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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.
MSC:
74D10 Nonlinear constitutive equations for materials with memory
74S40 Applications of fractional calculus in solid mechanics
Software:
Maple; Mathematica
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