Determination of hourglass coefficients in the theory of a Cosserat point for nonlinear elastic beams |
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| Institution: | 1. Department of Marine, Earth, and Atmospheric Sciences, North Carolina State University, Raleigh, NC, 27695, USA;2. Department of Electrical and Computer Engineering, Duke University, Durham, NC, 27708, USA;3. Department of Chemistry, Juniata College, Huntingdon, PA, 16652, USA;4. Army Research Laboratory, Aberdeen Proving Ground, MD, 21005, USA;5. Department of Geochemistry, University of Göttingen, Göttingen, 37077, Germany;6. Department of Geology, Colgate University, Hamilton, NY, 13346, USA;1. Faculty of Informatics and Management, University of Hradec Kralove, Hradec Kralove, Czech Republic;2. Faculty of Science, University of Hradec Kralove, Rokitanskeho 62, Hradec Kralove 50003, Czech Republic;3. Faculty of Information Technology, Ho Chi Minh City University of Technology (HUTECH), Ho Chi Minh City, Viet Nam;4. DaSCI Andalusian Institute of Data Science and Computational Intelligence, University of Granada, Granada, Spain;5. Faculty of Software and Information Science, Iwate Prefectural University, Iwate, Japan |
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| Abstract: | The theory of a Cosserat point has recently been used Int. J. Solids Struct. 38 (2001) 4395] to formulate the numerical solution of problems of nonlinear elastic beams. In that theory the constitutive equations for inhomogeneous elastic deformations included undetermined constants associated with hourglass modes which can occur due to nonuniform cross-sectional extension and nonuniform torsion. The objective of this paper is to determine these hourglass coefficients by matching exact solutions of pure bending and pure torsion applied in different directions on each of the surfaces of the element. It is shown that the resulting constitutive equations in the Cosserat theory do not exhibit unphysical stiffness increases due to thinness of the beam, mesh refinement or incompressibility that are present in the associated Bubnov–Galerkin formulation. Also, example problems of a bar hanging under its own weight and a bar attached to a spinning rigid hub are analyzed. |
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