On the instability, nonexistence and spatial behaviour of the one-dimensional response of a new class of elastic bodies-Reference-Cited by-同舟云学术

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On the instability, nonexistence and spatial behaviour of the one-dimensional response of a new class of elastic bodies

Published:2021-05-22 Issue:3 Volume:86 Page:565-576
ISSN:0272-4960
Container-title:IMA Journal of Applied Mathematics
language:en
Short-container-title:

Author:

Quintanilla R¹,Rajagopal K R²

Affiliation:

1. Departament de Matemàtiques, U. P. C. Colom 11, 08222 Terrassa, Barcelona, Spain

2. Mechanical Engineering, Texas A & M University, College Station, TX 77843-3123, USA

Abstract

Abstract In this note we consider 1D problems within the context of a new class of elastic bodies. Under suitable conditions on the constitutive equations we prove instability and nonexistence of solutions similar to those in place for the linearized theory. The last section is devoted to describing the spatial behavior of the solutions.

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics

Link

http://academic.oup.com/imamat/article-pdf/86/3/565/38495753/hxab014.pdf

Reference23 articles.

1. Recherches sur l’ équilibre et le mouvement intérieur des corps solides ou fluids, élastiques ou non élastiques;Cauchy;Bull. Soc. Philomath.,1823

2. Sur les équations qui experiments des conditions d’ équilibre ou le lois du mouvement intérieur, d’ un corps solide, élastique un non élastique;Cauchy;Oeuvres (2),1828

3. Saint-Venant’s principle in linear elastodynamics;Chirita;J. Elasticity,1996

4. Energy bounds in dynamical problems for a semi-infinite elastic beam;Flavin,1990

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