Derivation of the nonlinear bending–torsion model for a junction of elastic rods
2012 ◽
Vol 142
(3)
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pp. 633-664
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Keyword(s):
We derive the one-dimensional bending–torsion equilibrium model for 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 three-dimensional rods tends to zero, and by using ideas from the theory of Γ-convergence, we find 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; balance of contact forces and contact couples.
2009 ◽
Vol 139
(5)
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pp. 1037-1070
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Keyword(s):
1968 ◽
Vol 64
(3)
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pp. 895-913
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Keyword(s):
1991 ◽
Vol 11
(4)
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pp. 365-395
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Keyword(s):
2001 ◽
Vol 627
(7)
◽
pp. 1626-1630
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2021 ◽
Keyword(s):
1981 ◽
Vol 42
(19)
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pp. 445-449
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