Computational algorithms for FE formulations involving fractional operators

DOI10.1007/BF00296422zbMath0616.73066MaRDI QIDQ1821605

Yanyan Li

Publication date: 1987

Published in: Computational Mechanics (Search for Journal in Brave)

zbMATH Keywords

finite element simulationsimplicitexplicitfractional integrodifferential operatorsmodified Euler schemecentral difference operatorsformal error estimationsGrunwald-Liouville-Riemann formalismNewmark beta methodnormal mode procedurepredictor corrector typetransient solution algorithmsviscoelastic problems

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Finite element methods applied to problems in solid mechanics (74S05) Integral, integro-differential, and pseudodifferential operators (47Gxx)

Related Items (24)

An adaptation of the Gear scheme for fractional derivatives ⋮ General response of viscoelastic systems modelled by fractional operators ⋮ On the numerical handling of fractional viscoelastic material models in a FE analysis ⋮ A fractional rate‐dependent cohesive‐zone model ⋮ Efficient solutions of systems of fractional PDEs by the differential transform method ⋮ The finite element method for fractional non-local thermal energy transfer in non-homogeneous rigid conductors ⋮ Solution of time‐fractional generalized Hirota‐Satsuma coupled KdV equation by generalised differential transformation method ⋮ Modeling of materials with fading memory using neural networks ⋮ A generalized differential transform method for linear partial differential equations of fractional order ⋮ Phenomenological isotropic visco-hyperelasticity: a differential model based on fractional derivatives ⋮ Simulation of fractionally damped mechanical systems by means of a Newmark-diffusive scheme ⋮ Role of prehistories in the initial value problems of fractional viscoelastic equations ⋮ Nonlinear fractional-order viscoelasticity at large strains ⋮ Consistent modelling of infinite beams by fractional dynamics ⋮ Asymptotic steady state behavior of fractionally damped systems ⋮ Approximate analytical solution for the fractional modified Kdv by differential transform method ⋮ Dynamics of polymer and polymer composite rotors -- an operator based finite element approach ⋮ Homogenised finite element for transient dynamic analysis of unconstrained layer damping beams involving fractional derivative models ⋮ Simulation of a viscoelastic flexible multibody system using absolute nodal coordinate and fractional derivative methods ⋮ New method for solving linear fractional differential equations ⋮ Power Time Numerical Integration Algorithm for Nonlinear Fractional Differential Equations ⋮ A Condensation Technique for Finite Element Dynamic Analysis Using Fractional Derivative Viscoelastic Models ⋮ The G^α -scheme for Approximation of Fractional Derivatives: Application to the Dynamics of Dissipative Systems ⋮ Adaptive discretization of fractional order viscoelasticity using sparse time history

Cites Work

• On solutions to multiply-connected nonself-adjoint systems subject to deterministic and nondeterministic excitations
• On gyroscopic problems in elasticity
• L'intégrale de Riemann-Liouville et le problème de Cauchy
• The solution of non-linear hyperbolic equation systems by the finite element method
• Fractional calculus - A different approach to the analysis of viscoelastically damped structures
• A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity
• Fractional calculus in the transient analysis of viscoelastically damped structures
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