A Wavelet-Galerkin Method for a 1D Elastic Continuum with Long-Range Interactions

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An elastic continuum model with long-range forces is addressed in this study. Themodel stems from a physically-based approach to non-local mechanics where non-adjacentvolume elements exchange mutual central forces that depend on the relative displacement and onthe product between the interacting volume elements; further, they are taken as proportional to amaterial dependent and distance-decaying function. Smooth-decay functions lead to integrodifferentialequations while hypersingular, fractional-decay functions lead to a fractionaldifferential equation of Marchaud type. In both cases the governing equations are solved by theGalerkin method with different sets of basis functions, among which also discrete wavelets areused. Numerical applications confirm the accuracy of the Galerkin solution as compared to finitedifference solutions.
Original languageEnglish
Number of pages0
Publication statusPublished - 2009


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