On boundary element - transfer matrix analysis of layered systems

The chain pattern of certain elastic systems such as layered softs lends itself to be exploited in ad hoc solution procedures. A method of this kind proposed earlier (1977, 1984) combines the boundary integral approach (in its discretised, boundary element version) and the transfer matrix concept and exhibits a special appeal as for simplicity, elegance and compactness of the final reduced equation system. In this paper we analyse such BE-TM technique using mechanical interpretations and some notions of numerical analysis (primarily on matrix conditioning). The findings are as follows: outside of a relatively narrow range of geometry ratios (layer thickness over a typical discretization length) certain submatrices to invert are bound to become ill-conditioned, causing significant inaccuracies in the resulting tractions; this intrinsic limitation of applicability strongly depends on the adopted computation precision. Alternative methods, which avoid such limitation but still exploit the chain pattern, are envisaged and developed in a parallel paper