Determination of centers of flexure using the boundary element method

Abstract

The center of flexure of a beam of an arbitrary cross-section can be shown to be given in terms of two harmonic functions which satisfy Neumann type boundary conditions. The problem is thus suitable for solution by the boundary element method. It is shown that the determination of the center of flexure can be carried out without resorting to area integrals once the values of the two harmonic functions on the boundary are known. Numerical examples are given for: semi-circular ring sections; an equilateral triangular section; and a right triangular section.