Banca de DEFESA: MARCELO VITOR OLIVEIRA ARAUJO

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
DISCENTE : MARCELO VITOR OLIVEIRA ARAUJO
DATA : 15/08/2022
HORA: 13:30
LOCAL: Link da videochamada: https://us02web.zoom.us/j/84374165920?pwd=UzBrY0pTN0hKTWMzNmFqNkd5d2FPQT09
TÍTULO:

ENERGY ANALYSIS OF THE GENERALIZED FINITE-VOLUME THEORY AND APPLICATION TO TOPOLOGY OPTIMIZATION WITH COMPLIANCE MINIMIZATION

PALAVRAS-CHAVES:

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

PÁGINAS: 122
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 finite-volume theory's checkerboard-free property by performing topology optimization algorithms without filtering techniques and employing elastic and elastoplastic formulations. The formation of checkerboard regions is directly associated with discretized domains connected by nodes, usually observed in topology optimization techniques based on the finite element method. On the other hand, the finite-volume theory satisfies the continuity conditions between common faces of adjacent subvolumes, which is more likely from the continuum mechanics point of view. An incremental elastoplastic formulation of the standard finite-volume theory is performed to verify how the plastic strain could interfere with the optimized topologies and reduce their stress concentration. The topology optimization algorithms based on the finite-volume theory are also performed using a mesh independent filter that regularizes the subvolume sensitivities, providing optimized 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:
Presidente - 2544065 - MARCIO ANDRE ARAUJO CAVALCANTE
Interno - 072.485.254-99 - DAVID LEONARDO NASCIMENTO DE FIGUEIREDO AMORIM - UFS
Interno - 1121260 - EDUARDO NOBRE LAGES
Interno - 1545555 - FRANCISCO PATRICK ARAUJO ALMEIDA
Externo ao Programa - 1837162 - ROMILDO DOS SANTOS ESCARPINI FILHO
Externo à Instituição - VALÉRIO DA SILVA ALMEIDA