The Displacement Discontinuity Method

The displacement discontinuity method can be regarded as the extension to elasticity of the boundary element method discussed in Chap. 1 for a constant strength dipole source D along a straight line segment in an infinite homogeneous region. Now, however, the source is a displacement discontinuity vector with components \(D_{x}\) and \(D_{y}\) , 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 displacement 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 displacement 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 double layer potential for elasticity.