Low-Mach-number and slenderness limit for elastic Cosserat rods and its numerical investigation

Autor:	Franziska Baus, Raimund Wegener, Nicole Marheineke, Axel Klar
Přispěvatelé:	Publica
Rok vydání:	2020
Předmět:	010101 applied mathematics Physics symbols.namesake Mach number General Mathematics 0103 physical sciences symbols Limit (mathematics) Mechanics 0101 mathematics 01 natural sciences Rod 010305 fluids & plasmas
Zdroj:	Asymptotic Analysis. 120:103-121
ISSN:	1875-8576 0921-7134
DOI:	10.3233/asy-191581
Popis:	This paper deals with the relation of the dynamic elastic Cosserat rod model and the Kirchhoff beam equations. We show that the Kirchhoff beam without angular inertia is the asymptotic limit of the Cosserat rod, as the slenderness parameter (ratio between rod diameter and length) and the Mach number (ratio between rod velocity and typical speed of sound) approach zero, i.e., low-Mach-number–slenderness limit. The asymptotic framework is exact up to fourth order in the small parameter and reveals a mathematical structure that allows a uniform handling of the transition regime between the models. To investigate this regime numerically, we apply a scheme that is based on a Gauss–Legendre collocation in space and an α-method in time.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6d40ab6ae6bd190ea4300e3fbbd53bd5 https://doi.org/10.3233/asy-191581 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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