Optimized designing spherical void structures in 3D domains

Optimized layout of variable-sized spheres in a disconnected polyhedral domain is considered. The problem is motivated by optimized design of void structures in additive manufacturing. The spheres must be arranged in the container; however, a certain protruding is permitted subject to the corresponding center inside the container. The distance between the objects must be at least a certain given threshold. The objective is to find coordinates of the centers and radii of the spheres maximizing the total volume of the spheres for two cases: with and without balancing conditions. Two nonlinear programming models are provided. Corresponding nonlinear optimization problem is formulated and solved. Numerical results are presented to illustrate the main constructions. © 2022 Elsevier Inc. All rights reserved.