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Research Papers

Modeling and Experiments of Buckling Modes and Deflection of Fixed-Guided Beams in Compliant Mechanisms

[+] Author and Article Information
Gregory L. Holst, Gregory H. Teichert

Brian D. Jensen1

Department of Mechanical Engineering,  Brigham Young University, Provo, Utah 84602bdjensen@byu.edu

1

Corresponding author.

J. Mech. Des 133(5), 051002 (Jun 02, 2011) (10 pages) doi:10.1115/1.4003922 History: Received December 22, 2010; Revised March 30, 2011; Published June 02, 2011; Online June 02, 2011

This paper explores the deflection and buckling of fixed-guided beams used in compliant mechanisms. The paper’s main contributions include the addition of an axial deflection model to existing beam bending models, the exploration of the deflection domain of a fixed-guided beam, and the demonstration that nonlinear finite element models typically incorrectly predict a beam’s buckling mode unless unrealistic constraints are placed on the beam. It uses an analytical model for predicting the reaction forces, moments, and buckling modes of a fixed-guided beam undergoing large deflections. The model for the bending behavior of the beam is found using elliptic integrals. A model for the axial deflection of the buckling beam is also developed. These two models are combined to predict the performance of a beam undergoing large deflections including higher order buckling modes. The force versus displacement predictions of the model are compared to the experimental force versus deflection data of a bistable mechanism and a thermomechanical in-plane microactuator (TIM). The combined models show good agreement with the force versus deflection data for each device.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Diagram of variables used for the fixed-guided buckling beam solution

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Figure 2

Shows the several bending modes with inflection points. Also shows values of φ corresponding to each inflection point of the beams.

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Figure 3

Plot showing how the demarcation line between first mode and second mode bending changes with respect to the slenderness ratio

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Figure 4

Vector plot of the reaction force magnitude and direction for an array of beam end displacements. The shaded region corresponds to the displacements that induce second mode buckling and the unshaded corresponds to first mode. Several displaced beam profiles are also shown. Plot specific for a beam with an arbitrary slenderness ratio of 43.3.

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Figure 7

Contour plot of the relative error between the ANSYS model and the combined model for the vertical reaction force predictions for a beam with a slenderness ratio of 100

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Figure 10

Force versus displacement curve for an example bistable mechanism showing the stable and unstable positions and the locations of the maximum and minimum forces

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Figure 12

Force versus displacement of the bistable mechanism with slenderness ratio of 161 compared to two finite element models and the combined model

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Figure 13

Photograph showing the beams of the bistable mechanism in first mode bending

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Figure 14

Photograph showing the beams of the bistable mechanism in second mode buckling

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Figure 15

Design of a thermomechanical in-plane microactuator (TIM) with a slenderness ratio of 692, showing the motion caused by current i heating the thin beams

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Figure 16

Diagram showing the variables used to model the TIM with the combined model solution. The figure also shows the displacement path of the end of the beam as a dotted line. The dashed lines show the buckling beam profiles.

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Figure 17

Comparison of the force versus displacement data for a thermomechanical in-plane microactuator and the model predictions. The solid lines represent the combined model solution for each heating current.

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Figure 5

(a) Screenshot of 2D plane strain beam modeled in ANSYS showing ninth mode buckling. (b) Screenshot of 2D plane strain beam modeled in ANSYS showing second mode buckling with an offset force applied to the center of the beam to bias the solution into second mode. The right end of the beam is fixed and the left end is displaced in an upper right direction away from the origin.

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Figure 6

Contour plot of the relative error between the ANSYS model and the combined model for the horizontal reaction force predictions for a beam with a slenderness ratio of 100

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Figure 8

Design of the bistable mechanisms with a slenderness ratio of 161 showing the two stable positions

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Figure 9

Diagram showing the variables used to analyze the bistable mechanism using the combined model

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Figure 11

Photograph of the bistable mechanism

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