Dynamisk programvara för visualisering av vridna prismatiska balkar med öppna tunnväggiga tvärsnitt

Reportedly in Swedish schools, there is no long tradition of investigative and laboratory work in the mathematics subject. Dynamic software is a term which encapsulates the purpose of software as a pedagogical instrument in teaching. There is great potential in this but also a need for teachers to engage and apply themselves to the new possibilities. Computer software in class does not automatically generate good results. As an example of how software can be developed in Python to aid in the learning of torsional beam theory, a user-friendly application is developed for 3D visualisation of a twisted beam element and for the determination of the maximal cross-sectional tensions and rotations. The software can e.g. be used by a student of mechanics as a pedagogical instrument, seeing as the theory itself is rather complex, in particular when it comes to warping constraints. Forming a base for the software are a number of open source Python bindings and modules: Visvis, NumPy, PyCALFEM and PyQt. The visualized beam element can be rotated, moved around and panned in the GUI with simple mouse clicks and keyboard actions. The 3D shape of the beam element is calculated with the FEM. Three types of open, thin-walled cross sections are available to the user: simply symmetrical I-profiles, symmetrical U-profiles with partially constant wall thickness and polar symmetrical Z-profiles with partially constant wall thickness. The material is modelled as linear elastic and the beam is either 1) freely supported with forks in each end or 2) fully fixed in each end or 3) a console. The maximal cross sectional tensions and rotations are further calculated according to St Venant’s and Vlasov’s beam theory and solutions to these are approximated with the FEM. The application is free to use for educational purposes.