Inverse Determination of Time-Dependent Loads in Viscoplastic Deformations Using Strain Measurements in the Deformed Configuration

Abstract

Load identification by inverse analysis has been investigated extensively in many elastic studies; however, very few studies on inverse load identification in plastic and especially viscoplastic deformations have been reported until now. In this paper, a new inverse method for identification of time-dependent loads in viscoplastic deformations is presented. It is assumed that the general form for variation of the load with respect to time is known; however, the prescribed load–time model includes some parameters, which should be found by an inverse analysis. These unknowns are determined without any measurements during the loading process. In dead, the inverse analysis is carried out using measured strains at some sampling points only in the deformed configuration. In the inverse analysis, the well-known damped Gauss–Newton method has been used to get the optimization direction and the Armijo’s rule is employed to select a suitable step size. To demonstrate the performance of the method, several numerical examples are presented. The effects of the number of sensors, and measurements errors on the inverse solutions are investigated too.