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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

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 & 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.  Google Scholar

[2]

E. Bulgariu, On the Saint-Venant's problem in microstretch elasticity, Libertas Mathematica, 31 (2011), 147-162.  Google Scholar

[3]

S. Chiriţă, Saint-Venant's problem for anisotropic circular cylinder, Acta. Mechanica, 34 (1979), 243-250. doi: 10.1007/BF01227988.  Google Scholar

[4]

S. Chiriţă, Saint-Venant's problem and semi-inverse solutions in linear viscoelasticity, Acta Mechanica, 94 (1992), 221-232. doi: 10.1007/BF01176651.  Google Scholar

[5]

S. De Cicco and L. Nappa, Torsion and flexure of microstretch elastic circular cylindes, Int. J. Engng. Sci., 35 (1997), 573-583. Google Scholar

[6]

S. C. Cowin and J. W. Nunziato, Linear elastic materials with voids, J. Elasticity, 13 (1983), 125-147. doi: 10.1007/BF00041230.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[10]

I.-D. Ghiba, On the deformation of transversely isotropic porous elastic circular cylinder, Arch. Mech. (Arch. Mech. Stos.), 61 (2009), 407-421.  Google Scholar

[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.  Google Scholar

[12]

D. Ieşan, On Saint-Venant's problem, Arch. Rational Mech. Anal., 91 (1986), 363-373. doi: 10.1007/BF00282340.  Google Scholar

[13]

D. Ieşan, A theory of thermoelastic materials with voids, Acta Mechanica, 60 (1986), 67-89. Google Scholar

[14]

D. Ieşan, "Saint-Venant's Problem," Lecture Notes in Mathematics, 1279, Springer-Verlag, Berlin, 1987.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[17]

D. Ieşan, "Thermoelastic Models of Continua," Solid Mechanics and its Applications, 118, Kluwer Academic Publishers Group, Dordrecht, 2004.  Google Scholar

[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.  Google Scholar

[19]

D. Ieşan, Thermal stresses in inhomogeneous porous elastic cylinders, Journal of Thermal Stresses, 30 (2007), 145-164. Google Scholar

[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.  Google Scholar

[21]

D. Ieşan, "Classical and Generalized Models of Elastic Rods," CRC Series: Modern Mechanics and Mathematics, CRC Press, Boca Raton, FL, 2009.  Google Scholar

[22]

D. Ieşan, Deformation of porous Cosserat elastic bars, Int. J. Solids Struct., 48 (2010), 573-583. Google Scholar

[23]

D. Ieşan, Thermal stresses in Chiral elastic beams, J. Thermal Stresses, 34 (2011), 458-487. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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.  Google Scholar

[2]

E. Bulgariu, On the Saint-Venant's problem in microstretch elasticity, Libertas Mathematica, 31 (2011), 147-162.  Google Scholar

[3]

S. Chiriţă, Saint-Venant's problem for anisotropic circular cylinder, Acta. Mechanica, 34 (1979), 243-250. doi: 10.1007/BF01227988.  Google Scholar

[4]

S. Chiriţă, Saint-Venant's problem and semi-inverse solutions in linear viscoelasticity, Acta Mechanica, 94 (1992), 221-232. doi: 10.1007/BF01176651.  Google Scholar

[5]

S. De Cicco and L. Nappa, Torsion and flexure of microstretch elastic circular cylindes, Int. J. Engng. Sci., 35 (1997), 573-583. Google Scholar

[6]

S. C. Cowin and J. W. Nunziato, Linear elastic materials with voids, J. Elasticity, 13 (1983), 125-147. doi: 10.1007/BF00041230.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[10]

I.-D. Ghiba, On the deformation of transversely isotropic porous elastic circular cylinder, Arch. Mech. (Arch. Mech. Stos.), 61 (2009), 407-421.  Google Scholar

[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.  Google Scholar

[12]

D. Ieşan, On Saint-Venant's problem, Arch. Rational Mech. Anal., 91 (1986), 363-373. doi: 10.1007/BF00282340.  Google Scholar

[13]

D. Ieşan, A theory of thermoelastic materials with voids, Acta Mechanica, 60 (1986), 67-89. Google Scholar

[14]

D. Ieşan, "Saint-Venant's Problem," Lecture Notes in Mathematics, 1279, Springer-Verlag, Berlin, 1987.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[17]

D. Ieşan, "Thermoelastic Models of Continua," Solid Mechanics and its Applications, 118, Kluwer Academic Publishers Group, Dordrecht, 2004.  Google Scholar

[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.  Google Scholar

[19]

D. Ieşan, Thermal stresses in inhomogeneous porous elastic cylinders, Journal of Thermal Stresses, 30 (2007), 145-164. Google Scholar

[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.  Google Scholar

[21]

D. Ieşan, "Classical and Generalized Models of Elastic Rods," CRC Series: Modern Mechanics and Mathematics, CRC Press, Boca Raton, FL, 2009.  Google Scholar

[22]

D. Ieşan, Deformation of porous Cosserat elastic bars, Int. J. Solids Struct., 48 (2010), 573-583. Google Scholar

[23]

D. Ieşan, Thermal stresses in Chiral elastic beams, J. Thermal Stresses, 34 (2011), 458-487. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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