Topology optimization has seen increased interest with the development of additive manufacturing (AM) as a manufacturing method, because of its ability to utilize the geometric complexity that AM offers. However AM still imposes some restrictions on the design, most notably on its minimum feature size, overhang, and enclosed voids. Enclosed voids are problematic because for most AM methods it is impossible to remove supports from them, additionally for powder-based AM these enclosed voids trap unmelted powder adding parasitic mass. In this thesis, two new methods have been investigated to alleviate this issue, the eigenfrequency method and the flood fill method. The eigenfrequency method utilizes the eigenfrequency of an inverted density field, which changes enclosed voids to floating masses. These floating masses have rigid body modes, which can then be prevented by applying a minimum eigenfrequency constraint. The eigenfrequency method encountered a large problem in the form of intermediate densities, which were used to satisfy the eigenfrequency constraint instead of the elimination of enclosed voids. The flood fill method utilizes a modified flood fill algorithm, which is a filter with a resulting density field where every enclosed void element is changed to solid. The flood fill method did successfully eliminate enclosed voids in both 2D and 3D problems, at the cost of very little additional computational effort. It also allows for direct control over the location, amount, and size of the void elimination features by varying boundary elements, running additional flood fills, and morphologic operators, respectively.