On the thermal stresses in anisotropic porous cylinders

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December 2013, 6(6): 1539-1550. doi: 10.3934/dcdss.2013.6.1539

On the thermal stresses in anisotropic porous cylinders

Emilian Bulgariu ^1, and Ionel-Dumitrel Ghiba ^1,

1.	"Al.I. Cuza" University of Iaşi, Department of Mathematics, Blvd. Carol I, no. 11, 700506 Iaşi, Romania, Romania

Received June 2012 Revised September 2012 Published April 2013

Abstract
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In this paper we study the deformation of right porous cylinders subjected to a prescribed thermal field. We assume that the cylinder is filled by an inhomogeneous anisotropic porous material. In the first part of the paper we study the problem of extension-bending-torsion, when the thermal field is independent of the axial coordinate and then we study the problem of extension-bending-torsion-flexure when the thermal field is considered linear in the axial coordinate. The considered problems are reduced to some generalized plane strain problems in the cross-section of the cylinder. Our analysis shows how the considered thermal fields influence the deformation of the porous cylinders.

Keywords: anisotropic material, Porous cylinders, relaxed Saint-Venant's problem, generalized plane strain problems, thermal effects., semi-inverse solution.

Mathematics Subject Classification: 74F05, 74E10, 74E05, 74G05, 35Q8.

Citation: Emilian Bulgariu, Ionel-Dumitrel Ghiba. On the thermal stresses in anisotropic porous cylinders. Discrete and Continuous Dynamical Systems - S, 2013, 6 (6) : 1539-1550. doi: 10.3934/dcdss.2013.6.1539

References:

[1]	R. C. Batra and J. S. Yang, Saint-Venant's principle for linear elastic porous materials, J. Elasticity, 39 (1995), 265-271. doi: 10.1007/BF00041841.
[2]	E. Bulgariu, On the Saint-Venant's problem in microstretch elasticity, Libertas Mathematica, 31 (2011), 147-162.
[3]	S. Chiriţă, Saint-Venant's problem for anisotropic circular cylinder, Acta. Mechanica, 34 (1979), 243-250. doi: 10.1007/BF01227988.
[4]	S. Chiriţă, Saint-Venant's problem and semi-inverse solutions in linear viscoelasticity, Acta Mechanica, 94 (1992), 221-232. doi: 10.1007/BF01176651.
[5]	S. De Cicco and L. Nappa, Torsion and flexure of microstretch elastic circular cylindes, Int. J. Engng. Sci., 35 (1997), 573-583.
[6]	S. C. Cowin and J. W. Nunziato, Linear elastic materials with voids, J. Elasticity, 13 (1983), 125-147. doi: 10.1007/BF00041230.
[7]	F. Dell'isola and R. C. Batra, Saint-Venant's problem for porous linear elastic materials, J. Elasticity, 47 (1997), 73-81. doi: 10.1023/A:1007478322647.
[8]	C. Galeş, On Saint-Venant's problem in micropolar viscoelasticity, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 46 (2000), 131-148.
[9]	I.-D. Ghiba, Semi-inverse solution for Saint-Venant's problem in the theory of porous elastic materials, European Journal of Mechanics A Solids, 27 (2008), 1060-1074. doi: 10.1016/j.euromechsol.2007.12.008.
[10]	I.-D. Ghiba, On the deformation of transversely isotropic porous elastic circular cylinder, Arch. Mech. (Arch. Mech. Stos.), 61 (2009), 407-421.
[11]	M. A. Goodman and S. C. Cowin, A Continuum theory for granular materials, Arch. Rational Mech. Anal., 44 (1972), 249-266. doi: 10.1007/BF00284326.
[12]	D. Ieşan, On Saint-Venant's problem, Arch. Rational Mech. Anal., 91 (1986), 363-373. doi: 10.1007/BF00282340.
[13]	D. Ieşan, A theory of thermoelastic materials with voids, Acta Mechanica, 60 (1986), 67-89.
[14]	D. Ieşan, "Saint-Venant's Problem," Lecture Notes in Mathematics, 1279, Springer-Verlag, Berlin, 1987.
[15]	D Ieşan and M. Ciarletta, "Nonclassical Elastic Solids," Pitman Research Notes in Mathematics Series, 293, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1993.
[16]	D. Ieşan and L. Nappa, Extension and bending of microstretch elastic circular cylinders, Int. J. Engng. Sci., 33 (1995), 1139-1151. doi: 10.1016/0020-7225(94)00123-2.
[17]	D. Ieşan, "Thermoelastic Models of Continua," Solid Mechanics and its Applications, 118, Kluwer Academic Publishers Group, Dordrecht, 2004.
[18]	D. Ieşan and A. Scalia, On the deformation of functionally graded porous elastic cylinder, J. Elasticity, 87 (2007), 147-159. doi: 10.1007/s10659-007-9101-9.
[19]	D. Ieşan, Thermal stresses in inhomogeneous porous elastic cylinders, Journal of Thermal Stresses, 30 (2007), 145-164.
[20]	D. Ieşan, Thermal effects in orthotropic porous elastic beams, Z. Angew. Math. Phys., 60 (2009), 138-153. doi: 10.1007/s00033-008-7144-9.
[21]	D. Ieşan, "Classical and Generalized Models of Elastic Rods," CRC Series: Modern Mechanics and Mathematics, CRC Press, Boca Raton, FL, 2009.
[22]	D. Ieşan, Deformation of porous Cosserat elastic bars, Int. J. Solids Struct., 48 (2010), 573-583.
[23]	D. Ieşan, Thermal stresses in Chiral elastic beams, J. Thermal Stresses, 34 (2011), 458-487.
[24]	J. W. Nunziato and S. C. Cowin, A nonlinear theory of elastic materials with voids, Arch. Rational Mech. Anal., 72 (1979), 175-201. doi: 10.1007/BF00249363.
[25]	A. Scalia, Extension, bending and torsion of anisotropic microstretch elastic cylinders, Mathematics and Mechanics of Solids, 5 (2000), 31-40. doi: 10.1177/108128650000500103.

show all references

References:

[1]	R. C. Batra and J. S. Yang, Saint-Venant's principle for linear elastic porous materials, J. Elasticity, 39 (1995), 265-271. doi: 10.1007/BF00041841.
[2]	E. Bulgariu, On the Saint-Venant's problem in microstretch elasticity, Libertas Mathematica, 31 (2011), 147-162.
[3]	S. Chiriţă, Saint-Venant's problem for anisotropic circular cylinder, Acta. Mechanica, 34 (1979), 243-250. doi: 10.1007/BF01227988.
[4]	S. Chiriţă, Saint-Venant's problem and semi-inverse solutions in linear viscoelasticity, Acta Mechanica, 94 (1992), 221-232. doi: 10.1007/BF01176651.
[5]	S. De Cicco and L. Nappa, Torsion and flexure of microstretch elastic circular cylindes, Int. J. Engng. Sci., 35 (1997), 573-583.
[6]	S. C. Cowin and J. W. Nunziato, Linear elastic materials with voids, J. Elasticity, 13 (1983), 125-147. doi: 10.1007/BF00041230.
[7]	F. Dell'isola and R. C. Batra, Saint-Venant's problem for porous linear elastic materials, J. Elasticity, 47 (1997), 73-81. doi: 10.1023/A:1007478322647.
[8]	C. Galeş, On Saint-Venant's problem in micropolar viscoelasticity, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 46 (2000), 131-148.
[9]	I.-D. Ghiba, Semi-inverse solution for Saint-Venant's problem in the theory of porous elastic materials, European Journal of Mechanics A Solids, 27 (2008), 1060-1074. doi: 10.1016/j.euromechsol.2007.12.008.
[10]	I.-D. Ghiba, On the deformation of transversely isotropic porous elastic circular cylinder, Arch. Mech. (Arch. Mech. Stos.), 61 (2009), 407-421.
[11]	M. A. Goodman and S. C. Cowin, A Continuum theory for granular materials, Arch. Rational Mech. Anal., 44 (1972), 249-266. doi: 10.1007/BF00284326.
[12]	D. Ieşan, On Saint-Venant's problem, Arch. Rational Mech. Anal., 91 (1986), 363-373. doi: 10.1007/BF00282340.
[13]	D. Ieşan, A theory of thermoelastic materials with voids, Acta Mechanica, 60 (1986), 67-89.
[14]	D. Ieşan, "Saint-Venant's Problem," Lecture Notes in Mathematics, 1279, Springer-Verlag, Berlin, 1987.
[15]	D Ieşan and M. Ciarletta, "Nonclassical Elastic Solids," Pitman Research Notes in Mathematics Series, 293, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1993.
[16]	D. Ieşan and L. Nappa, Extension and bending of microstretch elastic circular cylinders, Int. J. Engng. Sci., 33 (1995), 1139-1151. doi: 10.1016/0020-7225(94)00123-2.
[17]	D. Ieşan, "Thermoelastic Models of Continua," Solid Mechanics and its Applications, 118, Kluwer Academic Publishers Group, Dordrecht, 2004.
[18]	D. Ieşan and A. Scalia, On the deformation of functionally graded porous elastic cylinder, J. Elasticity, 87 (2007), 147-159. doi: 10.1007/s10659-007-9101-9.
[19]	D. Ieşan, Thermal stresses in inhomogeneous porous elastic cylinders, Journal of Thermal Stresses, 30 (2007), 145-164.
[20]	D. Ieşan, Thermal effects in orthotropic porous elastic beams, Z. Angew. Math. Phys., 60 (2009), 138-153. doi: 10.1007/s00033-008-7144-9.
[21]	D. Ieşan, "Classical and Generalized Models of Elastic Rods," CRC Series: Modern Mechanics and Mathematics, CRC Press, Boca Raton, FL, 2009.
[22]	D. Ieşan, Deformation of porous Cosserat elastic bars, Int. J. Solids Struct., 48 (2010), 573-583.
[23]	D. Ieşan, Thermal stresses in Chiral elastic beams, J. Thermal Stresses, 34 (2011), 458-487.
[24]	J. W. Nunziato and S. C. Cowin, A nonlinear theory of elastic materials with voids, Arch. Rational Mech. Anal., 72 (1979), 175-201. doi: 10.1007/BF00249363.
[25]	A. Scalia, Extension, bending and torsion of anisotropic microstretch elastic cylinders, Mathematics and Mechanics of Solids, 5 (2000), 31-40. doi: 10.1177/108128650000500103.

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