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Research Papers

Efficient and Automated Analysis of Potentially Slender Structures

[+] Author and Article Information
Kavous Jorabchi

 University of Wisconsin at Madison, 2050 Mechanical Engineering Building, 1513 University Avenue, Madison, WI 53706kjorabchi@wisc.edu

Joshua Danczyk

 University of Wisconsin at Madison, 2050 Mechanical Engineering Building, 1513 University Avenue, Madison, WI 53706jrdanczyk@wisc.edu

Krishnan Suresh

 University of Wisconsin at Madison, 2050 Mechanical Engineering Building, 1513 University Avenue, Madison, WI 53706suresh@engr.wisc.edu

The COMSOL geometric modeler was not sufficiently robust to carry out a full geometric optimization … it often failed to rebuild the geometry even when the geometry was valid. This is a limitation of the CAD environment, rather than the proposed methodology. We are currently in the process of migrating to a more robust CAD environment.

J. Comput. Inf. Sci. Eng 9(4), 041001 (Oct 16, 2009) (9 pages) doi:10.1115/1.3243631 History: Received April 08, 2008; Revised February 06, 2009; Published October 16, 2009

Computer-based engineering analysis is now a routine process in virtual product design. However, when an object becomes slender, i.e., beam, plate, or shell like, 3D computational analysis is known to slowdown, or even lead to erroneous results. Indeed, the recommended method for analyzing slender objects is to replace them with equivalent lower-dimensional entities. However, explicit geometric reduction and replacement is impractical during automated product design, and requires specialized software tools. In this paper, we therefore develop an implicit dimensional reduction method, where the reduction is achieved through an algebraic process. The proposed reduction method is computationally efficient, and numerically equivalent to explicit geometric reduction. Moreover, standard off-the-shelf 3D finite element packages can be used to implement the proposed methodology. The efficacy of the proposed method is demonstrated within the context of shape optimization. Finally, the related problem of “automatic slenderness-detection” is also addressed briefly.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Three different configurations of an artifact

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Figure 2

The medial axis (transform) in 2D and 3D

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Figure 3

A coarse finite element mesh

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An illustrative cantilever beam-like solid

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A 27-noded hexahedral element

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Condition number as a function of aspect ratio

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Relative error in the predicted tip displacement

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Proposed shape optimization algorithm

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Figure 9

An illustrative cantilever solid

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Shape parameter regions

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Results for experiment 1

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Results for experiment 2

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Cantilever structure

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Postprocessing: stress distribution

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A C-flex bearing

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Torsional loading on a C-flex bearing

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Poor quality finite element mesh

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Figure 18

C-flex design exploration study 1

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Figure 19

C-flex design exploration study 2

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