Structural Optimization of Bell Crank using Adaptive Response Surface Optimization

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Virginia Tech


This research contributes to the development of a structural optimization software system designed to support design optimization. The focus of this thesis work is on formulating strategies to obtain accurate solutions and enhance the efficiency of the optimization process, particularly when dealing with large and complex finite element (FE) models, utilizing statistical concepts. A potential avenue explored in this study is the adaptive response surface optimization process. The adaptive response surface optimization method involves the adaptive control of samples selected through the design of experiments and empirical models constructed via the response surface methodology, with the sampling of the design space and empirical model terms dynamically adjusted throughout the optimization progression. The empirical models are constructed with statistically significant terms to maximize the utilization of information from each sample generated using the design of experiments. If the available information is fully utilized by the empirical model and the adaptive response surface optimization process needs to progress further until an optimal solution is identified, additional samples are generated. The methodology is applied to a benchmark bell crank problem, optimizing the bell crank for maximum operational value by simultaneously increasing fatigue life and reducing the overall component cost. This demonstration showcases the structural optimization software's capability to handle both design and manufacturing aspects seamlessly. The approach to solving the structural optimization problem involves constructing a constrained parametric bell crank part in Abaqus/CAE as it facilitates easy manipulation of the geometry. The entire process of geometry generation, meshing, simulation, and output extraction was supported by developing Python scripts. Response surface model building and other statistical analyses are conducted using the JMP statistical software. Nonlinear constrained optimization is executed through the sequential quadratic programming (SLSQP solver) from the SciPy library, allowing optimization on the response surfaces representing the objective function and constraints to identify the optimal solution. The optimal solution is obtained utilizing a small composite design with individual response surface models for the objective function and each constraint, is compared with results from the Abaqus finite element model, and the percentage difference was 0.9% at the optimal design variable values.



Adaptive Response Surface Optimization, Finite Element Analysis, Scripting