Mechanics of Rods in Space

  • Yury Vetyukov
Part of the Foundations of Engineering Mechanics book series (FOUNDATIONS)


Beginning with the direct approach, we develop the general nonlinear theory of rods with initial twist and curvature. The principle of virtual work for a material line produces the equations of equilibrium, the expressions for the strain measures, and the general form of the constitutive relations. Further we discuss a transition to the classical theory with constrained shear. Linearized equations in the vicinity of a pre-deformed state are used for obtaining closed-form solutions of buckling problems. The relation with the results of the asymptotic splitting in the non-reduced three-dimensional problem is discussed. Numerical simulations, which are based on both the differential equations and the variational formulation of the rod theory, are presented with the source code in a Mathematica environment. The chapter is concluded with a discussion of a finite element scheme, which is specially designed for classical rods in space. Simulation results and convergence studies are presented in comparison with analytical solutions.


Constitutive Relation Virtual Work Newton Iteration Reference Configuration Torsional Stiffness 
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Copyright information

© Springer-Verlag Wien 2014

Authors and Affiliations

  • Yury Vetyukov
    • 1
  1. 1.Institute of Technical MechanicsJohannes Kepler UniversityLinzAustria

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