An isogeometric boundary element approach for topology optimization using the level set method

Among the various types of structural optimization, topology has been occupying a prominent place over the last decades. It is considered the most versatile because it allows structural geometry to be determined taking into account only loading and fixing constraints. This technique is extremely useful in the design phase, which requires increasingly complex computational modeling. Modern geometric modeling techniques are increasingly focused on the use of NURBS basis functions. Consequently, it seems natural that topology optimization techniques also use this basis in order to improve computational performance. In this paper, we propose a way to integrate the isogeometric boundary techniques to topology optimization through the level set function. The proposed coupling occurs by describing the normal velocity field from the level set equation as a function of the normal shape sensitivity. This process is not well behaved in general, so some regularization technique needs to be specified. Limiting to plane linear elasticity cases, the numerical investigations proposed in this study indicate that this type of coupling allows to obtain results congruent with the current literature. Moreover, the additional computational costs are small compared to classical techniques, which makes their advantage for optimization purposes evident, particularly for boundary element method practitioners.