Warping Torsion in 3D Beam Finite Elements

Olsen, Dennis Nedergaard ; Andersen, Lynge Udengaard

4. term

Structural and Civil Engineering, Master

2015

2015-06-10

56

Dette projekt undersøger torsion—den vridning, der opstår i bjælker og aksler—ved hjælp af både analytiske metoder (ligninger) og numeriske beregninger (computermodeller). Rapporten begynder med at udlede centrale resultater fra rumlig bjælleteori, som beskriver, hvordan slanke konstruktioner opfører sig i tre dimensioner. Undersøgelsen ser på to scenarier, der afhænger af støtte- og lastbetingelser: en ensartet (homogen) torsion og en ikke-ensartet (ikke-homogen) torsion. Begge scenarier behandles analytisk. Derudover analyseres den ikke-homogene torsion numerisk med en egenudviklet MATLAB-kode, og resultaterne sammenlignes med dem fra ABAQUS, et kommercielt program til avanceret numerisk analyse. Sammenligningen bruges til at kontrollere nøjagtigheden af den egenudviklede model.

This project examines torsion—the twisting that occurs in beams and shafts—using both analytical methods (equations) and numerical calculations (computer models). The report begins by deriving key results from spatial beam theory, which describes how slender structures behave in three dimensions. The study considers two scenarios that depend on support and load conditions: a uniform (homogeneous) torsion case and a non-uniform (non-homogeneous) torsion case. Both are addressed with analytical solutions. In addition, the non-homogeneous case is analyzed numerically with a custom MATLAB code, and the results are compared with those from ABAQUS, a commercial program for advanced numerical analysis. This comparison is used to check the accuracy of the in-house model.

[This abstract was generated with the help of AI]

beam finite element ; finite element ; warping ; torsion ; vlasov torsion ; beam theory ; non-homogeneous torsion

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Andersen, Lynge Udengaard:

• Warping Torsion in 3D Beam Finite Elements (2016)