Inversion of loading time history using displacement response of composite laminates: Three-dimensional cases

Abstract

An inverse procedure is proposed to reconstruct the time history of transient loads on the surface of composite laminates from the knowledge of dynamic displacement response at only one receiving point. A hybrid numerical method (HNM) is adopted as the forward solver to compute the dynamic displacement response of composite laminates subjected to arbitrary loads. By introducing a kernel displacement function - the dynamic displacement response of composite laminates excited by a point step-impact load and the displacement response subjected to a load with an arbitrary force function are expressed in a form of convolution integral. The force history is reconstructed by employing an inversion algorithm, in which the least-squares optimization method being adopted to deconvolute the integral. Both point loads and loads with small spatial distribution are investigated and numerical verifications are given. The robustness of the procedure in the presence of noise is also investigated. Good agreements between the identified and true functions for all cases demonstrate the effectiveness of the present inverse procedure. The present inverse procedure is useful for determining impact loads on material surface using response on a point remote to the impact point.