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DISCENTE : MARCELO VITOR OLIVEIRA ARAUJO

DATA : 01/04/2021

HORA: 14:00

LOCAL: Videoconferência no Aplicativo ZOOM

TÍTULO:

TOPOLOGY OPTIMIZATION BASED ON THE FINITE-VOLUME THEORY: ENERGY AND STRESS-BASED APPROACHES

PALAVRAS-CHAVES:

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

PÁGINAS: 77

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. This contribution also addresses a new topology optimization technique, where the objective is to minimize the maximal von Mises stress, employing a p-norm parameter that approximates the maximum values of this function, subject to a volume constraint based on the standard finite-volume theory for elastic stress analysis. 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, including when a non-filtering technique is employed. In the absence of filtering techniques, the proposed approach has shown efficiency by optimizing the obtained values for compliance and maximum von Mises stress estimations in the structure and obtaining well-defined “black and white” designs.

MEMBROS DA BANCA:

Presidente - 2544065 - MARCIO ANDRE ARAUJO CAVALCANTE

Interno - 1120064 - SEVERINO PEREIRA CAVALCANTI MARQUES

Interno - 1121260 - EDUARDO NOBRE LAGES

Interno - 1120928 - ADEILDO SOARES RAMOS JUNIOR

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