In the past, we have introduced the Beam Constraint Model (BCM), which captures pertinent non-linearities to predict the constraint characteristics of a generalized beam flexure in terms of its stiffness and error motions. In this paper, a non-linear strain energy formulation for the beam flexure, consistent with the transverse-direction load-displacement and axial-direction geometric constraint relations in the BCM, is presented. An explicit strain energy expression, in terms of beam end-displacements, that accommodates generalized loading conditions, boundary conditions, initial curvature, and beam shape is derived. Using the Principle of Virtual Work, this strain energy expression for a generalized beam is employed in determining the load-displacement relations, and therefore constraint characteristics, for flexure mechanisms comprising multiple beams. The benefit of this approach is evident in its mathematical efficiency and succinctness, which is to be expected with the use of energy methods. All analytical results are validated to a high degree of accuracy via non-linear Finite Element Analysis. Furthermore, the proposed energy formulation leads to new insights into the nature of the BCM.
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ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 15–18, 2010
Montreal, Quebec, Canada
Conference Sponsors:
- Design Engineering Division and Computers in Engineering Division
ISBN:
978-0-7918-4410-6
PROCEEDINGS PAPER
Beam Constraint Model: A Non-Linear Strain Energy Formulation for Generalized Two-Dimensional Beam Flexures
Shorya Awtar,
Shorya Awtar
University of Michigan, Ann Arbor, MI
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Shiladitya Sen
Shiladitya Sen
University of Michigan, Ann Arbor, MI
Search for other works by this author on:
Shorya Awtar
University of Michigan, Ann Arbor, MI
Shiladitya Sen
University of Michigan, Ann Arbor, MI
Paper No:
DETC2010-28184, pp. 375-386; 12 pages
Published Online:
March 8, 2011
Citation
Awtar, S, & Sen, S. "Beam Constraint Model: A Non-Linear Strain Energy Formulation for Generalized Two-Dimensional Beam Flexures." Proceedings of the ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 2: 34th Annual Mechanisms and Robotics Conference, Parts A and B. Montreal, Quebec, Canada. August 15–18, 2010. pp. 375-386. ASME. https://doi.org/10.1115/DETC2010-28184
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