UC Berkeley

This dissertation presents the formulation and validation of a new 3d mixed cable element that is based on a two-field variational formulation and is suitable for the nonlinear static and dynamic analysis of cable structures.

The new cable element is derived in general curvilinear coordinates under finite deformations, and identifies conjugate strain and stress measures for the nonlinear catenary problem. The formulation uses the weak form of the strain-displacement relation and the principle of virtual work to propose two numerical implementations of the element, one with a continuous axial force distribution and one with a discontinuous one.

This dissertation also proposes a new filtered energy-momentum conserving algorithm for obtaining the dynamic response of cable structures in time. This new algorithm exactly conserves the Hamiltonian structure of the two-field mixed catenary problem for any {non\-linear} elastic complementary energy, and provides a consistent time integration in the case of inelastic material response. A postprocessing Savitzky-Golay filter is included to address the high-frequency contributions that appear in cables with a large sag-to-span ratio, without jeopardizing the desired conserving properties.

The new element and the consistent time integration scheme are first validated under nonlinear elastic material response with several benchmark problems from the literature. In these examples, the mixed cable element obtains very accurate results for coarse meshes, and displays especially accurate axial force distributions compared to other models. For cables with a small sag-to-span ratio, the energy-conserving scheme and the Newmark method yield nearly identical results, while in the case of cables with a large sag-to-span ratio, for which the Newmark time integrator diverges, the new scheme gives accurate results and exactly conserves the total energy of the system.

The proposed formulations are also validated under viscoelastic material response. In the case of small viscoelastic strains, the new element behaves robustly and gives excellent results. A new finite viscoelastic material model is formulated for large viscoelastic strains, and results show that it reduces to the infinitesimal model when small deformations are considered. Simple benchmark problems involving the free vibration and the earthquake response of simply-supported cables demonstrate that small relaxation times can reproduce the internal physical mechanisms that dissipate the high-frequency waves in the axial force field, while long relaxation times account for the decay of the dynamic response.

The study concludes with the structural analysis of three-dimensional cable nets using the proposed 3d mixed cable elements. First, numerical joints are introduced to accommodate the discontinuities in the axial force field that appear in physical cable joints. These complex structures show excellent results for displacements and axial forces. For available experimental results, the proposed formulations give the smallest relative error compared to other models in the literature.