No abstract

SUMMARYMost papers on topology optimization consider that there is a linear relation between the strains and displacements of the structure, implicitly assuming that the displacements of the structure are small. However, when the external loads applied to the structure are large, the displacements also become large, so it is necessary to suppose that there is a nonlinear relation between strains and displacements. In this case, we say that the structure is geometrically nonlinear. In practice, this means that the linear system that needs to be solved each time the objective function of the problem is evaluated is replaced by an ill‐conditioned nonlinear system of equations. Moreover, the stiffness matrix and the derivatives of the problem also become harder to compute.The objective of this work is to solve topology optimization problems under large displacements through a new optimization algorithm, named sequential piecewise linear programming. This method relies on the solution of convex piecewise linear programming subproblems that include second order information about the objective function. To speed up the algorithm, these subproblems are converted into linear programming ones. The new algorithm is not only globally convergent to stationary points but our numerical experiments also show that it is efficient and robust. Copyright © 2014 John Wiley & Sons, Ltd.

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.

No abstract