Inverse Equivalent Elastic and Viscoelastic Loading Problems - Analytical and Computational Simulations of Experiments

Analytical protocols are presented for the determination of experimentally realizable relatively "simple" loading functions, consisting of concentrated loads that mimic actual quasistatic and/or dynamic more complicated loadings, to produce similar nearly equal equivalent deflection patterns. These computational simulations in essence represent a series of virtual experiments. Two protocols are formulated for the determination of equivalent loads. The first consists of "lumped loads" and in the second, Galerkin's method is used to determine the system of equivalent concentrated loads. The accuracy of the protocol is examined and shown that the simulation error can be made negligible with a manageable finite number of equivalent concentrated loads.