Mass minimization with conflicting dynamic constraints by topology optimization using sequential integer programming

Abstract

In this paper mass minimization of hysteretically damped structures subjected to static and time-harmonic loading is studied via the Topology Optimization of Binary Structures (TOBS) method. Elements are removed or added to the finite element model of a structure in every iteration based on the solution to an integer linear program (ILP). The ILP is constructed from the sensitivity information of the objective function and the constraints which are in the form of the static and dynamic compliance. The proposed methodology is demonstrated on a 2D clamped–clamped beam and compared with published results for a 2D cantilever beam. The optimization starts from the full design domain and solutions with low mass that fulfill the constraints for a range of different bounds are found. The results also indicate that the mass is much more sensitive to changes in the static compliance constraint than in the dynamic compliance constraint. The effect of mass and upper bound of the constraints on the dynamic compliance at the fundamental resonance frequency is also studied, though no clear conclusions can be drawn. Finally the sensitivity information at the converged topology is studied and it is shown that the algorithm converges because the structural regions that are non-critical for the different constraints do not overlap. • The TOBS method is used to solve forced vibration problems. • Tightening the dynamic compliance constraint forces a change in topology. • At optimality, non-critical areas for different constraints lack overlap. • Minimum mass is more sensitive to static compliance constraints than dynamic.