Efficient structural reanalysis for high-rank modification plays an important role in engineering computations which require repeated evaluations of structural responses, such as structural optimization and probabilistic analysis. To improve the efficiency of engineering computations, a novel approximate static reanalysis method based on system reduction and iterative solution is proposed for statically indeterminate structures with high-rank modification. In this approach, a statically indeterminate structure is divided into the basis system and the additional components. Subsequently, the structural equilibrium equations are rewritten as the equation system with the stiffness matrix of the basis system and the pseudo forces derived from the additional elements. With the introduction of spectral decomposition, a reduced equation system with the element forces of the additional elements as the unknowns is established. Then, the approximate solutions of the modified structure can be obtained by solving the reduced equation system through a pre-conditioned iterative solution algorithm. The computational costs of the proposed method and the other two reanalysis methods are compared and numerical examples including static reanalysis and static nonlinear analysis are presented. The results demonstrate that the proposed method has excellent computational performance for both the structures with homogeneous material and structures composed of functionally graded beams. Meanwhile, the superiority of the proposed method indicates that the combination of system reduction and pre-conditioned iterative solution technology is an effective way to develop high-performance reanalysis methods.

翻译：在工程计算中,需要反复评价结构反应,例如结构优化和概率分析。为了提高工程计算的效率,为静态的不确定结构提出了一种基于系统减少和迭代解决方案的新型近似静态再分析方法,以系统减少和迭代解决方案为基础,静态不确定结构经过高层次修改。在这种方法中,静态不确定结构分为基系统和额外组成部分。随后,结构平衡方程式作为公式系统与基准系统的僵硬矩阵和从附加要素产生的假力量一起重新编写。随着光谱分解的采用,一个使用未知因素的元素要素要素的元素力量的减少等式系统。然后,通过预先设定的迭代解决方案算法解决降低的公式系统,即可获得经修改的结构的近似解决办法。拟议方法和其他两个再分析方法的计算成本进行了比较,并提供了数字实例,包括静态再分析和静态非线性非线性分析。结果显示,拟议方法具有极佳的计算性能,同时采用同质材料和高性定型结构结构,同时形成功能性平级组合法。