On the quasi-static approximation in the initial boundary value problem of linearised elastodynamics

R. J. Knops; R. Quintanilla

doi:10.1007/s10665-020-10072-5

On the quasi-static approximation in the initial boundary value problem of linearised elastodynamics

R. J. Knops^*, R. Quintanilla

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Continuous data dependence estimates are employed to rigorously derive conditions that validate the quasi-static approximation for the initial homogeneous boundary value problem in the theory of small elastic deformations superposed upon large elastic deformations. This theory imposes no sign-definite assumptions on the linearised elastic moduli and in consequence the requisite estimates are established using methods principally motivated by known Lagrange identity arguments.

Original language	English
Article number	11
Journal	Journal of Engineering Mathematics
Volume	126
Issue number	1
Early online date	28 Jan 2021
DOIs	https://doi.org/10.1007/s10665-020-10072-5
Publication status	Published - Feb 2021

Keywords

Continuous dependence
Dirichlet boundary conditions
Lagrange identities arguments
Linearised elastodynamics
Quasi-static approximation

ASJC Scopus subject areas

General Mathematics
General Engineering

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10.1007/s10665-020-10072-5

Cite this

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title = "On the quasi-static approximation in the initial boundary value problem of linearised elastodynamics",

abstract = "Continuous data dependence estimates are employed to rigorously derive conditions that validate the quasi-static approximation for the initial homogeneous boundary value problem in the theory of small elastic deformations superposed upon large elastic deformations. This theory imposes no sign-definite assumptions on the linearised elastic moduli and in consequence the requisite estimates are established using methods principally motivated by known Lagrange identity arguments.",

keywords = "Continuous dependence, Dirichlet boundary conditions, Lagrange identities arguments, Linearised elastodynamics, Quasi-static approximation",

author = "Knops, {R. J.} and R. Quintanilla",

note = "Funding Information: The work of R. Quintanilla has been supported by Ministerio de Econom{\'i}a y Competitividad under the research project “An{\'a}lisis Matem{\'a}tico de Problemas de la Termomec{\'a}nica” (MTM2016-74934-P), (AEI/FEDER, UE), and Ministerio de Ciencia, Innovaci{\'o}n y Universidades under the research project “An{\'a}lisis matem{\'a}tico aplicado a la termomec{\'a}nica” (PID2019-105118GB-I00). Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

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On the quasi-static approximation in the initial boundary value problem of linearised elastodynamics

Abstract

Keywords

ASJC Scopus subject areas

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