Spectral extended finite element method for band structure calculations in phononic crystals

JOURNAL OF COMPUTATIONAL PHYSICS

卷:427

Article

Chin, Eric B.¹  Mokhtari, Amir Ashkan²  Srivastava, Ankit²  Sukumar, N.³ 

[1] Lawrence Livermore Natl Lab, 7000 East Ave, Livermore, CA 94550 USA

[2] IIT, Dept Mech Mat & Aerosp Engn, Chicago, IL 60616 USA

[3] Univ Calif Davis, Dept Civil & Environm Engn, Davis, CA 95616 USA

关键词: Phononic crystals;    Band structure diagram;    Dispersion curves;    Extended finite element method;    Spectral element method;    Euler's homogeneous function theorem;   

DOI  :  10.1016/j.jcp.2020.110066

来源: Elsevier

【 摘 要 】

In this paper, we compute the band structure of oneand two-dimensional phononic composites using the extended finite element method (X-FEM) on structured higher order (spectral) finite element meshes. On using partition-of-unity enrichment in finite element analysis, the X-FEM permits use of structured finite element meshes that do not conform to the geometry of holes and inclusions. This eliminates the need for remeshing in phononic shape optimization and topology optimization studies. In two dimensions, we adopt a rational Bezier representation of curved (circular) geometries, and construct suitable material enrichment functions to model two-phase composites. A Bloch-formulation of the elastodynamic phononic eigenproblem is adopted. Efficient computation of weak form integrals with polynomial integrands is realized via the homogeneous numerical integration scheme-a method that uses Euler's homogeneous function theorem and Stokes's theorem to reduce integration to the boundary of the domain. Ghost penalty stabilization is used on finite elements that are cut by a hole. Band structure calculations on perforated (circular holes, elliptical holes, and holes defined as a level set) materials as well as on two-phase phononic crystals are presented that affirm the sound accuracy and optimal convergence of the method on structured, higher-order spectral finite element meshes. Several numerical examples are presented to demonstrate the advantages of p-refinement made possible by the spectral extended finite element method. In these examples, fourth-order spectral extended finite elements deliver O(10-8) accuracy in frequency calculations with more than thirty-fold fewer degrees-of-freedom when compared to quadratic finite elements. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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