In active control of structures, it may be necessary to determine real-time displacements from measured deformations. Recently an inverse finite element method, iFEM, has been proposed to recover ‘small’ displacement fields for plate and shell structures from (small) strain measurements. A procedure to handle large displacements and nonlinear strains is presented in this paper. A similar least-squares error functional as in linear iFEM is used, but the linear strains are replaced with the Green-Lagrange strains, and a ‘total Lagrangian’ formulation is developed. As in the linear iFEM, the focus is again principally towards plate and shell structures. The functional is minimized with the finite element method. The nonlinear iFEM formulation is presented in detail and applied to a cantilever beam undergoing very large displacements. The relatively simple example is used to explore the formulation’s performance to recover large displacements. The results indicate that the approach is able to recover the large displacement field. Additional work is required to develop the method for practical application.
Modelling of heat generation in linear friction welding using a small strain finite element method
