In geographical terms, the Nordic countries are slightly isolated from the Continent and Europe.

If you drew a line through southern Denmark and along the same latitude all the way around the globe, the Nordic countries would be the most densely populated region north of the line. The Gulf Stream is what has made it possible for Scandinavians to live as far north and in such numbers as we do.

The extraordinary variety of changing light scenes here is unparalleled in the rest of Europe, and is something that we feel intensely and closely. While the bright summer nights of June may seem endless, we also know that light will be in short supply in winter. Daylight is a precious thing, but it is a lack we all experience. Daylight brings people together. If we do not have enough daylight, we feel cheated and robbed. Our working routines mean that in winter we rarely spend time out of doors. This is the reason why daylight plays such an important role in our architecture and lifestyle, and why we are among the few countries in the world where daylight requirements are written into the official building regulations.We demand daylight in all contexts, and particularly in our buildings. But Scandinavians are not afraid of the dark. We don’t have dark and gloomy corners here in the Nordic countries – we have areas especially well-suited to star-gazing! Compared with other prosperous parts of the world, Scandinavians still live in a society where there is no tradition of using lighting to monitor or create security for citizens. Enjoyment and relaxation are also associated with subdued lighting, and we just “looove” to light candles and create a cosy atmosphere, “pools of light”, warmth and security!

Software for structural analysis has been mainstream for decades, and the “New Features“ list grows for every new release. But one feature remains absent from these lists – the ability to perform limit state analysis of reinforced concrete structures. Why is that? You might find the answer in the headline of this post – See it?

If not, then try and let me explain – In order to solve structural problems commercial software products today implement an elastic finite element model. If we take a look under the hood of these applications we might get closer to the answer. When passed a problem (mesh data, material data, boundary condition etc.) the software assembles a system of equation based on the problem data. A neat feature of these equations is that the number of equations matches the number of variables. When proposed in matrix form, this gives a square matrix which can easily be solved using standard algorithms and provides one unique solution for a given problem.

Unfortunately, this approach is not suitable when dealing with limit state analysis of reinforced concrete structures. Extensive research has shown that rigid plastic models are very good in their prediction of the ultimate load bearing capacity of such structures. So why is this model not implemented in the commercial products we use today? Well, when casting problems using the rigid plastic model, the square matrix from the elastic formulation is replaced with a rectangular matrix which contains more variables then equations. This problem cannot be solved using the standard methods, because no unique solution exists, which leads to some interesting optimization problems. Advanced algorithms are required to solve these optimization problems. Techniques for solving these problems has not been developed to the same extend as ‘regular’ methods, which might probably is the reason that these methods have not yet been implemented in commercial product.

In September 2007, Rambøll and The Danish University of Technology (DTU) launched a new research project aiming at refining existing and develop new methods for implementing rigid plastic models in commercial applications using general finite element formulations and specialized optimization software.