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Research Papers

Dual Representation Methods for Efficient and Automatable Analysis of 3D Plates

[+] Author and Article Information
Vikalp Mishra

Department of Mechanical Engineering, University of Wisconsin-Madison, 1513 Univeristy Avenue, Madison, WI 53706

Krishnan Suresh

Department of Mechanical Engineering, University of Wisconsin-Madison, 1513 Univeristy Avenue, Madison, WI 53706suresh@engr.wisc.edu

J. Comput. Inf. Sci. Eng 10(4), 041002 (Nov 23, 2010) (11 pages) doi:10.1115/1.3510587 History: Received September 10, 2009; Revised July 03, 2010; Published November 23, 2010; Online November 23, 2010

It is well recognized that 3D finite element analysis is inappropriate for analyzing thin structures such as plates and shells. Instead, a variety of highly efficient and specialized 2D methods have been developed for analyzing such structures. However, 2D methods pose serious automation challenges in today’s 3D design environment. Specifically, analysts must manually extract cross-sectional properties from a 3D computer aided design (CAD) model and import them into a 2D environment for analysis. In this paper, we propose two efficient yet easily automatable dual representation methods for analyzing thin plates. The first method exploits standard off-the-shelf 3D finite element packages and achieves high computational efficiency through an algebraic reduction process. In the reduction process, a 3D plate bending stiffness matrix is constructed from a 3D mesh and then projected onto a lower-dimensional space by appealing to standard 2D plate theories. In the second method, the analysis is carried out by integrating 2D shape functions over the boundary of the 3D plate. Both methods do not entail extraction of the cross-sectional properties of the plate. However, the user must identify the plate or thickness direction. The proposed methodologies are substantiated through numerical experiments.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 5

Eight-noded and 27-noded hexahedral elements

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Figure 6

Rectangular plate element

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Figure 13

Uniformly loaded plate with built-in edges

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Figure 14

3D tetrahedral mesh for uniformly loaded plate with built-in edges

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Figure 15

Surface triangulation for uniformly loaded plate with built-in edges

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Figure 16

Relative error in maximum deflection, for the plate in Fig. 1

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Figure 17

Mesh used by different methods

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Figure 22

First six mode shapes for plate in Fig. 1

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Figure 23

Relative error in first modal frequency

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Figure 24

Rectangular plate with two longitudinal and two transverse stiffeners

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Figure 25

Relative error in modal frequencies

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Figure 1

A stiffened 3D plate structure

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Figure 2

The stiffened plate structure modeled in 2D

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Figure 3

A plate structure with additional features

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Figure 4

An illustrative clamped plate

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Figure 7

A tetrahedral mesh of the plate structure

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Figure 8

Poor quality elements are acceptable

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Figure 9

A 2D geometry containing the projection of plate

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Figure 10

The 2D geometry discretized into quad elements

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Figure 11

A surface triangulation of the plate structure

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Figure 12

(a) Surface triangulation, (b) desired integration over quad element, and (c and d) triangulation of quad element

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Figure 18

Relative error in maximum deflection versus number of quad elements

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Figure 19

Uniformly loaded plate structures

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Figure 20

Deflected edge 1 of plate in Fig. 1

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Figure 21

Relative error in first six modal frequencies

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