Green’s Functions for Dissimilar or Homogeneous Materials Containing Interfacial Crack, Under Axisymmetric Singular Loading Sources

Abstract

A review of Green's functions for dissimilar or homogeneous elastic space containing penny-shaped or annular interfacial cracks under singular ring-shaped loading sources is presented. The solutions are based on fictitious singular loading sources and superposition of the fundamental solutions of the following two problems: (a) Dissimilar elastic solid without crack under singular source, and (b) Dissimilar elastic solid containing crack under surface tractions. The above Green's functions have the following advantages: (i) No multi-region BE modeling for the dissimilar material is necessary, and (ii) No discretization of the crack surface is necessary. Numerical examples are presented and discussed.

Seabed Dynamic Response of Offshore Wind Turbine Foundation under Vertical Harmonic Loading: An Analytic Solution

“…A fundamental contact mechanics solution based on Green's functions and boundary integral equation solution has been achieved in [8] for the stress analysis of the soil-foundation interaction under static torsion. Analytical solutions for dissimilar or homogeneous elastic medium (space and half-space) containing interfacial cracks, under axial, radial, and torsional loading sources are provided in [9][10][11][12][13][14][15][16]. Using double integral transforms, the dual integral equations for wave propagation of a cracked medium under transient dynamic loading are originally solved in [17].…”