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

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