Warping Torsion in 3D Beam Finite Elements

Hvælvingsvridning i 3D Bjælke Elementer

Andersen, Lynge Udengaard

4. term

Structural and Civil Engineering, Master

2016

93

This thesis investigates torsion with cross‑sectional warping in 3D beam finite elements using both analytical and numerical approaches. It first establishes the theoretical foundation of spatial beam theory, including equilibrium, kinematic and constitutive relations, and presents analytical solutions for homogeneous torsion (St. Venant) and non‑homogeneous torsion (Vlasov), with emphasis on open thin‑walled sections such as I/H profiles. Building on this, a finite element formulation is developed from the principle of virtual displacements, including shape functions and stiffness matrices, and a seventh degree of freedom is introduced to represent warping. Non‑homogeneous torsion is then analyzed numerically in a custom Matlab code and compared against results from the commercial software ABAQUS to verify the implementation. The excerpt does not report detailed numerical findings, focusing instead on theory, formulation, and the validation setup.

Specialet undersøger vridning med tværsnitsforvridning (warping) i 3D bjælkefinitelementer gennem både analytiske og numeriske studier. Arbejdet opstiller først det teoretiske grundlag i rumlig bjælketeori med ligevægts-, kinematiske og konstitutive relationer og giver analytiske løsninger for både homogen torsion (St. Venant) og ikke-homogen torsion (Vlasov) for især åbne tyndvæggede tværsnit som I/H-profiler. På denne baggrund udvikles en finite element‑formulering baseret på princippet om virtuelle forskydninger, herunder formfunktioner og stivhedsmatricer, og der indføres en 7. frihedsgrad til at beskrive tværsnittets warping. Den ikke‑homogene torsion analyseres numerisk i en egenudviklet Matlab-kode, og resultaterne sammenlignes med beregninger fra den kommercielle software ABAQUS med henblik på verifikation af modellen. Uddraget indeholder ikke detaljerede resultater, men fokuserer på teori, formulering og sammenligningsrammen.

[This apstract has been generated with the help of AI directly from the project full text]

Hvælving ; Bunden vridning ; Ikke-homogen vridning

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Andersen, Lynge Udengaard:

• Warping Torsion in 3D Beam Finite Elements (2015)