Author:

Keywords:

topology optimization, robust design optimization, manufacturing errors, monte carlo method, compliant mechanisms, design, variables, filters, models, Science & Technology, Technology, Physical Sciences, Engineering, Multidisciplinary, Mathematics, Interdisciplinary Applications, Mechanics, Engineering, Mathematics, Topology optimization, Robust design optimization, Manufacturing errors, Monte Carlo method, DESIGN, MECHANISMS, VARIABLES, FILTERS, 01 Mathematical Sciences, 09 Engineering, Applied Mathematics, 40 Engineering, 49 Mathematical sciences

Abstract:

This paper presents a robust approach for the design of macro-, micro-, or nano-structures by means of topology optimization, accounting for spatially varying manufacturing errors. The focus is on structures produced by milling or etching; in this case over- or under-etching may cause parts of the structure to become thinner or thicker than intended. This type of error is modeled by means of a projection technique: a density filter is applied, followed by a Heaviside projection, using a low projection threshold to simulate under-etching and a high projection threshold to simulate over-etching. In order to simulate the spatial variation of the manufacturing error, the projection threshold is represented by a (non-Gaussian) random field. The random field is obtained as a memoryless transformation of an underlying Gaussian field, which is discretized by means of an EOLE expansion. The robust optimization problem is formulated in a probabilistic way: the objective function is defined as a weighted sum of the mean value and the standard deviation of the structural performance. The optimization problem is solved by means of a Monte Carlo method: in each iteration of the optimization scheme, a Monte Carlo simulation is performed, considering 100 random realizations of the manufacturing error. A more thorough Monte Carlo simulation with 10000 realizations is performed to verify the results obtained for the final design. The proposed methodology is successfully applied to two test problems: the design of a compliant mechanism and a heat conduction problem. (C) 2011 Elsevier B.V. All rights reserved.