前屈曲分析中的局部线性化方法

Local linearization mothed in pre-buckling analysis

非线性有限元分析,最终都归结为求解非线性代数方程组或非线性特征值问题。在增量法的解点上,利用局部线性化方法,将非线性特征值问题化为线性特征值问题。对于特征值问题的求解,本文给出了以主对角元素构造的原点平移加速算法的迭代计算公式。最后通过算例验证了本算法良好的收敛特性,计算结果是令人满意的。

Nonlinear finite element analysis is virtually the solution of nonlinear algebraic equations or characteristic value. On the basis of solution points of incremental method and by adopting local linearization,the nonlinear characteristic value is reduced to linear characteristic value. For the solution of characteristic value, this paper presents an iterative algorithm which speeds up convergence by the origin parallel translation formed from main-diagonal elements. Numerical examples are given to validate the proposed method and satisfactory results are obtained.