A critical analysis of using the dynamic compliance as objective function in topology optimization of one-material structures considering steady-state forced vibration problems

Abstract

Material based models for topology optimization in harmonic vibration problems present some inconveniences, especially when the goal is to obtain low vibration monolithic structures for excitation frequencies above the first resonance of the initial design. In this article, the authors study the choice of the vibrational performance function to be minimized. It is shown that it is inadequate to use the dynamic compliance (the most frequently used measure in the literature for vibration optimization) as an objective function for this type of optimization (aiming to obtain one-material structures), even when applying the static compliance as a constraint function or as a weighted part of the objective function. Physical and mathematical characteristics of the dynamic compliance are presented, such as dependence on the excitation frequency, function differentiability, and tendency to a trivial minimum. Several examples are analyzed in order to illustrate the difficulties in using this measure in topology optimization of one-material structures subjected to time-harmonic external loading, even including a constraint on static compliance in an attempt to ensure engineering feasibility. After some discussion, the authors indicate the main features of a vibration measure that makes it a better candidate to represent an objective function in an optimization procedure for harmonic problems, such as the absence of antiresonances in its frequency plot and an adequate capacity of representing the global system's response.