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Research Papers

A Generalized Constraint Model for Two-Dimensional Beam Flexures: Nonlinear Load-Displacement Formulation

[+] Author and Article Information
Shorya Awtar1

Department of Mechanical Engineering, University of Michigan, 2350 Hayward Street, Ann Arbor, MI 48109awtar@umich.edu

Shiladitya Sen

Department of Mechanical Engineering, University of Michigan, 2350 Hayward Street, Ann Arbor, MI 48109shiladit@umich.edu

1

Corresponding author.

J. Mech. Des 132(8), 081008 (Aug 18, 2010) (11 pages) doi:10.1115/1.4002005 History: Received October 16, 2009; Revised May 16, 2010; Published August 18, 2010; Online August 18, 2010

To utilize beam flexures in constraint-based flexure mechanism design, it is important to develop qualitative and quantitative understanding of their constraint characteristics in terms of stiffness and error motions. This paper provides a highly generalized yet accurate closed-form parametric load-displacement model for two-dimensional beam flexures, taking into account the nonlinearities arising from load equilibrium applied in the deformed configuration. In particular, stiffness and error motions are parametrically quantified in terms of elastic, load-stiffening, kinematic, and elastokinematic effects. The proposed beam constraint model incorporates a wide range of loading conditions, boundary conditions, initial curvature, and beam shape. The accuracy and effectiveness of the proposed beam constraint model is verified by nonlinear finite elements analysis.

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Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Comparison of various constraint elements

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Figure 2

Simple beam flexure

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Figure 3

Initially slanted and curved beam

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Figure 4

DoF force (fy1) versus DoF displacement (uy1) for initially slanted or curved beams

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Figure 5

DoC displacement (ux1) versus DoF displacement (uy1) for initially slanted or curved beams

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Figure 6

DoC stiffness versus DoF displacement (uy1) for initially slanted or curved beams

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Figure 7

Straight beam with varying cross-section

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Figure 8

Variable cross-section beam

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Figure 9

Elastic stiffness coefficients: BCM versus FEA

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Figure 10

Load stiffening coefficients: BCM versus FEA

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Figure 11

Elastokinematic coefficients: BCM versus FEA

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