A Hybrid Stress Finite Element Method for Integro-Differential Equations Modelling Dynamic Fractional Order Viscoelasticity

A Hybrid Stress Finite Element Method for Integro-Differential Equations Modelling Dynamic Fractional Order Viscoelasticity

Year:    2024

Author:    Menghan Liu, Xiaoping Xie

International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 2 : pp. 221–243

Abstract

We consider a semi-discrete finite element method for a dynamic model for linear viscoelastic materials based on the constitutive law of fractional order. The corresponding integro-differential equation is of a Mittag-Leffler type convolution kernel. A 4-node hybrid stress quadrilateral finite element is used for the spatial discretization. We show the existence and uniqueness of the semi-discrete solution, then derive some error estimates. Finally, we provide several numerical examples to verify the theoretical results.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ijnam2024-1009

International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 2 : pp. 221–243

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    Integro-differential equation fractional order viscoelasticity hybrid stress finite element error estimate.

Author Details

Menghan Liu

Xiaoping Xie