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Volume 21, Issue 2
A Hybrid Stress Finite Element Method for Integro-Differential Equations Modelling Dynamic Fractional Order Viscoelasticity

Menghan Liu & Xiaoping Xie

DOI: 10.4208/ijnam2024-1009

Int. J. Numer. Anal. Mod., 21 (2024), pp. 221-243.

Published online: 2024-04

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  • 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.

  • Keywords

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

  • AMS Subject Headings

35Q74, 35R09, 65M12, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-21-221, author = {Liu , Menghan and Xie , Xiaoping}, title = {A Hybrid Stress Finite Element Method for Integro-Differential Equations Modelling Dynamic Fractional Order Viscoelasticity}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2024}, volume = {21}, number = {2}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2024-1009}, url = {http://global-sci.org/intro/article_detail/ijnam/23025.html} }
TY - JOUR T1 - A Hybrid Stress Finite Element Method for Integro-Differential Equations Modelling Dynamic Fractional Order Viscoelasticity AU - Liu , Menghan AU - Xie , Xiaoping JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 221 EP - 243 PY - 2024 DA - 2024/04 SN - 21 DO - http://doi.org/10.4208/ijnam2024-1009 UR - https://global-sci.org/intro/article_detail/ijnam/23025.html KW - Integro-differential equation, fractional order viscoelasticity, hybrid stress finite element, error estimate. AB -

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.

Menghan Liu & Xiaoping Xie. (2024). A Hybrid Stress Finite Element Method for Integro-Differential Equations Modelling Dynamic Fractional Order Viscoelasticity. International Journal of Numerical Analysis and Modeling. 21 (2). 221-243. doi:10.4208/ijnam2024-1009
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