PSI - Issue 78

Mauro Mazzei et al. / Procedia Structural Integrity 78 (2026) 1649–1656

1654

Therefore, it can be shown that any two lines in the same family do not lie in the same plane (they are skewed). Every line of a family intersects all the lines of the other family (except the one opposite, which is parallel) and that any three lines of the same family are never parallel to the same plane. 3. Data modelling The design envisages that the main rods are made of laminated wood with an increased cross-section, and the ribbed surfaces can be made of laminated wood, or of steel with an adequate cross-section to support deformable photovoltaic panels and to maintain the tensile stresses in the rods that are subjected to high stresses resting on the nodes of the supporting structure. The supporting structure consisting of rods and nodes is subjected to structural analysis. To realise this particular structure, the stresses of certain types of three-dimensional structures, in particular a hyperbolic paraboloid, are analysed in general. To this end, a calculation programme was implemented for the automatic generation of the coordinates of the model nodes in a three-dimensional Cartesian reference using the OpenSees framework, see Tab. 1 and Tab 2. Currently, the most powerful structural calculation tool is the finite element tool. Its use in the analysis of structures provides a very authentic representation that is able to capture even complex geometric shapes of frameworks of existing structures. The finite element discretization method consists of subdividing a structure into a set of small elements, connected to each other at vertices, which are called “nodes”. The structure is then represented by a set of elements that interact exclusively through these material points; these elements are subjected to external load actions, appropriately schematised as equivalent nodal loads. The unknown degrees of freedom of the structure generally coincide with the displacements of the nodes, once these are known, it is possible to determine the range of displacements within each element through the form functions, and to determine the state of tension and deformation of each element.

Table 1. 3D nodes of the analyzed module. ID nodes X

Y

Z 0 0 0 0

1 2 3 4 5 6 7 8 9

250 250 750 750 500

750 250 250 750

1000

612 612 612 612 612

0

500

500

0

1000

500 500

500

Table 2. 3D rods of the analyzed module. Rods Nodes

ID. rods

Length 500,0 707,1 500,0 707,1 707,1 707,1 500,0 707,1 707,1 707,1 500,0 707,1 707,1 707,1 707,1 707,1 707,1 500,0 500,0 500,0 500,0

Total length

1 2 3 4 5 6 7 8 9

1 1 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 5 6 7 8

2 3 4 5 6 9 3 6 7 9 4 7 8 9 5 8 9 9 9 9 9

500 1207 1707 2414 3121 3828 4328 5036 5743 6450 6950 7657 8364 9071 9778

10 11 12 13 14 15 16 17 18 19 20 21

10485 11192 11692 12192 12692 13192