TOPOLOGY OPTIMIZATION OF CONTINUUM ELASTIC STRUCTURES EMPLOYING THE FINITE-VOLUME THEORY AND THE EVOLUTIONARY STRUCTURAL OPTIMIZATION METHOD

Resumo

In this paper, an original approach that combines Finite-Volume Theory (FVT) and Evolutionary
Structural Optimization (ESO) is presented. ESO is based on the simple idea that the optimal structure can be
delivered by gradually removing the ineffectively used material from the design domain. Through this procedure,
the resulting structure will evolve towards its optimal shape and topology. In theory, one cannot guarantee that
such an evolutionary procedure would always generate the best solution. However, the ESO technique provides a
useful way for designers to explore forms and shapes of structures during the conceptual design stage. In literature,
it is frequent that the design domain is constructed aiming at a Finite Element Analysis (FEA). However, some
problems are related to numerical issues, such as the checkerboard pattern and mesh dependence. The checkboard
effect is related to the assumptions of the finite element method, as the satisfaction of equilibrium and continuity
conditions in the element nodes. FVT overcomes this problem because it satisfies the equilibrium equations at the
subvolume level and the compatibility conditions are established through the adjacent subvolume interfaces, as
expected from the continuum mechanics point of view. Some ESO’s classical problems are investigated to
compare FVT and FEA results.