Banca de DEFESA: MARCELO VITOR OLIVEIRA ARAUJO

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
DISCENTE : MARCELO VITOR OLIVEIRA ARAUJO
DATA : 30/08/2021
HORA: 14:00
LOCAL: Link da videochamada: https://meet.google.com/men-ayxr-gsm
TÍTULO:

NEW CONTRIBUTIONS FOR THE GENERALIZED FINITE-VOLUME THEORY: FROM ENERGY ANALYSIS TOWARDS TOPOLOGY OPTIMIZATION OF COMPLIANCE MINIMIZATION PROBLEMS


PALAVRAS-CHAVES:

topology optimization; checkerboard-free designs; energy analysis; convergence analysis; energy balance; finite-volume theory; continuum elastic structures; compliance minimization.


PÁGINAS: 76
RESUMO:

The finite-volume theory is an equilibrium-based approach and has been successfully employed in solid mechanics analysis due to the equilibrium equations' local satisfaction and the imposition of continuity conditions in a surface-averaged sense through the subvolume interfaces. Previous investigations include stress and displacement fields convergence and computational cost, showing the approach's efficiency, especially in heterogeneous materials and structures. However, those investigations did not include an energy analysis, which is especially important in compliance minimization problems. As the finite element method, energy-based approaches impose energy balance, which guarantees a monotonic energy convergence. The first idea of this contribution is to address a numerical investigation about the main mechanical energy aspects involving the generalized finite-volume theory for continuum elastic structures in quasi-static analyzes. The obtained results are verified with analytical and finite element-based analyzes, showing a monotonic energy convergence for the three versions of the finite-volume theory and the energy balance's satisfaction for the higher-order versions when a sufficiently refined mesh is employed. Topology optimization is a well-suited method to establish the best material distribution inside an analysis domain. It is common to observe some numerical instabilities in its gradient-based version, such as the checkerboard pattern, mesh dependence, and local minima. This research demonstrates the generalized finite-volume theory's checkerboard-free property by performing topology optimization algorithms without filtering techniques. The formation of checkerboard regions is associated with the finite element method's displacement field assumptions, where the equilibrium and continuity conditions are satisfied through the element nodes. On the other hand, the generalized finite-volume theory satisfies the continuity conditions between common faces of adjacent subvolumes, which is more likely from the continuum mechanics point of view. The topology optimization algorithms based on the generalized finite-volume theory are performed using a mesh independent filter that regularizes the subvolume sensitivities, providing optimum topologies that avoid the mesh dependence and length scale issues. The solid isotropic material with penalization (SIMP) approach is employed to avoid discrete optimization problems. The proposed optimization problem has shown to be efficient, avoiding numerical instabilities, such as checkerboard pattern, mesh dependence, and length scale issues.


MEMBROS DA BANCA:
Interno - 1120928 - ADEILDO SOARES RAMOS JUNIOR
Externo à Instituição - ANDERSON PEREIRA - PUC - RJ
Interno - 1121260 - EDUARDO NOBRE LAGES
Externo à Instituição - EMILIO CARLOS NELLI SILVA - USP
Externo à Instituição - GLÁUCIO HERMOGENES PAULINO - Georgia Tech
Presidente - 2544065 - MARCIO ANDRE ARAUJO CAVALCANTE
Notícia cadastrada em: 25/08/2021 13:38
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