De Saint-Venant flexure-torsion problem handled by Line Element-less Method (LEM)

Abstract

In this paper, the De Saint-Venant flexure-torsion problem is developed via a technique by means of a novel complex potential function analytic in all the domain whose real and imaginary parts are related to the shear stresses. The latter feature makes the complex analysis enforceable for the shear problem. Taking full advantage of the double-ended Laurent series involving harmonic polynomials, a novel element-free weak form procedure, labelled Line Element-less Method (LEM), is introduced, imposing that the square of the net flux across the border is minimized with respect to expansion coefficients. Numerical implementation of the LEM results in systems of linear algebraic equations involving positive-definite and symmetric matrices solving only contour integrals. Some numerical applications are reported to assess not only the efficiency and accuracy of the method to handle shear stress problems but also the robustness in the sense that exact solutions when available are captured straight away.