Topology optimization: Approaching the material distribution problem using a topological function description

The present paper is on finding the optimal material distribution on a given reference domain, i.e. the topology of a structure. Typically the topology representation is directly linked to the finite element discretization used. In the present paper a mesh independent topology representation is investigated. For this purpose a topology function is defined as a function that maps each point of the reference domain to a value that unambiguously determines the material content using a threshold value. This topology function will be constructed using simple functions that are determined by a few continuous design parameters only. The set of parameters that determines the optimal structure is then sought. This approach is applied to a standard test cases, which confirms the potential of the proposed approach.