The wide use of fir-tree root and groove in turbine structures prompts the expectation to find optimum configurations, which ensure that stresses are in the safe limits to avoid mechanical failure. To perform the optimization, the reasonable characterization of root configuration is required. The existing researches characterized the fir-tree root with straight line, arc or even elliptic fillet, then the parameters of these features were defined as design variables to perform root profile optimization. However, this feature-based optimization technique yields configuration which is only optimal under the feature assumption, the question why choose these feature and whether there is a better feature modeling technique is difficult to answer. In this work, instead of the feature-based method, spline curves technique is involved to characterize the root and groove configuration, and the horizontal coordinates of the control points are selected as design variables, which are modified in the vicinity of their initial values during optimization process. The objective function is to minimize the peak stress in the root and groove regions. With the Multi-island genetic algorithm, the optimal fir-tree root configuration can be obtained with better stress distributions and low stress concentrations. The proposed spline-based optimization approach may shed lights on the conceptual design of blade root and can be easily extended to other industrial equipment design.

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