Finite element formulation of viscoelastic constitutive equations using fractional time derivatives

Nonlinear Dynamics

Volumn 29, Issue 1-4, 2002, Pages 37-55

  Schmidt, André ^a   Gaul, Lothar ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Damping; Finite Element Method; Fractional derivatives; Viscoelasticity

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CURVE FITTING; DAMPING; EQUATIONS OF MOTION; FINITE ELEMENT METHOD; FREQUENCY DOMAIN ANALYSIS; INTEGRATION; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; PARAMETER ESTIMATION; PROBLEM SOLVING; STRUCTURAL ANALYSIS; TIME DOMAIN ANALYSIS;

FRACTIONAL DERIVATIVES;

VISCOELASTICITY;

EID: 0036650160     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1016552503411     Document Type: Article

References (27)

1. Power law and fractional calculus model of viscoelasticity
2. A theoretical basis for the application of fractional calculus to viscoelasticity
3. On the fractional calculus model of viscoelastic behaviour
4. Vibrations on an infinite viscoelastic layer with a dissipative memory
5. A new dissipation model based on memory mechanism
6. Some approaches to the analyses of nonproportionally damped viscoelastic structures
7. Time-domain finite element analysis of viscoelastic structures with fractional derivatives constitutive relations
8. Formulation and integration of the standard linear viscoelastic solid with fractional order rate laws
9. The influence of damping on waves and vibrations
10. A comparative study of three boundary element approaches to calculate the transient response of viscoelastic solids with unbounded domains
11. A method of analyzing experimental results obtained from elasto-viscous bodies
12. On fractional differentials
13. Über 'begrenzte' derivationen und deren anwendung
14. Applications of fractional calculus to the theory of viscoelasticity
15. Mémoire sur le calcul des différentielles à indices quelconques
16. Mémoire sur quelques quéstions de géomerie et de mécanique, et sur un nouveau genre de calcul pour résoudre ces quéstions
17. Mémoire sur le théoreme des fonctions complémentaires
18. A new general law of deformation
19. Computational algorithms for FE formulations involving fractional operators
20. A brief history and exposition of the fundamental theory of fractional calculus
21. Application of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids
22. An application of the theory of quasi-properties to the treatment of anomalous strain-stress relations