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Computational Mechanics
Erschienen in: Computational Mechanics 4/2021

07.07.2021 | Original Paper

Nodally integrated thermomechanical RKPM: Part I—Thermoelasticity

verfasst von: Michael Hillman, Kuan-Chung Lin

Erschienen in: Computational Mechanics | Ausgabe 4/2021

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Abstract

In this two-part paper, a stable and efficient nodally-integrated reproducing kernel particle method (RKPM) is introduced for solving the governing equations of generalized thermomechanical theories. Part I investigates quadrature in the weak form using coupled and uncoupled classical thermoelasticity as model problems. It is first shown that nodal integration of these equations results in spurious oscillations in the solution many orders of magnitude greater than pure elasticity. A naturally stabilized nodal integration is then proposed for the coupled equations. The variational consistency conditions for nth order exactness and convergence in the two-field problem are then derived, and a uniform correction on the test function approximations is proposed to achieve these conditions. Several benchmark problems are solved to demonstrate the effectiveness of the proposed method. In the sequel, these methods are developed for generalized thermoelasticity and generalized finite-strain thermoplasticity theories of the hyperbolic type that are amenable to efficient explicit time integration.
Vorheriger Artikel Dynamics of double emulsion interfaces under the combined effects of electric field and shear flow
Nächster Artikel Nodally integrated thermomechanical RKPM: Part II—generalized thermoelasticity and hyperbolic finite-strain thermoplasticity

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Metadaten
Titel
Nodally integrated thermomechanical RKPM: Part I—Thermoelasticity
verfasst von
Michael Hillman
Kuan-Chung Lin
Publikationsdatum
07.07.2021
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 4/2021
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-021-02047-9

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