Selective finite element refinement in torsional problems based on the membrane analogy

This work presents a selective finite element refinement strategy based on the h-refinement type, in the context of a posteriori error estimates considerations (error computed after the application of the proposed refining scheme), based on a graphical procedure to determine progressively better estimates for the maximum shearing stress in prismatic torsional members. It is structured in an integrated FORTRAN code and DELPHI based environment to refine an initial arbitrary finite element mesh. The proposed procedure is founded on the membrane analogy that exists between membrane deflections and the torsion problem in the sense that the location of the membrane largest gradient drives the refining procedure. It is shown that multiple level application of the proposed method to two members with different cross sectional geometries with known analytic solutions leads to progressively more accurate estimates (< 1.0% error in most cases) for the maximum shearing stresses calculations. Finally, the proposed method is applied to the torsional analysis of an L section member, showing that for this practical case the procedure results in a very accurate calculation as well.