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Research Papers

Real-Time Visualization of Finite Element Models Using Surrogate Modeling Methods

[+] Author and Article Information
Ryan C. Heap

Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
e-mail: ryan.heap.byu@gmail.com

Ammon I. Hepworth

Research Staff
Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
e-mail: ammon.hepworth@byu.edu

C. Greg Jensen

Professor
Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
e-mail: cjensen@byu.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received March 31, 2014; final manuscript received November 6, 2014; published online January 13, 2015. Assoc. Editor: Charlie C. L., Wang.

J. Comput. Inf. Sci. Eng 15(1), 011007 (Mar 01, 2015) (12 pages) Paper No: JCISE-14-1107; doi: 10.1115/1.4029217 History: Received March 31, 2014; Revised November 06, 2014; Online January 13, 2015

Parametric finite element analysis (FEA) models are commonly used in iterative design processes to obtain an optimum model given a set of loads, constraints, objectives, and design parameters to vary. In some instances, it is desirable for a designer to obtain some intuition about how changes in design parameters can affect the FEA solution of interest, before simply sending the model through the optimization loop. For example, designers who wish to explore the design space and understand how each variable changes the output in a visual way, looking at the whole model and not just numbers or a response surface of a single FEA node. This could be accomplished by running the FEA on the parametric model for a set of part family members, but this can be very time consuming and only gives snapshots of the model's real behavior. This paper presents a method of visualizing the FEA solution of the parametric model as design parameters are changed in real-time by approximating the FEA solution using parametric FEA modeling, surrogate modeling methods, and visualization methods. The implementation develops a parametric FEA mode that includes mesh morphing algorithms that allow the mesh to change parametrically along with the model geometry. This allows the surrogate models assigned to each individual node to use the nodal solution of multiple finite element analyses as regression points to approximate the FEA solution. The surrogate models can then be mapped to their respective geometric locations in real-time. The results of the FEA calculations are updated in real-time as the parameters of the design model change allowing real-time visualization.

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References

Figures

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Fig. 1

Response surface generated from Eq. (1)

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Fig. 3

Example of equation P(u) = P1 + u(P2 − P1)

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Fig. 4

Mesh morphing: All nodes morph to a parametrically identical location. The circled node is 20% along the length and 0% along the width in both family members. (a) Length = y0, width = x0 and (b) Length = y1, width = x1.

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Fig. 5

Overall view of the automated workflow: The FEA solution drives the surrogate models and the surrogate models drive the visualization

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Fig. 6

Example of a DOE with two design variables, x and y, which both have a range from zero to one

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Fig. 7

Representation of how the inputs from the DOE and the nodal solutions are mapped to a surrogate model

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Fig. 8

The first GUI the designer would see when running the visualization program

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Fig. 9

A box-plot of the approximations versus log(RMS error) generated from the jmp statistics software

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Fig. 10

The visualization GUI of the program

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Fig. 11

The workflow for generating the training data for surrogate model initialization

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Fig. 12

Rectangular cross section beam load case

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Fig. 15

Visualization comparison for the rectangular beam model. (a) Rectangular beam visualization example and (b) rectangular beam ansys example.

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Fig. 16

Visualization comparison for the C-beam model. (a) C-beam visualization example and (b) C-beam ansys example.

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Fig. 17

Visualization comparison for the I-beam model. (a) I-beam visualization example and (b) I-beam ansys example.

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