An iterative method for the inverse elasto-static problem

This brief communication describes the use of an iterative algorithm to tackle the inverse elasto-static problem which has two important applications: identifying the required initial body shape which deforms into a desired one when subject to a given set of loads; identifying the unloaded shape of a structure from a given deformed shape and a prescribed set of loads. The iterative algorithm stems from the rather intuitive observation that a better estimate of the required initial shape can be obtained by adding a correction to the previous shape estimate equal to the computed mismatch in the deformed shapes. A detailed convergence analysis explains the reason behind the success of the proposed algorithm. Compared to other techniques described in the literature to solve such inverse problems, this iterative scheme offers the advantage of being easy to implement and readily compatible with the use of commercial solver packages. Two benchmark problems are treated to illustrate the success of the algorithm: that of a punctured membrane and that of a cantilever beam in cross flow. The latter illustrates that the concepts described here readily applies to steady fluid–structure interaction problems leading to an interesting range of new applications.