This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a sequential piecewise linear programming (SPLP) algorithm. Five distinct strategies have been proposed to control the frequency of the factorizations of the Jacobian matrices of the nonlinear equilibrium equations. Aiming at speeding up the overall iterative scheme while keeping the accuracy of the approximate solutions, three of the strategies also use an ICA scheme for the adjoint linear system associated with the sensitivity analysis. The robustness of the proposed reanalysis strategies is corroborated by means of numerical experiments with four benchmark problems -- two structures and two compliant mechanisms. Besides assessing the performance of the strategies considering a fixed budget of iterations, the impact of a theoretically supported stopping criterion for the SPLP algorithm was analyzed as well.

翻译：这项工作将不精确的牛顿方法与迭代组合近似(ICA)混合在一起,在假设几何非线性的情况下解决地形优化问题。基于密度的问题配方法通过连续的片段线性编程算法(SPLP)来解决。提出了五个不同的战略,以控制非线性平衡方程的雅各布基质的因子化频率。为了加速整个迭代制,同时保持近似解决办法的准确性,其中三个战略还使用了与敏感度分析相关的联合线性线性系统的ICA计划。提议的再分析战略的稳健性通过四个基准问题 -- -- 两个结构和两个遵守机制 -- -- 的数字实验得到证实。除了评估考虑固定迭代法的战略的绩效外,还分析了理论支持的SPLP算法停止标准的影响。