Efficient Level Set Algorithm for Topology Optimization

Abstract

In this paper, we consider the spectral level set methodology for the performance enhancement of multidisciplinary design tools. This methodology formulates topology optimization problems, which may integrate the large-scale design, using less design variables than traditional techniques, thus suggesting the possibility of providing a faster solution. The fundamental problem in structural topology optimization is the determination of an optimal layout of material. The topological approach admits the structure is a set whose topology can be changed during the optimization procedure. Consequently, breakages and merges of the set may occur, and holes may appear or disappear during the search for an optimal structure. According to the level set methods, the boundary of the set is an interface defined as the zero level set of a function. The spectral level set methodology expands this function into a truncated Fourier series, and considers the Fourier coecients as design variables. The paper focus on improving the eciency of the proposed methodology and its coupling with optimization algorithms. In particular, we take steps towards making its implementation independent of the previous experience of the designer and parameter tuning. We also adopt an optimization algorithm which uses quadratic instead of linear approximations to the objective and constraints functions. To evaluate the new strategy, we determine the layout of active actuators operating on a morphing airfoil to produce optimal flight characteristics.