Abstract
This paper considers the development of transient solution algorithms for finite element simulations of viscoelastic problems involving fractional integrodifferential operators. Specifically, numerical approximations are developed for the Grunwald-Liouville-Riemann formalism. This includes establishing formal error estimations. Based on the numerical representations of the fractional operators, implicit, explicit and predictor corrector type transient algorithms are derived for viscoelastic finite element simulations. To illustrate their computational properties, the results of several numerical benchmark experiments are presented. These emphasize the efficiency and stability of the various algorithms developed.
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Communicated by S.N. Atluri, August 19, 1986
Work partially supported by NASA Langley through Grant NAG-1-444
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Padovan, J. Computational algorithms for FE formulations involving fractional operators. Computational Mechanics 2, 271–287 (1987). https://doi.org/10.1007/BF00296422
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DOI: https://doi.org/10.1007/BF00296422