Open AccessProblems on equilibrium of a thin elastic rod constrained on a surface
Author(s) -
Yun Xiao,
Liqun Chen,
Yanzhu Liu
Publication year - 2004
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.53.2040
Subject(s) - classical mechanics , physics , cylinder , constraint (computer aided design) , differential equation , dimensionless quantity , surface (topology) , mechanics , algebraic equation , solid mechanics , nonlinear system , mathematical analysis , mathematics , geometry , thermodynamics , quantum mechanics
Nonlinear mechanics of thin elastic rod, as a model of DNA, aroused extensive interest as a joint research subject of mechanics and molecular biology. The study of the equilibrium of a thin elastic rod constrained on a surface found an important application in industry, especially in molecular biology. In the present paper the constraint equations and constraint forces of the elastic rod are analyzed, and the differential/algebraic equations of equilibrium are established with the arc-coordinate of the central line as the independent variable. In a special case when the constraint surface is a cylinder the dimensionless differential equations contain only one physical parameter, the ratio of the bending and torsional stiffness of the cross section. A special solution of helical equilibrium can be derived and is corresponding to a regular precession of the Lagrange heavy rigid body about a fixed point. The numerical analysis shows that the geometrical form of the central line is dependent on the initial conditions of the rod more than its physical parameters.