Nonlinear static and dynamic isogeometric analysis of slender spatial cable and beam type structures

Abstract

In this thesis, a bending-stabilized cable element with three degrees of freedom per control point, and a four degrees of freedom Euler-Bernoulli beam element, has been derived in a dynamic isogeometric setting. The elements are particularly suitable for structures that are pre-twisted or have initially curved geometry. By utilizing NURBS basis functions, curved geometry can be exactly represented, and higher continuity is easily obtained between elements.

The cable formulation is derived from a 3D continuum, it uses only translational degrees of freedom, and includes modeling of membrane and bending effects. Torsion is not included, and bending is confined to the osculating plane of the middle curve. The formulation is suitable for three-dimensional, large-deformation structural dynamics. In the case where structural loading and response are confined to a plane, the formulation is reduced to a 2D Euler--Bernoulli beam of finite thickness, which is one of the benefits of the proposed modeling approach. The same bending-stabilized cable formulation may be applied to model beams dominated by bending, and very thin cables that are dominated by membrane effects, in a unified fashion. In the case of thin cables, the presence of bending terms provides a stabilizing effect and greatly enhances the robustness of the numerical procedures when the cable is under compression. The case of multiple cables, and cable-shell coupling, is handled using the bending strip technique.

The four degrees of freedom Euler-Bernoulli beam element includes the modeling of torsion, thus increasing the range of applicability, although at the expense of introducing one rotational degree of freedom. The nonlinear isogeometric beam formulation is also derived from a 3D continuum, where large-deformation kinematics and the St. Venant--Kirchhoff constitutive law are assumed. It is assumed that the beam cross sections are double symmetric and planar, and that the tangent to the middle curve stays normal to the beam cross section during deformation. The beam geometry representation reduces to a curve in 3D space.

A comprehensive numerical study, including a wide range of benchmark and application problems, demonstrate the accuracy and robustness of the two elements in linear as well as nonlinear static and nonlinear dynamic analysis.