Bubble method for topology and shape optimization of structures

This paper addresses a novel method of topology and shape optimization. The basic idea is the iterative positioning of new holes (so-called bubbles) into the present structure of the component. This concept is therefore called the bubble method. The iterative positioning of new bubbles is carried out by means of different methods, among others by solving a variational problem. The insertion of a new bubble leads to a change of the class of topology. For these different classes of topology, hierarchically structured shape optimizations that determine the optimal shape of the current bubble, as well as the other variable boundaries, are carried out.