Nodal Based Mappings Between Finite Element Meshes

[+] Author and Article Information
David A. Field

 General Motors Research and Development and Planning Center, Mail Code 480-106-359, 30500 Mound Road, Warren, MI 48090-9055dfield@gmr.com

J. Comput. Inf. Sci. Eng 7(4), 309-313 (May 21, 2007) (5 pages) doi:10.1115/1.2795296 History: Received October 28, 2004; Revised May 21, 2007

Due to the demands on mathematical models that simulate physical properties and behaviors of automotive components, different finite element meshes often partition the same component for each disparate simulation. Commercial packages that transfer mesh dependent results from one finite element analysis to initialize another typically use a variation of a specific nodal based mapping. The simplicity and ease of implementation make this mapping very attractive. In its simplest form, the mapping first assigns a node in the analyzed model the average value of the elements that share the node. A node in the unanalyzed mesh receives its value from the closest node in the analyzed mesh. Nodal based interpolants on the new element initialize elemental values. When an element in the unanalyzed mesh requires a constant value such as its thickness, the element receives the average value at the nodes that define the element. This brief paper documents some undesirable characteristics of this nodal based transfer of material properties from one mesh to another.

Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

The (i+1)th element in A1 contains the jth element in U1 and the (j−1)th element in U1 contains the ith element in A1

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Figure 2

The distributions of nodes for WLA to reproduce the same results as in LA and the NDM

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Figure 3

The nine NDM values of γj−1 when xi−2⩽wj−2⩽xi−1⩽wj−1⩽xi depend on the proximities of wj−2 to xi−2 and xi−1 and of wj−1 to xi−1 and xi

Grahic Jump Location
Figure 4

The mesh in A1 has greater local density than the mesh in U1

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Figure 5

The mesh in A1 has greater local density than the mesh in U1

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Figure 6

The results of using LA and nodal based mapping lie above the two copies of the mesh shown in Fig. 5. The ith element in A1 contains the (j−1)th, jth, and (j+1)th elements in U1.

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Figure 7

The shaded triangle, the forming element with the smallest thickness, projects into two quadrilateral structural elements

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Figure 8

The shaded triangle, the forming element with the smallest thickness, no longer contributes to the thickness of any structural element



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