Topology optimization employing adaptive inner-front (AIF) level set method

Abstract

A new topology optimization employing adaptive inner-front level set method is presented. In the conventional level set based topology optimization, the optimum topology strongly depends on the initial level sets due to the incapability of inner-front creation during optimization process. In the present work, in this regard, an algorithm for inner-front creation is proposed, in which the sizes, the shapes, the positions, and the number of new inner-fronts during the optimization process can be globally and consistently identified. In the algorithm, the criterion of inner-front creation for compliance minimization problem of a linear elastic structure is chosen as the strain energy density along with volumetric constraint. In order to facilitate the inner-front creation process, the inner-front creation map is constructed and used to define new level set function. In the implementation of inner-front creation algorithm, to suppress the numerical oscillation of solutions due to the sharp edges in the level set function, the domain regularization is carried out by solving the edge smoothing partial differential equation dgesmoothing PDE). In order to update the level set function during the optimization process, in the present work, the least-squares finite element method (LSFEM) is adopted. Through the LSFEM, a symmetric positive definite system matrix is constructed, and non-diffused and non-oscillatory solution for the hyperbolic PDE such as level set equation can be obtained. Two-dimensional structural topology optimization problems subjected to volume constraint are treated for verification purpose. As a real-world application, topology optimization of three-dimensional shell structures is carried out. From the numerical examples, it is shown that the present method brings in much needed flexibility in topologies during the level set based topology optimization process.