engleski

Derivation of the nonlinear bending-torsion model for a junction of elastic rods

In this paper we derive the one-dimensional bending-torsion equilibrium model modeling the junction of straight rods. The starting point is a three-dimensional nonlinear elasticity equilibrium problem written as a minimization problem for a union of thin rod--like bodies. By taking the limit as the thickness of the 3D rods goes to zero, and by using ideas from the theory of Gamma-convergence, we obtain that the resulting model consists of the union of the usual one--dimensional nonlinear bending-torsion rod models which satisfy the following transmission conditions at the junction point: continuity of displacement and rotation of the cross--sections and balance of contact forces and contact couples.

rods; one-dimensional model; junction; contact conditions

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