Maximum principles and bounds on stress concentration factors in the torsion of grooved shafts of revolution

Abstract

This paper provides an analytical approach for obtaining bounds for stress concentration factors in the theory of axisymmetric torsion of circumferentially grooved shafts of revolution. The analysis is based on application of maximum principles for linear second-order elliptic partial differential equations. The particular case of a straight shaft with a semi-circular groove is considered in detail. Explicit estimates are obtained and compared with existing results for this problem.

Bounds on stress concentration factors in finite anti-plane shear

“…Suppose that the body is composed of a homogeneous, isotropic, incompressible elastic , All tensor and vector components are taken with respect to the fixed rectangular coordinate system previously chosen. Greek and Latin subscripts have the respective ranges (1,2) and (1,2,3), repeated subscripts are summed, and a subscript preceded by a comma indicates partial differentiation with respect to the corresponding x-coordinate. material characterized by an elastic potential I¢ representing the strain.energy density per unit undeformed volume.…”

“…Application of a priori estimation techniques to some stress concentration problems arising in classical linear elasticity is discussed in [1][2][3]. The purpose of the present paper is to consider analogous issues in the finite theory.…”