The numerical modeling of phononic crystals using the finite element method requires a mesh that accurately describes the geometric features. In an optimization setting, involving shape and/or topological changes, this implies that a new matching mesh needs to be generated in every design iteration. In this paper a mesh-independent description for both the interior and exterior boundaries of the periodic unit cell is proposed. A method is developed to apply Bloch-Floquet periodic boundary conditions to edges that are non-matching to the mesh. The proposed method is applied to a one-dimensional phononic crystal and is demonstrated to exhibit improved performance over the commonly used interface material averaging. We show that this method provides an accurate mesh-independent model.
Mesh-Independent Design of Phononic Crystals Using an Advanced Finite Element Formulation
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van den Boom, SJ, Aragón, AM, & van Keulen, F. "Mesh-Independent Design of Phononic Crystals Using an Advanced Finite Element Formulation." Proceedings of the ASME 2016 International Mechanical Engineering Congress and Exposition. Volume 13: Acoustics, Vibration, and Wave Propagation. Phoenix, Arizona, USA. November 11–17, 2016. V013T01A021. ASME. https://doi.org/10.1115/IMECE2016-66928
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