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Mixed convolved action for the fractional derivative Kelvin-Voigt model. (English) Zbl 1458.74024
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.
74D10 Nonlinear constitutive equations for materials with memory
74S40 Applications of fractional calculus in solid mechanics
Mathematica; Maple
Full Text: DOI
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