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| Author(s): |
Daniel Candeloro Cunha
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Mecânica |
| Defense date: | 2023-12-01 |
| Examining board members: |
Renato Pavanello;
Emilio Carlos Nelli Silva;
Renato Picelli Sanches;
José Roberto de França Arruda;
William Martins Vicente
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| Advisor: | Renato Pavanello |
| Abstract | |
Inverse homogenization problems can be numerically solved to develop metamaterials: artificial materials that can have uncommon properties, according to their microstructures. Considering periodic metamaterials, topology optimization methods may be used to obtain microstructures that yield desired effective properties. In this work, the periodic cell that defines the microstructure is hexagonal and it has dihedral D3 symmetry, which ensures isotropic homogenized properties. The considered problem is to design metamaterials with prescribed Poisson ratios and minimal values for Young’s modulus. Discrete topology optimization methods are used. The problems are approached through sequential integer linear programming. The main task of this approach is the linearization of the functions of binary variables, referred to as sensitivity analysis. In most works, this procedure is performed through a continuous relaxation of the functions, which are then linearized by first-order truncation of their Taylor series. This results in a procedure with relatively low computational costs, in which sensitivity expressions developed for continuous methods can be reused. However, when such relaxation is not rigorously performed, the linearization errors may be too high, affecting the effectiveness and stability of the optimization. In this thesis, systematic sensitivity analyses that are suitable for discrete methods are proposed. The usual expressions are obtained as particular cases, less accurate, of the developed approach, referred to as "Conjugate Gradient Sensitivity". This approach does not require continuous relaxations and it provides a sequence of expressions with increasing accuracy for the sensitivity values. Expressions were developed for the case of mechanical compliance minimization, then, they were extended to the case of designing isotropic metamaterials. Furthermore, it is proposed to use artificial neural networks to estimate the exact sensitivity values from the approximated values obtained by the proposed approach. To develop these networks, extensive datasets were generated. The codes used to generate the data have been made available in public GitHub repositories. By making them available, other researchers who work with topology optimization methods assisted by machine learning can benefit from these datasets. The proposed networks were trained and their performances were evaluated in test datasets. Generalization capabilities with respect to mesh refinement were also evaluated for each trained network. Lastly, the finite variation sensitivity analysis assisted by artificial neural networks was used to design metamaterials under realistic settings. Promising results were obtained. The developed networks successfully provided more accurate sensitivity values and, by using these improved sensitivity values, the optimization procedures became more effective and stable. Relevant contributions were made to this underexplored field, of sensitivity analysis for discrete optimization methods, and to the even less explored field, of using machine learning techniques to improve such analyses. A formal definition of the sensitivity analysis was presented for sequential integer linear programming approaches, novel sensitivity expressions were described, extensive datasets were generated, artificial neural networks were developed and many numerical examples were exhibited to illustrate each contribution. After discussing each result and drawing conclusions, some pertinent topics for future work are presented (AU) | |
| FAPESP's process: | 19/19237-7 - Exploring the potentialities of artificial neural networks on metamaterials topological design |
| Grantee: | Daniel Candeloro Cunha |
| Support Opportunities: | Scholarships in Brazil - Doctorate |