SoftwareChallenging application cases of modeFRONTIER in civil engineering
Fig.1 - Example of shape
resistant structures
Permasteelisa Group is the worldwide leader in the design, fabrication and installation of external facades for monumental buildings. They produces shape resistant structures, charachterised by main steel frameworks (arches, parabolic, with pre-stressed cables) and a ‘shell’ of glasses, with pre-stressed steel cable reinforcement. In the structure optimised by modeFRONTIER (fig.1), the upper arch is a square tubular shape; the lower arch is a pre-strassed cable; the connecting elements are cables. secondary structures are cables and steel shapes.
The objective of the optimisation are the minimisation of the overall cost, and the minimisation of the overall roof surface, underc onstraints of maximum stress and deflection and limitations to the overall size, while the design variables become the arch shape and size, spacing of connectors, upper arch rectangular tubular shape, section and prestress of lower arch cable, thickness of glass panels and of secondary structures of the shell, eccentricity of the vault cables, and shape and size of the side beams.
Fig.3 – Best solution obtained
The optimisation approach consisted on a Sobol DOE, after which a statistical analysis with t-Student and correlation matrix allowed to find out the most significant variables, and then MOSA and MOGAII algorithms were used to optimise the objectives, while the computation for each configuration has been made by the FE model Straus7.
From the Pareto front solutions obtained, it was selected in particular one, whose final shape is reported in fig.3.
Fig.4 – Athens Olympic
Stadium covering
Another application of modeFRONTIER was relative to the building of the Athens Olympic Stadium covering. The structure consists of two roof coverings each spanning approximately 304 m and varying in width from 60 m to 100 m. When joined, the inside perimeter of the two coverings provides an elliptical opening over the football field of the main stadium.
Each covering is supported by a curved truss structure consisting of two arches: an upper ARCH TUBE and a lower TORSION TUBE. The tubes are 3 m in diameter with a wall thickness of up to 90 mm. The two arches are connected with cables. The main roof girders are positioned orthogonal to, and built into the, lower arch. They are supported at the opposite end by cables anchored to the upper arch. The entire structure is supported at four points.
Fig.5 – Stadium covering FE model
The steel work for the roof of the stadium was awarded to Cimolai (Pordenone, Italy), who had the task of constructing unique structure of its kind, due to the complexity of the solutions adopted and the challenging methods of erections: modeFRONTIER was employed to determine the exact amount of pre-stress in cables (input variables) such to achieve the final post-tensions (objective) determined through on-site measurements; the FE model used integrated with modeFRONTIER to compute each configuration tensions is Straus7. A simplex algorithm was used to minimise the objective (mean difference between computed post-tensions and target ones), and it has been initialised by a Montecarlo DOE.
Fig.6 – Convergence of Simplex algorithm
The results obtained were very significant, since the maximum difference of the tensioning sequence from the computing was less of 2%, and the two roof structures closed at the main node with an error of less than 2 cm!