Asymptotic analysis of a bit brace shaped junction of thin rods

• Published in: Zeitschrift für angewandte Mathematik und Mechanik Vol. 100; no. 1
• Main Authors: Leugering, Günter, Nazarov, Sergei A., Slutskij, Andrey S., Taskinen, Jari
• Format: Journal Article
• Language: English
• Published: Weinheim Wiley Subscription Services, Inc 01-01-2020
• Subjects: asymptotic analysis; Asymptotic properties; Crankshafts; Drill bits; Exact solutions; junction; Korn inequality; Rods; thin elastic rod; variational formulation
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201900227

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.
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.