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A Modified Strain Gradient Beam Constraint Model
  • Mohammad Arhami,
  • Hamid Moeenfard
Mohammad Arhami
Ferdowsi University of Mashhad Faculty of Engineering

Corresponding Author:[email protected]

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Hamid Moeenfard
Ferdowsi University of Mashhad Faculty of Engineering
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Abstract

The objective of this paper is to develop a modified strain gradient beam constraint model (MSGBCM) to improve modeling accuracy of small-scale compliant mechanisms. First, a simple nano/micro flexure beam under the effect of end loads is considered. The virtual work principle is employed to formulate the load-displacement behavior of the system based on the modified strain gradient theory. It is observed that as the size of the structure becomes smaller, the elements of the elastic stiffness and load stiffening matrices severely deviate from their corresponded values in the beam constraint model (BCM). Then, a closed-form expression is proposed for the nonlinear strain energy of the nano/micro flexure beams in terms of their tip displacements. This energy expression is then utilized to model load-displacement relationship of micron/submicron size parallelogram (P) flexures. Moreover, analytical formulas are derived for the axial, transverse and rotational stiffnesses of P-flexures. The most important observation is that the axial stiffness loss of small-scale P-flexures resulted from the movement of the stage in the transverse direction, may be seriously overestimated by the BCM. The MSGBCM developed in this paper can be easily extended for investigating static and dynamic behavior of more complex micron and submicron size flexure units.
27 Oct 2021Submitted to Mathematical Methods in the Applied Sciences
01 Nov 2021Submission Checks Completed
01 Nov 2021Assigned to Editor
04 Nov 2021Reviewer(s) Assigned
22 May 2022Review(s) Completed, Editorial Evaluation Pending
22 May 2022Editorial Decision: Revise Major
25 Jun 20221st Revision Received
25 Jun 2022Submission Checks Completed
25 Jun 2022Assigned to Editor
01 Jul 2022Reviewer(s) Assigned
01 Jul 2022Review(s) Completed, Editorial Evaluation Pending
02 Aug 2022Editorial Decision: Revise Minor
20 Aug 20222nd Revision Received
22 Aug 2022Submission Checks Completed
22 Aug 2022Assigned to Editor
22 Aug 2022Review(s) Completed, Editorial Evaluation Pending
22 Aug 2022Editorial Decision: Accept
11 Sep 2022Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.8700