Topology optimization with geometric uncertainties by perturbation techniques. (English) Zbl 1242.74075
Summary: The aim of this paper was to present a topology optimization methodology for obtaining robust designs insensitive to small uncertainties in the geometry. The variations are modeled using a stochastic field. The model can represent spatially varying geometry imperfections in devices produced by etching techniques. Because of under-etching or over-etching parts of the structure may become thinner or thicker than a reference design supplied to the manufacturer. The uncertainties are assumed to be small and their influence on the system response is evaluated using perturbation techniques. Under the above assumptions, the proposed algorithm provides a computationally cheap alternative to previously introduced stochastic optimization methods based on Monte Carlo sampling. The method is demonstrated on the design of a minimum compliance cantilever beam and a compliant mechanism.
MSC:
| 74P15 | Topological methods for optimization problems in solid mechanics |
| 74G10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics |
| 74S60 | Stochastic and other probabilistic methods applied to problems in solid mechanics |
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