弹性杆结点非线性弯扭模型的推导
Derivation of the nonlinear bending-torsion model for a junction of elastic rods
摘要：
本文推导了直杆连接处的一维弯扭平衡模型。出发点是一个三维非线性弹性平衡问题，作为一个最小化问题的薄杆状体的工会。将三维杆的极限厚度取为零，并利用$Γ$ -收敛理论的思想，得到了该模型由通常的一维非线性弯扭杆模型的联合组成，这些模型在连接点处满足以下传递条件：横截面的位移和转动的连续性以及接触力和接触力偶的平衡。
英文摘要：
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 $Γ$-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.
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