Mixed convolved action for the fractional derivative Kelvin–Voigt model

Based upon the concept of mixed convolved action, a true variational statement for a fractional derivative Kelvin–Voigt model is presented. In this formulation, a single functional is defined as a series of convolution integrals, where the stationarity of this functional leads to all the governing d...

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Bibliographic Details
Published inActa mechanica Vol. 232; no. 2; pp. 661 - 684
Main Author Kim, Jinkyu
Format Journal Article
LanguageEnglish
Published Vienna Springer Vienna 01.02.2021
Springer
Springer Nature B.V
Subjects
Analysis
Classical and Continuum Physics
Control
Convolution
Convolution integrals
Derivatives
Differential equations
Dynamical Systems
Engineering
Engineering Fluid Dynamics
Engineering Thermodynamics
Heat and Mass Transfer
Initial conditions
Mathematical analysis
Numerical methods
Original Paper
Solid Mechanics
Theoretical and Applied Mechanics
Vibration
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Summary:Based upon the concept of mixed convolved action, a true variational statement for a fractional derivative Kelvin–Voigt model is presented. In this formulation, a single functional is defined as a series of convolution integrals, where the stationarity of this functional leads to all the governing differential equations as well as pertinent initial conditions. Thus, the entire description of a fractional-derivative Kelvin–Voigt model is encapsulated within this framework. This new formulation provides an elegant basis for a development of effective numerical methods involving finite element representation over a temporal domain. Here, the simplest temporal finite element approach is developed, and some computational examples are provided to validate this proposed approach.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-020-02825-1