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A General-Purpose Element-Based Approach to Compute Dispersion Relations in Periodic Materials with Existing Finite Element Codes

    https://doi.org/10.1142/S2591728519500051Cited by:3 (Source: Crossref)

    The numerical determination of dispersion relations in periodic materials via the finite element method is a difficult task in most standard codes. Here, we propose a novel technique which allows the computation of these band structures from local elemental subroutines in contrast with existing methods which impose Bloch boundary conditions on the global arrays. The proposed local approach is thus readily applicable to several physical contexts and space dimensionalities. Here we present the details of this element-based algorithm and provide verification results for three different kinematic assumptions applied to phononic crystals in a classical and a micropolar elastic medium. The paper also includes in the form of supplementary material, a fully-coded user subroutine and a test-problem to be used in a commercial finite element code.