Multi-constrained 3D topology optimization via augmented topological level-set

• Addresses a variety of constraints in topology optimization.
• Topological sensitivity field is combined with augmented Lagrangian formulation.
• Assembly-free deflated finite element method is exploited for efficient analysis.
• Constraints are classified into soft and hard constraints to avoid early termination.

The objective of this paper is to introduce and demonstrate a robust methodology for solving multi-constrained 3D topology optimization problems. The proposed methodology is a combination of the topological level-set formulation, augmented Lagrangian algorithm, and assembly-free deflated finite element analysis (FEA).The salient features of the proposed method include: (1) it exploits the topological sensitivity fields that can be derived for a variety of constraints, (2) it rests on well-established augmented Lagrangian formulation to solve constrained problems, and (3) it overcomes the computational challenges by employing assembly-free deflated FEA. The proposed method is illustrated through several 3D numerical experiments.