The Complexity of the Copenhagen Opera House roof |Finite Element Analysis using LUSAS

Updated: Jul 2, 2020

Quick FACTS 🧾

  • The roof of the new Copenhagen Opera House is one of the largest canopy roof structures in the world.

  • With a plan dimensions of 158m by 90 m, it equates to the size of three football fields.

  • LUSAS finite element analysis was used for the design of the structure in order to ensure the necessary strength, stability and dynamic response was achieved. 

  • Static, dynamic and thermal assessment of the roof for in-service loadings were made.

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What is Finite Element Analysis (FEA)?

Finite Element Analysis or FEA is the simulation of a physical phenomenon using a numerical mathematic technique referred to as the Finite Element Method, or FEM. Engineers can use these FEM to reduce the number of physical prototypes and run virtual experiments to optimize their designs. 

Consider a concrete beam with support at both ends, facing a concentrated load on its centre span. The deflection at the centre span can be determined mathematically in a relatively simple way, as the initial and boundary conditions are finite and in control.

However, once you transport the same beam into a practical application, such as within a bridge, the forces at play become much more difficult to analyze with simple mathematics.

Roof design and construction

To design the roof a number of technical challenges had to be overcome:

  1. It had to be shown that the structure possessed the necessary strength and stiffness as preliminary calculations had shown that it was almost impossible to design the entire structure using common truss girders in two directions

  2. It was important that in any final roof design the first mode shapes involved not only localised deformations of the outer corners but included deformations of the whole roof structure to ensure a dynamic response of the roof within acceptable limits. 

  3. It had to be able to safely resist the large temperature differences in winter between the cantilevered part and the internal roof over the foyer.