Research Papers

An Adaptive Meshless Method for Analyzing Large Mechanical Deformation and Contacts

[+] Author and Article Information
Qiang Li

The G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 801 Ferst Drive, Atlanta, GA 30332-0405

Kok-Meng Lee1

The G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 801 Ferst Drive, Atlanta, GA 30332-0405kokmeng.lee@me.gatech.edu


Corresponding author.

J. Appl. Mech 75(4), 041014 (May 14, 2008) (10 pages) doi:10.1115/1.2912938 History: Received May 10, 2007; Revised March 28, 2008; Published May 14, 2008

Design for manufacturing of equipment (that handles deformable objects) and disposable medical devices (such as medical needles, optic fibers, and catheters for inserting into the human body) involves solving mechanical contact problems. Unlike rigid component manufacturing, which has been relatively well established, the handling of deformable bodies remains a challenging research. This paper offers an adaptive meshless method (MLM) for solving mechanical contact problems, which automatically insert additional nodes into large error regions identified in terms of mechanical stresses. This adaptive MLM employs a sliding line algorithm with penalty method to handle contact constraints. The method does not rely on small displacement assumptions; thus, it can solve nonlinear contact problems with large deformation. We validate the method by comparing results against those computed by using a commercial FEM software and analytical solution for two different situations, namely, large deformation and contact. Four practical applications are illustrated: large deflection of a compliant finger, mechanical contact, snap-fit assembly, and surgical needle insertion.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

Illustration of contact between two bodies

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Figure 2

Contact gap function between two discretized bodies

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Figure 3

RKP basis function with two different support sizes

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Figure 4

Voronoi plot with three large error point

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Figure 5

Partition unity integration cells

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Figure 6

FEM mesh and its deformed result (ANSYS )

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Figure 7

Percentage error of MLM for four consecutive adaptive computations

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Figure 8

MLM nodes after the final adaptive computation

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Figure 9

Rigid punch contacts with elastic foundation

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Figure 10

Adaptive node insertion

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Figure 11

Comparison between MLM, FEM, and analytical result

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Figure 12

Geometry of a snap-fit mechanism

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Figure 14

Initial geometry and node distribution (deformable body: Young’s modulus E=1×106Pa; Poisson’s ratio μ=0.4)

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Figure 15

Result after each adaptive computation at the first position

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Figure 16

Results of MLM simulation

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Figure 17

Equivalent stress distribution (N∕m2)




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