Comparison among three boundary element methods for torsion problems: CPM, CVBEM, LEM

Abstract

This paper provides solutions for De Saint-Venant torsion problem on a beam with arbitrary and uniform cross-section. In particular three methods framed into complex analysis have been considered: Complex Polynomial Method (CPM), Complex Variable Boundary Element Method (CVBEM) and Line Element-less Method (LEM), recently proposed. CPM involves the expansion of a complex potential in Taylor series, computing the unknown coefficients by means of collocation points on the boundary. CVBEM takes advantage of Cauchy’s integral formula that returns the solution of Laplace equation when mixed boundary conditions on both real and imaginary parts of the complex potential are known. LEM introduces the expansion in the double-ended Laurent series involving harmonic polynomials, proposing an element-free weak form procedure, by imposing that the square of the net flux of the shear stress across the border is minimized with respect to the series coefficients. These methods have been compared with respect to numerical efficiency and accuracy. Numerical results have been correlated with analytical and approximate solutions that can be already found in literature.