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Spatially defined optimization of FEA using nodal surrogate models

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Abstract

Optimization of the structural response for a part relies upon computationally expensive simulations such as finite element analysis (FEA). Surrogate models are able to make cheap predictions of the results; however, traditionally they can only predict a single value (SV) such as a maximum stress or weight value. Recently, a surrogate modeling method has been developed for predicting the full field (FF) of nodal responses in an FEA simulation. This research applies FF surrogate models to optimization, and explores various techniques that are uniquely enabled by these cheap—yet detailed—predictions. Because the FF surrogate models predict the response at every node, constraints and objectives can be spatially defined on a part rather than act on a single value. Regional constraints allow for control over a subset of the nodes in areas of interest on the part. Location-based objectives find designs that either draw a response closer to or drive a response away from a particular node. Pattern-matching objectives find designs in the design space that have a response pattern across the part surface that is as similar as possible to a pre-defined response pattern. These techniques extend the usefulness of FF surrogate models as well as optimization of FEA results for exploring a design space and improving a design.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Brigham Young University, Provo, Utah, 84604, USA

    Christopher Thelin, Spencer Bunnell, Steven Gorrell, Landon Wright & John Salmon

Authors
  1. Christopher Thelin
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  2. Spencer Bunnell
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  3. Steven Gorrell
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  4. Landon Wright
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  5. John Salmon
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Corresponding author

Correspondence to John Salmon.

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The authors declare that they have no conflict of interest.

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Responsible Editor: Ming Zhou

Replication of results

The above analysis and optimization process used the Transonic Purdue Research Compressor blade available to researchers. The finite element analysis and extraction of nodal coordinate and stress results for the modal and structural analyses was performed using ANSYS, but could be performed with any commercially available finite element analysis package. The data compilation, emulation (surrogate models), and visualization were performed with proprietary code supported by Pratt and Whitney, but the emulation and visualization of nodal results can be accomplished with Python packages such as scipy.interpolate (for emulation, with a variety of surrogate model options such as rbf) and PyOpenGL (for visualization). The optimization was performed using Python with the scipy package (scipy.optimize.minimize) available at PyPi or conda. Specific code used for the optimization routines can be made available upon request to the corresponding author.

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Thelin, C., Bunnell, S., Gorrell, S. et al. Spatially defined optimization of FEA using nodal surrogate models. Struct Multidisc Optim 64, 813–828 (2021). https://doi.org/10.1007/s00158-021-02894-3

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  • DOI: https://doi.org/10.1007/s00158-021-02894-3

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