Asymptotic analysis of a bit brace shaped junction of thin rods

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http://hdl.handle.net/10138/327104

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Leugering , G , Nazarov , S A , Slutskij , A S & Taskinen , J 2019 , ' Asymptotic analysis of a bit brace shaped junction of thin rods ' , Zeitschrift für Angewandte Mathematik und Mechanik , vol. 100 , no. 1 , 201900227 . https://doi.org/10.1002/zamm.201900227

Title: Asymptotic analysis of a bit brace shaped junction of thin rods
Author: Leugering, Günter; Nazarov, Sergei A.; Slutskij, Andrey S.; Taskinen, Jari
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2019-11-07
Language: eng
Number of pages: 11
Belongs to series: Zeitschrift für Angewandte Mathematik und Mechanik
ISSN: 0044-2267
URI: http://hdl.handle.net/10138/327104
Abstract: We present a 1-D model of a junction of five thin elastic rods forming the shape of a bit brace (hand drill), or, a crankshaft. The distinguishing feature of this junction is the existence of the so-called movable elements, which are rods and knots requiring modifications of the classical asymptotic ansatze. These consist of constant longitudinal displacements on the edges of the skeleton of the junction and affect the transmission conditions at its nodes. We provide asymptotic formulas for the displacements, stresses and elastic energy, as well as error estimates. An exact solution of the model is given for a particular loading.
Subject: asymptotic analysis
junction
Korn inequality
thin elastic rod
variational formulation
111 Mathematics
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