The Boundary Integral Equation Method for Torsion of an Inhomogeneous Variable Diameter Shaft

Abstract

A Boundary Integral Equation (BIE) formulation is developed which is capable of analyzing the torsion of a variable diameter shaft with an axisymmetric shear modulus in a particular form. The governing differential equation for this problem is the equation of the Generalized Bi-axially Symmetric Potential Theory (GBSPT), and its fundamental solution can be obtained by considering the "ring of potential". Piecewise-quadratic shape functions are used for the approximations of the functions and the boundary. Gaussian quadrature with four Gaussian points are used for the numerical integration.

Stress concentration problems for the homogeneous U-grooved shaft, fillet shoulder shaft and the inhomogeneous U-grooved shaft with an axial hole are examined. Possible future studies are suggested.