DETERMINING A FORCE ACTING ON A PLATE - AN INVERSE PROBLEM

It is traditional in the study of elasticity to determine the response of a structure to a known force. Such problems may be described as direct problems as they involve the determination of the unknown effects of a known cause. The problem of determining the force acting on a structure from measurements of the response of the structure to the force is the inverse problem. Presented here is a method for determining the location and magnitude of a static point force acting on a simply-supported elastic rectangular plate from a number of displacement readings at discrete points on the plate. This problem reduces to a nonlinear least-squares one. It is solved by calculating an approximate solution from a simplified set of equations that is then used as an initial estimate in an iterative procedure for a solution of the actual nonlinear least-squares problem. Results of numerical simulations illustrate the use of the method, and a confidence criterion is supplied. Presented also is a demonstration of the robustness of the algorithm to the effects of measurement noise, as well as a means by which the method may be extended to problems of a more general nature.