A new calculation method designed to secure the critical parts and stress concentrations of concrete structures
With the method, computational resources are automatically allocated to the stress concentrations related to the critical parts of the structures. “The calculation method is ideal for the analysis of large span concrete structures, for instance. Such structures include, for example, the intermediate floor slabs of buildings, bridge decks and water towers,” says Professor Antti H. Niemi from the University of Oulu.
The main objective of structural design is to dimension load-bearing structures so that the likelihood of collapse or undergoing significant deformations that lead to loss of load-bearing capacity is adequately low. The areas where the stresses, meaning the internal forces within the structure, are largest are the most susceptible to damage. Such stress concentrations occur, for example, in the vicinity of holes, sharp corners, and concentrated loads or near other sudden changes in the geometry of the structure or the properties of the material, for instance.
Reliable verification of the load-bearing capacity of a structure requires that all local stress concentrations are known accurately, which in turn requires significant computational resources.
The developed discontinuous Petrov-Galerkin method (DPG) is very flexible, and it can be considered both a minimum residual (MINRES) and a least squares (LS) method. These features allow for efficient error control and algorithmic performance. Advanced theories of variational calculus and partial differential equations have been applied in the design of the method.
The study is linked to the research of structural mechanics performed at the Civil Engineering Research Unit of the University of Oulu, and it benefits also other areas of engineering that use structural analysis. Learn more at the research unit’s website.
An article about the study was published in the Numerische Mathematik journal.
Research article: Führer, T., Heuer, N. & Niemi, A.H. A DPG method for shallow shells. Numer. Math. 152, 67–99 (2022). https://doi.org/10.1007/s00211-022-01308-w
The research has been funded by Oulun rakennustekniikan säätiö, Ruth och Nils-Erik Stenbäcks stiftelse, and the Faculty of Technology at the University of Oulu. The results were presented at a conference at the Pontifical Catholic University of Chile in Santiago: Minimum Residual & Least-Squares Finite Element Methods Workshop.