Packing Approach to Generate Void Structures in Lightweighted Parts for Additive Manufacturing

This paper presents a topology optimization approach that enables the creation of void structures that reduce part weight while meeting stress constraints for additive manufacturing, using an optimization packing problem. The problem is aimed at maximizing a total area of elliptical voids within an irregular polygonal domain, subject to minimum-distance constraints. Geometric feasibility conditions are expressed analytically using the phi-function technique, ensuring exact enforcement of 3D printing standards. A corresponding nonlinear programming mathematical model is constructed. A stress condition is incorporated in the model using an equivalent mechanical stress computed from the resulting geometry. A solution strategy is proposed that integrates geometric design and solid mechanics within a unified optimization approach. To solve the constrained optimization problem, a local optimization algorithm is developed, based on feasible directions method. Gradients of geometric constraints and the objective function are computed analytically, while the stress gradient is estimated numerically using a finite difference approximation. This permits the simultaneous consideration of geometric and mechanical constraints without requiring an explicit stress function. Numerical experiments demonstrate that the approach produces optimized designing parts with controlled peak stress and achieves competitive performance compared with known topology optimization techniques.