6. Hexadome (Healey Problem)

This test checks the performance of rod elements in the post-buckling range. It consists of a shallow truss structure referred to as a hexadome. The hexadome was first analysed by Tim Healey[14]. The rods have a length L=9m, with the height h=1.5m and the rod cross section area A=1cm2. At each of the intersection nodes (where more than two bars are attached to a node), an external force F=10N is applied. The structure is simply supported. Every bar in the structure is modelled with one rod element.

Healey dome geometry (top view)

Figure 30. Healey dome geometry (top view)

The nodes of the rod elements have three translational degrees of freedom. For this reason the rod elements can only be simply supported, the bending stiffness of a rod element being zero. The dome only buckles as a result of the instability of the construction, not as a result of Euler buckling of a single bar! Due to the forces, the rods shorten and at a certain point the dome becomes unstable and it buckles. Since rods have only stiffness in axial direction only one element can be used to model a bar over the length L. The material is linear isotropic, see input file b2test.mdl.

The results as displayed in Figure 31 were obtained with the

increment_control_type hyperplane

increment control type (to make sure that the whole path is captured), an initial load factor increment of 0.01, a maximum step size of 0.2, and a final load factor of 5.0. The load factor increases and decreases several times, as shown in the load-displacement curve for the mid-point node.

Table 1. List of peak values of the load factor PA

1.04 -0.95 1.52 -1.65 1.65 -1.5 0.95 -1.0 5.0

Load-displacement curve of mid-point node

Figure 31. Load-displacement curve of mid-point node

The test checks the final displacement state for a load fact or of 5.0. Intermediate steps are not checked.

[14] A group theoretic approach to computational bifurcation problems with symmetry', Computer Methods in Applied Mechanics and Engineering, Vol. 67 pp. 257-295, 1988.