Asymptotic expansions for efficient and accurate numerical evaluation of integral transforms

Analyses of practical engineering problems often require the repeated evalu ation of semi-infinite integral transforms whereby a single variable is cha nged incrementally through a large range of values. Common examples include time-history analyses of dynamical systems, and fatigue analyses of solid bodies, In such situations, any savings in the time required to evaluate th e integral once could amount to substantial savings in the time required to perform the overall analysis. Usually these integrals are evaluated numeri cally from zero to some number that is deemed sufficiently large to capture most of the value of the integral: the: larger the value, the more accurat e the integration. An alternative approach is presented herein which enhanc es both the efficiency and accuracy of evaluating such integrals by approxi mating the tail of the integrand by its first-order asymptotic expansion. T he method is presented in the context of determining the static stresses wi thin the two-layered elastic half-plane subjected to normal and tangential Hertzian contact tractions, With the aid of Fourier transforms, analytic ex pressions are derived for the displacement, strain and stress functions in the frequency domain. Detailed stress distributions beneath the contact pat ch are computed using the proposed method. Copyright (C) 1999 John Wiley & Sons, Ltd.