Load identification for a viscoelastic solid by an accurate meshfree sensitivity analysis

This article presents a novel inverse method for identification of a space- and time-dependent load, applied to a two-dimensional viscoelastic solid. Measured strains at several points are considered as sampling quantities. An improved meshfree radial point interpolation method is employed to solve the direct problem. The inverse problem is treated by an optimization approach, where the cost function is described in terms of the differences between measured and computed strains. The damped Gauss Newton method is utilized to solve the inverse problem. A new approach for the sensitivity analysis based on direct differentiation of governing equations is presented. The Tikhonov regularization method is employed to eliminate the undesired oscillations of the solutions of the inverse problem. Using a method based on the condition number of the sensitivity matrix, an appropriate configuration for sensors is determined. The effects of the location and the number of sensors on the accuracy of the identified loads are investigated. The robustness of the presented method to handle noisy measured data is investigated too.