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Asymptotic analysis of a bit brace shaped junction of thin rods
Author(s) -
Leugering Günter,
Nazarov Sergei A.,
Slutskij Andrey S.,
Taskinen Jari
Publication year - 2020
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201900227
Subject(s) - brace , rod , crankshaft , asymptotic analysis , materials science , mathematical analysis , mathematics , mechanics , geometry , structural engineering , physics , engineering , thermodynamics , medicine , alternative medicine , pathology
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 ansätze. 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.