  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.
