Ambiguous phase assignment of discretized 3D geometries in topology optimization

• Published in: Computer methods in applied mechanics and engineering Vol. 369; p. 113201
• Main Authors: Barrera, Jorge L., Maute, Kurt
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.09.2020; Elsevier BV
• Subjects: Algorithms; Ambiguity; Ambiguous phase assignment; Ambiguous tetrahedra level set method; Configurations; Design optimization; Discretization; Extended finite element method; Finite element method; Immersed boundary technique; Optimization; Phase assignment; Topology ambiguity; Topology optimization; Ambiguous phase assignment; Topology optimization; Ambiguous tetrahedra level set method; Extended finite element method; Topology ambiguity; Immersed boundary technique
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2020.113201

This paper considers topology optimization approaches where the geometry is described by a level set method and the system’s response is discretized on nonconforming meshes while providing a crisp definition of interface and external boundaries. Since the interface is explicitly tracked, the elements intersected by the interface are divided into sub-elements to which a phase needs to be assigned. Due to loss of information in the discretization of the level set field, certain geometrical configurations allow for ambiguous phase assignment of sub-elements, and thus ambiguous definition of the interface. The study presented here focuses on investigating these topological ambiguities in embedded geometries constructed from discretized level set fields on hexahedral meshes. Three-dimensional problems where several intersection configurations can significantly affect the problem’s topology are considered. This is in contrast to two-dimensional problems where ambiguous topological features exist only in one intersection configuration, and identifying and resolving them is straightforward. A set of rules that resolve these ambiguities for two-phase problems is proposed, and algorithms for their implementations are provided. The influence of these rules on the evolution of the geometry in the optimization process is investigated with linear elastic topology optimization problems. These problems are solved by an explicit level set topology optimization framework that uses the extended finite element method to predict physical responses. This study shows that the choice of a rule to resolve topological features can result in drastically different final geometries. However, for the problems studied in this paper, the performances of the optimized design do not differ. •Ambiguities in embedded geometries may affect a problem’s topology.•Rules that resolve ambiguities and algorithms for their implementation are proposed.•The influence of these rules in the optimization process is investigated.•Examples are solved by an explicit level set topology optimization framework.•The choice of a rule does not affect the performances of the optimized design.