Tolerance range selection of topologically optimized structures with the effects of uncertainties of manufacturing process

Abstract

Robust design methods for topology optimization have received significant attention from researchers in recent years. There are various attempts in past to handle the manufacturing uncertainty of the topologically optimized components. In the present work, same issue is dealt by introducing a method of probabilistic distribution of material. Here, help from Karhunen–Loeve expansion of stochastic process, coupled with Monte Carlo method is taken. The proposed method retains the uncertainty characteristic of the specific manufacturing processes such as etching, e-beam lithography, laser micro machining, and milling. Hence, this method offers larger flexibility to the designer. The simulation for manufacturing uncertainty is utilized to determine the optimal tolerance range of the factors for robust and targeted performance, which is almost nonexistent in the literature. The methodology for tolerance range selection is capable to incorporate uncertainty of multiple factors simultaneously. In this method cross array design of experiment approach is used to analyze the effect of tolerance of each factor. The overall process for manufacturing uncertainty and tolerance range selection is illustrated using four benchmark problems. The chosen factors for considered structural problems are force, elasticity, volume fraction, and aspect ratio. Various combinations of tolerance ranges are used to simulate the performance of the optimized structure, which is expressed in terms of robustness and targeted values of compliance, and maximum deflection. Based on the simulated results of signal-to-noise ratio and mean values of performance, the combinations of tolerance range are suggested that gives a high level of robustness or targeted performance accuracy. To indicate the uniqueness of proposed approach, the obtained response for performances is compared with already available response for performance in literature for generalized approach. Current work is advantageous compared to usual robust design, and provides the performance for a specific scenario at each possible combination of tolerance ranges.