Optimal Packing in Additive Manufacturing. Issue 13 (2019) - Romanova, T.; Stoyan, Y.; Pankratov, A.; Litvinchev, I.; Yanchevsky, I.; Mozgova, I.
Abstract: The paper studies a packing problem for ellipses placed into an arbitrary disconnected polygonal domain. Neither a number of ellipses nor their sizes are fixed. The objective is maximizing packing factor. The ellipses can be continuously translated and rotated. Restrictions on the dimensions of the ellipses are taken into account. Placement constraints (distance constraints between ellipses and containment of ellipses into a polygonal domain) are formulated using the phi-function technique. Resulting packing problem is stated in the form of MIP model that is equivalent to a sequence of NLP subproblems. A new solution approach is proposed combining a feasible starting point algorithm and an optimization procedure to search for efficient locally optimal solutions. The approach as an addition to existing topology optimization algorithms, can be used to automate design of parts for «support-free» additive manufacturing taking into account requirements of static and/or fatigue strength.