An efficient topology optimization algorithm for large-scale three-dimensional structures

Abstract

Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems. The robustness of the algorithm is ensured by adopting a globally convergent sequential linear programming method with a stopping criterion based on the first-order optimality conditions of the nonlinear problem. To increase the algorithm's efficiency, it is combined with a multiresolution scheme that employs different discretizations to deal with displacement, design, and density variables. In addition, the time spent solving the linear equilibrium systems is substantially reduced using multigrid as a preconditioner for the conjugate gradient method. Since multiresolution can lead to the appearance of unwanted artefacts in the structure, we propose an adaptive strategy for increasing the degree of the displacement elements, with a technique for suppressing unnecessary variables that provides accurate solutions with a moderate impact on the algorithm's performance. We also propose a new thresholding strategy, based on gradient information, to obtain structures composed only by solid or void regions. Computational experiments carried out in Matlab prove that the new algorithm effectively generates high-resolution structures at a low computational cost.

Figures (24)

• Figure 1: Elements in multiresolution meshes, with $n_{mr} = 4$ and $d_{mr} = 2$.
• Figure 2: Neighborhood of a two-dimensional density element for $n_{mr} = 4$ and $d_{mr} = 2$.
• Figure 3: Two-dimensional structure with artefacts.
• Figure 4: Two-dimensional MBB beam obtained using multiresolution with $n_{mr} = d_{mr} = 2$ and $r_{min} = 0.8$.
• Figure 5: Final structure obtained after applying the adaptive strategy with quadratic Lagrange elements and projecting the densities.