Derivation of the model of elastic curved rods from three-dimensional micropolar elasticity
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Abstract
In this paper we derive a model of curved elastic rods from the threedimensional linearized micropolar elasticity. Derivation is based on the asymptotic expansion method with respect to the thickness of the rod. The method is used without any a priori assumption on the scaling of the unknowns. The leading term, displacement and microrotation, is identified as the unique solution of a certain one-dimensional problem. Appropriate convergence results are proved.
Keywords
Elastic curved rods Micropolar elasticity Asymptotic method One-dimensional model JustificationMathematics Subject Classification (2000)
74K10 74A35 35B25Preview
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References
- 1.Aganović, I., Tambača, J., Tutek, Z.: The asymptotic analysis of micropolar elastic rods. Submitted for publicationGoogle Scholar
- 2.Aganović I. and Tutek Z. (1986). A justification of the one-dimensional linear model of elastic beam. Math. Meth. Appl. Sci. 8: 1–14 CrossRefGoogle Scholar
- 3.Antman S.S. (1995). Nonlinear Problems of Elasticity. Springer, Berlin MATHGoogle Scholar
- 4.Bermudez A. and Viaño J.M. (1984). A justification of thermoelastic equations for variable-section beams by asymptotic methods. RAIRO Anal. Numer. 18: 347–376 MATHMathSciNetGoogle Scholar
- 5.Bernadou M., Ciarlet P.G. and Miara B. (1994). Existence theorems for two-dimensional linear shell theories. J. Elasticity 34: 111–138 MATHMathSciNetCrossRefGoogle Scholar
- 6.Ciarlet, P.G.: Mathematical elasticity. vol. II. Theory of plates. North-Holland, Amsterdam (1997)Google Scholar
- 7.Ciarlet P.G. and Destuynder P. (1979). A justification of the two dimensional linear plate model. J. Mécanique 18: 315–344 MATHMathSciNetGoogle Scholar
- 8.Erbay H.A. (2000). An asymptotic theory of thin micropolar plates. Internat. J. Eng. Sci. 38: 1497–1516 CrossRefMathSciNetGoogle Scholar
- 9.Eringen A.C. (1999). Microcontinuum Field Theories, I: Foundations and Solids. Springer, New York MATHGoogle Scholar
- 10.Goldenveizer A.L. (1962). Derivation of an approximate theory of bending a plate by a method of asymptotic integration of the equations in the theory of elasticity. J. Appl. Math. 19: 1000–1025 Google Scholar
- 11.Green A.E. and Naghdi P.M. (1967). Micropolar and director theories of plates. Quart. J. Mech. Appl. Math. 20: 183–199 MATHCrossRefGoogle Scholar
- 12.Jurak M. and Tambača J. (2001). Linear curved rod model. General curve. Math. Mod. Meth. Appl. Sci. 11: 1237–1253 MATHCrossRefGoogle Scholar
- 13.Lakes R.S. (1995). Experimental methods for study of Cosserat elastic solids and other generalized continua. In: Mühlhaus, H (eds) Continuum models for materials with micro-structure., pp 1–22. Wiley, New York Google Scholar
- 14.Landau L.D. and Lifshitz E.M. (1970). Theory of Elasticity. Pergamon, Oxford Google Scholar
- 15.Miara B. (1994). Justification of the asymptotic analysis of elastic plates. I. The linear case. Asymptotic Anal. 9: 47–60 MATHMathSciNetGoogle Scholar
- 16.Tambača, J.: One-dimensional models in theory of elasticity, (in Croatian). Master’s thesis, Department of Mathematics, University of Zagreb (1999)Google Scholar
- 17.Tambača, J.: Evolution model of curved rods, (in Croatian). PhD thesis, Department of Mathematics, University of Zagreb (2000)Google Scholar
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