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Inverse identification of time-harmonic loads acting on thin plates using approximated Green’s functions, Inverse Problems in Science and Engineering, 2016

In this paper, a non-iterative technique is proposed for the transverse
load identification on Kirchhoff plates using approximate Green’s
functions (AGFs). In this way, we firstly employ the recently introduced
meshless method to construct the AGFs, as the combination of a
series of Trefftz basis, i.e. Exponential basis functions (EBFs), and the
fundamental solutions of the governing equation. As will be explained,
using a proper set of EBFs, as well as a collocation technique, enables
us to construct the AGFs for different types of domain shape and
boundary conditions. In the second step, a set of artificially generated
results, in the absence of realistic experimental results, are used to
express the plate’s response field, i.e. deflection or velocity fields, as
a series of AGFs through a collocation technique. It will be shown
how the constant coefficients of the response series are related to
the intensity of the reconstructed force at a set of selected points. The
proposed method is capable of constructing both distributed and
concentrated loads with desirable accuracy. This ability is shown in
the solution of three sample problems of the static and time-harmonic
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