Large Displacements in Nonlinear Numerical Analyses for Cable Structures

Method for defining appropriate form of prestressed, tensile cable structures and for calculating stress and displacements for such structures is presented. The developed numerical model is taking into account the material and geometric nonlinearity. The described model represents a practical way of implementing the large displacements theory in the analysis of finding appropriate form of prestressed cable structures.

The behavior of the structure under an increasing load, from zero up to final is described. The load usually applied in two phases. The first phase can be prestressing. In the second phase, the structure is computed taking into account the dead and the live gravity load.

An approach to solving the problem of large displacements in the theory of structures is presented, based on an incremental approach of the Total Lagrange formulation with the small displacements. The model is based on the assumption that the FE are linear and small enough and thus tracking of large translational displacements can be approximated by a simple geometrical model. The resulting force, i.e. stress, inside FE are expressed within the large displacements, based on the successive approach of small displacements of each increment, using a singular quasi-tangent stiffness matrix. A solution of renewable of the internal forces and stress and their influence is presented. The renewal of the large translational displacements is based on their vector from increment to increment. The renewal of the geometry configuration is influenced to the renewal of basic stiffness, geometrical stiffness and large displacement stiffness.

Spatial discretization of the system is on two-node line elements. The fiber discretization of the cross section is on triangular elements where mechanical properties of each fiber are presented by the σ — ɛ diagram.

The numerical nonlinear material model is based upon nonlinear material properties defined in the form of a uniaxial σ — ɛ diagram. The developed model was tested on few practical examples. They are compared by the research computations of the other authors.