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

Abstract EN

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.