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

On the thermal stresses in anisotropic porous cylinders

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

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.
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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