Computational algorithms for FE formulations involving fractional operators. (English) Zbl 0616.73066
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.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 65R20 | Numerical methods for integral equations |
| 45J05 | Integro-ordinary differential equations |
| 47Gxx | Integral, integro-differential, and pseudodifferential operators |
Keywords:
Newmark beta method; central difference operators; modified Euler scheme; normal mode procedure; transient solution algorithms; finite element simulations; viscoelastic problems; fractional integrodifferential operators; Grunwald-Liouville-Riemann formalism; formal error estimations; implicit; explicit; predictor corrector typeReferences:
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