Inverse Shape Design of Deformable Structures and Deformable Wings

Abstract

Inverse methods are mathematical techniques by which the unknown input of a system is determined from a known or desired output. In this article, a new inverse method for the reverse design of deformable structures is presented. The inverse problem being addressed is the construction of the initial or unloaded shape of an structure such, when deformed under given loads, will acquire a desired pre-defined shape. The method can be used, among several other applications, for the inverse design of deformable airplane wings. For example, given a aerodynamically desired wing geometry, the method can be used to determine the real wing geometry that needs to be manufactured so that when such real wing deforms during flight under the influence of aerodynamic forces, it will naturally acquire the desired aerodynamic configuration. The presented inverse method is based on a novel and general approach which can be used with any structure made of hyperelastic materials. The inverse formulation is derived straightforwardly from the mathematical equations defining the standard direct approach of computational solid mechanics. On the computational side, this means that an inverse shape design code can be developed by making simple changes on an existing direct-analysis code.