Abstract
This study presents a hybrid framework for mechanical identification of materials and structures. The inverse problem is solved by combining experimental measurements performed by optical methods and non-linear optimization using metaheuristic algorithms. In particular, we develop three advanced formulations of Simulated Annealing (SA), Harmony Search (HS) and Big Bang-Big Crunch (BBBC) including enhanced approximate line search and computationally cheap gradient evaluation strategies. The rationale behind the new algorithms—denoted as Hybrid Fast Simulated Annealing (HFSA), Hybrid Fast Harmony Search (HFHS) and Hybrid Fast Big Bang-Big Crunch (HFBBBC)—is to generate high quality trial designs lying on a properly selected set of descent directions. Besides hybridizing SA/HS/BBBC metaheuristic search engines with gradient information and approximate line search, HS and BBBC are also hybridized with an enhanced 1-D probabilistic search derived from SA. The results obtained in three inverse problems regarding composite and transversely isotropic hyperelastic materials/structures with up to 17 unknown properties clearly demonstrate the validity of the proposed approach, which allows to significantly reduce the number of structural analyses with respect to previous SA/HS/BBBC formulations and improves robustness of metaheuristic search engines.
Highlights
Introduction and Theoretical BackgroundAn important type of inverse problems is to identify material properties involved in constitutive equations or stiffness properties that drive the mechanical response to applied loads.Since displacements represent the direct solution of the general mechanics problem for a body subject to some loads and kinematic constraints, the inverse solution of the problem is to identify structural properties corresponding to a given displacement field {u(x, y, z), v(x, y, z), w(x, y, z)}
The Hybrid Fast Simulated Annealing (HFSA), Hybrid Fast Harmony Search (HFHS) and Hybrid Fast Big Bang-Big Crunch (HFBBBC) algorithms developed in this study for mechanical identification problems were tested on two composite structures and a hyperelastic biological membrane
They were compared with other simulated annealing (SA)/HS/BBBC variants (e.g., [77,81,83,84] and their successive enhancements [162,163,164,165,166]) including gradient information in the optimization search, as well as with adaptive harmony search [170,171], big bang-big crunch with upper bound strategy (BBBC-UBS) [172], JAYA [35], MATLAB Sequential Quadratic Programming (MATLAB-SQP) [173] and ANSYS built-in optimization routines [174]
Summary
An important type of inverse problems is to identify material properties involved in constitutive equations or stiffness properties that drive the mechanical response to applied loads. Lamberti et al attempted to improve the convergence speed of SA (e.g., [77,81,83,84,162,163]), HS (e.g., [164,165,166]) and BBBC (e.g., [165,166]) in inverse and structural optimization problems While these SA/HS/BBBC variants clearly outperformed referenced algorithms in weight minimization of skeletal structures, improvements in computational cost were less significant for inverse problems as those variants evaluated gradients of error functional Ω using a “brute-force” approach based on finite differences. This occurred in spite of having enriched metaheuristic search with gradient information.
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