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Mechanical Sciences An open-access journal for theoretical and applied mechanics
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Volume 9, issue 1
Mech. Sci., 9, 71-79, 2018
https://doi.org/10.5194/ms-9-71-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Mech. Sci., 9, 71-79, 2018
https://doi.org/10.5194/ms-9-71-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 16 Feb 2018

Research article | 16 Feb 2018

Determining the range of allowable axial force for the third-order Beam Constraint Model

Fulei Ma1, Guimin Chen1, and Guangbo Hao2 Fulei Ma et al.
  • 1School of Electro-Mechanical Engineering, Xidian University, Xi'an, Shaanxi 710071, China
  • 2School of Engineering-Electrical and Electronic Engineering, University College Cork, Ireland

Abstract. The Beam Constraint Model (BCM) was developed for the purpose of accurately and analytically modeling nonlinear behaviors of a planar beam flexure over an intermediate range of transverse deflections (10% of the beam length). The BCM is expressed in the form of Taylor's expansion associated with the axial force. It has been found that the BCM may yield large predicting errors (> 5%) when the applied axial force goes beyond a certain boundary, even the deflection is still in the intermediate range. However, this boundary has not been clearly identified so far. In this work, we mathematically determine the non-dimensional boundary of the axial force by the condition that the strain energy expression of the BCM is a positive definite quadratic form, and by the buckling condition relate to compressing axial force. Several examples are analyzed to demonstrate the effects of the axial force on the modeling errors of the BCM. When using the BCM for modeling, it is always suggested to check if the axial force is within this boundary to avoid large modeling errors. If the axial force is beyond the boundary, the Chained Beam Constraint Model (CBCM) can be used instead.

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The Beam Constraint Model (BCM) may yield large predicting errors (> 5 %) when the applied axial force goes beyond a certain boundary. We mathematically determine the nondimensional boundary of the axial force by the conditions of the positive definite quadratic form of the strain energy expression and the buckling load expressions. If the axial force is beyond the boundary, the Chained Beam Constraint Model (CBCM) can be used instead.
The Beam Constraint Model (BCM) may yield large predicting errors ( 5 %) when the applied axial...
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