Advanced Metaheruistic Optimization Algorithms for Inverse Problems in Elasticity

Any inverse problem in Elasticity can be stated as an optimization problem where the goal is to minimize the difference between some target quantity that is representative of the structural response and its counterpart computed by means of finite element analysis. By comparing target quantities measured experimentally with finite element predictions, an error functional corresponding to the difference between experimental data and numerical predictions can be defined. This error functional depends on the unknown properties and must be minimized in order to identify mechanical behavior of the material/structure under investigation. Since inverse elasticity problems often are transformed into highly nonlinear and non-convex optimization problems, global optimization algorithms should be used for solving the identification problem. Global optimization algorithms search the optimum solution by generating randomly a certain number of trial designs. This is done in purpose to expand the portion of design space explored by the optimizer thus increasing the probability of finding the global optimum without getting stuck in local optima. To improve computational efficiency, meta-heuristic optimization algorithms perform the random search by following some principle inspired to physics, biology, astronomy, music, social sciences, etc. Hybridization of meta-heuristic algorithms with line-search strategies or infrequent gradient calculation may further increase computational efficiency. This chapter presents advanced formulations of three state-of-the-art meta-heuristic optimization algorithms: Simulated Annealing, Harmony Search and Big Bang-Big Crunch. The basic formulation of each algorithm currently available in literature is modified by introducing more efficient search mechanisms that allow to achieve substantial reductions in the number of structural analyses entailed by the identification process. Three inverse elasticity problems taken from literature are solved with the above mentioned meta-heuristic algorithms to check the effectiveness of the new formulations: (i) to determine the orthotropic elastic constants of an 8-ply woven-reinforced fiberglass-epoxy composite laminate utilized as substrate for printed circuit boards; (ii) to determine the orthotropic elastic properties and fiber orientations of a composite laminate for aeronautical use; (iii) to determine hyperelastic properties of a biological membrane (i.e. bovine pericardium patch) subject to inflation test. The new optimization algorithms developed in this research always converge to the expected solution and are significantly faster than literature formulations and commercial software.