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Shock and Vibration
Volume 2015 (2015), Article ID 672831, 10 pages
Research Article

Compliance Matrix of a Single-Bent Leaf Flexure for a Modal Analysis

1School of Mechanical Engineering, Yeungnam University, Gyeongsan 712-749, Republic of Korea
2Department of Mechanical Engineering, Dong-A University, Busan 604-714, Republic of Korea

Received 22 March 2015; Accepted 4 May 2015

Academic Editor: Chao Tao

Copyright © 2015 Nghia-Huu Nguyen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a compliance matrix for a single-bent leaf flexure (SBLF) that shows the relationships between the deformations and the six-axis loads applied to the SBLF. Higher-order beam theory that considers the variable shear and warping effect is considered in bending. The partially restrained warping at the junction between elements is also considered in torsion. The total strain energy is calculated, and the complete compliance matrix is derived by using Castigliano’s second theorem. Sensitivity analyses over the compliance elements are performed and verified via finite element analysis (FEA). The results show that the derived compliance elements are in good agreement with FEA, with errors of less than 7.6%. We suggest that theoretical compliance elements considering variable shear and warping in bending and partially restrained warping in torsion give highly accurate design equations representing the compliant mechanism of the SBLF. The present work could be used in a modal analysis of a single-bent leaf flexure.