On computing the forces from the noisy displacement data of an elastic body

This Study is concerned with the accurate computation of the unknown forces applied on the boundary of an elastic body using its measured displacement data with noise. Vision-based minimally intrusive force-sensing using elastically deformable grasping tools is the motivation for undertaking this problem. Since this problem involves incomplete and inconsistent displacement/force of ail elastic body, it leads to an ill-posed problem known as Cauchy's problem in elasticity. Vision-based displacement measurement necessitates large displacements of the elastic body for reasonable accuracy. Therefore, We use geometrically non-linear modelling of the elastic body, which was not considered by others who attempted to solve Cauchy's elasticity problem before. We present two methods to solve the problem. The first method uses the pseudo-inverse of an over-constrained system of equations. This method is shown to be not effective when the noise in the measured displacement data is high. We attribute this to the appearance of spurious forces at regions where there should not be any forces. The second method focuses on minimizing the spurious forces by varying the measured displacements within the known accuracy of the measurement technique. Both continuum and frame elements are used in the finite element modelling of the elastic bodies considered in the numerical examples. The performance of the two methods is compared using seven numerical examples, all of which show that the second method estimates the forces with an error that is not more than the noise in the measured displacements. An experiment was also conducted to demonstrate the effectiveness of the second method in accurately estimating the applied forces