A BEM approach to the evaluation of warping functions in the Saint Venant theory

The paper illustrates the numerical procedure, based upon a Boundary Element (BE) approach, developed to efficiently evaluate the warping functions in the Saint Venant theory of beam-like solids having both compact and thin-walled sections. Specifically, Chebyshev nodes are selected as collocation points of the BE formulation associated with the relevant pure Neumann problem and the entries of the resulting linear system of equations are evaluated analytically by invoking recursive formulas. Assuming a polynomial interpolation for the unknown function over each boundary element, we show that a reduction in the numerical accuracy of the solution is achieved if the polynomial degree exceeds a given order strictly related to the strategy adopted to discretize the boundary. For this reason, in order to automatically cope both with compact and thin-walled domains, a general criterion has been established for properly selecting the best combination of polynomial degree and edge discretization capable of reducing the numerical error of the procedure below a given tolerance.