The Stress Discontinuity Method

The stress discontinuity method can be regarded as the extension to elasticity of the boundary element method discussed in Chap.  1  for a constant strength simple source P along a straight line segment in an infinite homogeneous region. Now, however, the source is a stress discontinuity vector with components \(P_{x}\) and \(P_{y}\) , and superposition of N such sources along a boundary S leads to a system of 2N algebraic equations in 2N unknowns. Details are provided for obtaining the influence coefficients for the stress discontinuity elements for both isotropic and anisotropic (orthotropic) materials, and several examples are worked to demonstrate the accuracy of the approach. An extension of the basic method for higher order elements (piecewise quadratic variation of the stress discontinuities along the elements) is given, and it is shown that the basic method is equivalent to a numerical approximation of the boundary integral representation of the analogue of the single layer potential for elasticity. Because the stress discontinuities \(P_{x}\) and \(P_{y}\) are not in general physically meaningful the stress discontinuity method is an indirect method.