Filtering structures out of ground structures – a discrete filtering tool for structural design optimization

This paper presents an efficient scheme to filter structures out of ground structures, which is implemented using a nested elastic formulation for compliance minimization. The approach uses physical variables and allows control of the minimum ratio between the minimum and maximum areas in the final topology. It leads to a singular problem which is solved using a Tikhonov regularization on the structural problem (rather than on the optimization problem). The filter allows a multiple choice solution in which the user can control the global equilibrium residual in the final structural topology and limit variations of the objective function between consecutive iterations (e.g., compliance). As a result, an unambiguous discrete solution is obtained where all the bars that belong to the topology have well-defined finite areas. This filter feature, with explicit control of member areas, allows the user (e.g., engineer or architect) to play with different alternatives prior to selecting a specific structural configuration. Examples are provided to illustrate the properties of the present approach and the fact that the technique does not always lead to a fully stressed design. The method is efficient in the sense that the finite element solution is computed on the filtered structure (reduced order model) rather than on the full ground structure.