Irregular and Regular Assemblies in 2D Topology Optimal Design

In the present Chapter, the principles of shape and topology optimization with the continuous distribution of microscopic inhomogeneities or voids in problems of two-dimensional elasticity are deliberated. The structure under consideration is an assembly of interconnected “empty” and “material-filled” volume elements. From this viewpoint, the topological optimization can be carried out with various algorithms. The algorithms perform the “material introduction” into “empty” volume elements, “material removal” from “filled” ones or “redistribution” of material. Evidently, that the first action increase in the mass of the structure, the second— its reduction. The redistribution does not change the mass of the structure. The above procedure uses the cloud of microscopical voids. This means an infinite (or large) number of infinitesimally small voids or other inhomogeneities present in the structural element. The porosity function marks the volume density of cavities of inhomogeneities. In the topology optimization, the porosity function plays the role of control function.