Shape optimization approach based on the extended finite element method

Abstract

Purpose -This paper proposes to extend the combination of Extended Finite Element Method (XFEM) and Level Set Method (LSM) from structural mechanics to electromagnetics. Based on this approach, the actual stage of the research work, dedicated to the investigation, development, implementation and validation of a shape optimization methodology, particularly tailored for 2D electric structures is described. Design/methodology/approach -The proposed numerical approach is based on the efficiency of the XFEM and the flexibility of the LSM, to handle moving material interfaces without remeshing the whole studied domain at each optimization step. Findings -This approach eliminates the conventional use of discrete finite elements and provides efficient, stable, accurate and faster computation schemes in comparison with other methods. Research limitations/implications -This research is limited to shape optimization of two-dimensional electric structures, however, the work can be extended to 3D ones too. Practical implications -The implementation of the proposed numerical approach for the shape optimization of a planar resistor is hereby described. Originality/value -The main value of the proposed approach is a powerful and robust numerical shape optimization algorithm that demonstrates outstanding suppleness of handling topological changes, fidelity of boundary representation and a high degree of automation in comparison with other methods.

Stochastic analysis and optimum design of structures subjected to fracture

“…An extension also of this coupling (XFEM and LSM) from structural mechanics to electromagnetics, developed in a shape optimization framework, particularly tailored for 2D electric structures have been also proposed by Topa et al (2012).…”