Integrated method for performance analysis of reliability-based topologically optimized components

Abstract

The available robust and reliable topology optimization methods provide quick and efficient design output in an uncertain environment. However, the whole domain of performance function remains hidden during this design process. In the interest of the designer, it is required to know the overall behavior of performance functions in deterministic as well as uncertain/realistic environment. The current work achieves this by proposing an integrated methodology, which combines the design of experiments approach and reliability-based topology optimization. The proposed method enables the designer to simulate performance functions in a desired design-factors space, including uncertainties, via reliability value. For this analysis, compliance, maximum deflection, mechanical advantage, and von Mises stress values are selected as performance functions. Volume fraction, applied force, and dimensions or aspect ratio are chosen as design/control factors. The uncertainties of these design factors are captured using reliability-based topology optimization. The uncertainties due to noncontrollable factors such as material property, load direction, and magnitude are incorporated using the design of experiments approach. Under these uncertainties, the performance of topologically optimized problem is simulated for different experimental combinations of the design factors. The experimental combinations for uncertainties and design factors are generated using Taguchi's orthogonal array. Simulated results are analyzed using techniques such as analysis of mean and variance, signal-to-noise ratio, and response surface method. These analyses help in identifying statistical significance of factors and uncertainties, performance variations, and equivalence relation of performance vs. factor. The proposed methodology is illustrated by selecting monolithic structures such as, on MBB, cantilever beam, and force inverter mechanism.