A Numerical Solution for Viscoelastic Half Planes

The standard singular higher order transcendental functions, appearing in all the fundamental frequency domain response quantities of viscoelastic half planes, are identified and separated from the regular parts utilizing the notion of convolution algebra. The relevant mathematical properties of such logarithmic singularities have been investigated to recommend analytical differentiations and integrations in the space of distributions. Only the regular parts of the physical quantities are operated numerically. The foundation coefficients, both impedances and compliances, for the finite element analysis of soil-structure interaction problems, corresponding to any order of interpolation polynomial can be evaluated numerically using the algorithm developed here. Numerical results for the impedance coefficients and the foundation surface stress profiles associated with the finite element linear displacement field are illustrated as an example.