A finite element based methodology for inverse problem of determining contact forces using measured displacements.

摘要

The identification of unknown contact or applied forces on a solid body or structure is a special case of a general class of inverse problems. This problem becomes very complicated especially when there is insufficient boundary information in the region where the unknown forces are to be identified. For example, in the contact problem, the deformation or displacement of the contact zone is generally obscured and unknown. In this paper, the unknown loads or contact forces are identified by minimizing an objective function derived as the L2-norm of the differences between the measurements and the numerical results from the finite element method. A detail description of the formulation, analysis and solution of the inverse problems are provided. The influence of the amount of measurements and their locations on the results is examined and the applications for the method are also discussed.;Theoretically, the unknown contact forces can be quantified accurately from the measured data through the above method. However, in practice this process may yield erratic errors in the derived solution because of the measurement deficiency that cannot be eliminated. To reduce the influence of the measurement error, two kinds of regularization techniques (Tikhonov-Phillips method and iterative method) are used. Several numerical examples were chosen to demonstrate the applicability of the proposed method to identify the unknown forces from the measurements at points on the boundary.