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：高秩修正下的高效结构重分析在需要重复评估结构响应的工程计算（如结构优化和概率分析）中起着重要作用。为提升工程计算效率，针对高秩修正的静不定结构，提出一种基于体系缩减与迭代求解的新型近似静力重分析方法。该方法将静不定结构划分为基础体系与附加组件，进而将结构平衡方程改写为以基础体系刚度矩阵及由附加单元导出的伪力构成的方程组。通过引入谱分解，建立以附加单元内力为未知量的缩减方程组，进而采用预处理迭代求解算法求解缩减方程组，获得修正结构的近似解。将所提方法的计算成本与其他两种重分析方法进行对比，并给出静力重分析与静力非线性分析的数值算例。结果表明，对于均质材料结构及功能梯度梁组成的结构，该方法均具有优异的计算性能。同时，所提方法的优越性表明，体系缩减与预处理迭代求解技术的结合是开发高性能重分析方法的一条有效途径。