This study proposes a robust technique for large displacement analysis of slack cable structures subjected to dynamic loadings using a novel method, entitled Node Relaxation. Ordinary numerical methods are usually unable to analyze cable structures due to singularities arising from large displacements and rotations following any alteration of the applied loads. When dynamic loads are considered, handling these singularities in numerical analyses becomes even more challenging. In this paper, an effective iterative method is proposed for three-dimensional large-displacement dynamic analysis of structures consisting slack cables as the primary load-bearing system. The cable structure is modeled using a set of nonlinear springs with properties that are constantly updated as the structural form gradually responds to the applied loads. The large changes in the cable forms are captured by considering an impedance relation that is used to determine the displacement magnitude in the directions where the structure does not have an appreciable stiffness. The method is verified against closed-form solution of wave transfer phenomenon. The effectiveness of the method is also demonstrated by solving several numerical examples.

这项研究提出了一种强大的技术，可使用一种名为节点松弛的新型方法对承受动态载荷的松弛电缆结构进行大位移分析。普通的数值方法通常无法分析电缆结构，这是由于施加的载荷发生任何变化后，由于大的位移和旋转引起的奇异性。当考虑动态载荷时，在数值分析中处理这些奇异点将变得更具挑战性。本文提出了一种有效的迭代方法，对以松弛电缆为主要承载系统的结构进行三维大位移动力分析。使用一组非线性弹簧对电缆结构进行建模，这些非线性弹簧的特性会随着结构形式逐渐响应所施加的载荷而不断更新。通过考虑阻抗关系来捕获电缆形式的较大变化，该阻抗关系用于确定结构没有明显刚度的方向上的位移大小。针对波传递现象的闭式解验证了该方法。通过求解几个数值示例，也证明了该方法的有效性。