VIRTUAL ELEMENT METHOD VS FINITE ELEMENT METHOD FOR PRANDTL’S SOLUTION OF ST. VENANT TORSION PROBLEM

Resumo

This work presents a comparison of the novel virtual element method and the traditional finite
element method for Prandtl’s solution to the St. Venant torsion problem. The solved field is the Prandtl
function for a given cross-section that experiences torsion. This function is approximated using both
methods with a collection of different meshes. These meshes vary in properties such as the element size,
geometry (Delaunay triangulations and Voronoi tessellations are employed), and polynomial order
(linear and quadratic elements). The numerical error measurement is based on the torsion constant, a
global scalar associated with the solution, with physical significance for the problem. Two different
cross-sections with analytical solutions are used as benchmarks. The results are presented in a set of
convergence curves for each cross-section geometry. The virtual element method showed more
versatility regarding element geometry, while retaining the same convergence properties of the finite
element method.