iteration method is necessary. A method for avoiding divergence and accelerating the convergence in the iteration process is given. The obtained results have been compared with the previous solutions.