Analysis of Elastic Torsion in a Bar With Circular Holes by a Special Boundary Integral Method

Abstract

Special boundary integral equations developed in an earlier paper are generalized here for torsion of an elastic bar with circular holes. In this approach, the solution on the boundary of each hole is represented by a series of circular harmonics, and the coefficients in these series are determined by a special system of boundary integral equations. For a cross section with only one hole, the entire system of equations is reduced without approximation to a single integral equation involving only the warping function on the outer boundary. For multiple holes, approximate equations are derived that retain only the first harmonic in the solution representation on each hole. The latter equations are solved analytically for a circular cross section weakened by a concentric ring of circular holes. Simple expressions are derived for torsional rigidity, warping, and maximum stress. The results for torsional rigidity are an improvement over previous ones obtained by another approximate method.