On the thermal stresses in anisotropic porous cylinders

Previous Article
New results on the problem of the stabilization of equilibria for models of electrohydraulic servoactuators
DCDS-S Home
This Issue
Next Article
Structure of the space of 2D elasticity tensors

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
Related Papers

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.

[1]	E. Audusse. A multilayer Saint-Venant model: Derivation and numerical validation. Discrete and Continuous Dynamical Systems - B, 2005, 5 (2) : 189-214. doi: 10.3934/dcdsb.2005.5.189
[2]	Emmanuel Audusse, Fayssal Benkhaldoun, Jacques Sainte-Marie, Mohammed Seaid. Multilayer Saint-Venant equations over movable beds. Discrete and Continuous Dynamical Systems - B, 2011, 15 (4) : 917-934. doi: 10.3934/dcdsb.2011.15.917
[3]	Georges Bastin, Jean-Michel Coron, Brigitte d'Andréa-Novel. On Lyapunov stability of linearised Saint-Venant equations for a sloping channel. Networks and Heterogeneous Media, 2009, 4 (2) : 177-187. doi: 10.3934/nhm.2009.4.177
[4]	Hassen Arfaoui, Faker Ben Belgacem, Henda El Fekih, Jean-Pierre Raymond. Boundary stabilizability of the linearized viscous Saint-Venant system. Discrete and Continuous Dynamical Systems - B, 2011, 15 (3) : 491-511. doi: 10.3934/dcdsb.2011.15.491
[5]	Jean-Frédéric Gerbeau, Benoit Perthame. Derivation of viscous Saint-Venant system for laminar shallow water; Numerical validation. Discrete and Continuous Dynamical Systems - B, 2001, 1 (1) : 89-102. doi: 10.3934/dcdsb.2001.1.89
[6]	Marie-Odile Bristeau, Jacques Sainte-Marie. Derivation of a non-hydrostatic shallow water model; Comparison with Saint-Venant and Boussinesq systems. Discrete and Continuous Dynamical Systems - B, 2008, 10 (4) : 733-759. doi: 10.3934/dcdsb.2008.10.733
[7]	Albert Clop, Daniel Faraco, Alberto Ruiz. Stability of Calderón's inverse conductivity problem in the plane for discontinuous conductivities. Inverse Problems and Imaging, 2010, 4 (1) : 49-91. doi: 10.3934/ipi.2010.4.49
[8]	Xian Zhang, Vinesh Nishawala, Martin Ostoja-Starzewski. Anti-plane shear Lamb's problem on random mass density fields with fractal and Hurst effects. Evolution Equations and Control Theory, 2019, 8 (1) : 231-246. doi: 10.3934/eect.2019013
[9]	Li-Fang Dai, Mao-Lin Liang, Wei-Yuan Ma. Optimization problems on the rank of the solution to left and right inverse eigenvalue problem. Journal of Industrial and Management Optimization, 2015, 11 (1) : 171-183. doi: 10.3934/jimo.2015.11.171
[10]	Md. Ibrahim Kholil, Ziqi Sun. A uniqueness theorem for inverse problems in quasilinear anisotropic media. Inverse Problems and Imaging, , () : -. doi: 10.3934/ipi.2022008
[11]	Mirela Kohr, Sergey E. Mikhailov, Wolfgang L. Wendland. Dirichlet and transmission problems for anisotropic stokes and Navier-Stokes systems with L_∞ tensor coefficient under relaxed ellipticity condition. Discrete and Continuous Dynamical Systems, 2021, 41 (9) : 4421-4460. doi: 10.3934/dcds.2021042
[12]	Timir Karmakar, Meraj Alam, G. P. Raja Sekhar. Analysis of Brinkman-Forchheimer extended Darcy's model in a fluid saturated anisotropic porous channel. Communications on Pure and Applied Analysis, 2022, 21 (3) : 845-865. doi: 10.3934/cpaa.2022001
[13]	Hermann Gross, Sebastian Heidenreich, Mark-Alexander Henn, Markus Bär, Andreas Rathsfeld. Modeling aspects to improve the solution of the inverse problem in scatterometry. Discrete and Continuous Dynamical Systems - S, 2015, 8 (3) : 497-519. doi: 10.3934/dcdss.2015.8.497
[14]	Fioralba Cakoni, Houssem Haddar. A variational approach for the solution of the electromagnetic interior transmission problem for anisotropic media. Inverse Problems and Imaging, 2007, 1 (3) : 443-456. doi: 10.3934/ipi.2007.1.443
[15]	Shaoyong Lai, Yong Hong Wu. The asymptotic solution of the Cauchy problem for a generalized Boussinesq equation. Discrete and Continuous Dynamical Systems - B, 2003, 3 (3) : 401-408. doi: 10.3934/dcdsb.2003.3.401
[16]	Steve Rosencrans, Xuefeng Wang, Shan Zhao. Estimating eigenvalues of an anisotropic thermal tensor from transient thermal probe measurements. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 5441-5455. doi: 10.3934/dcds.2013.33.5441
[17]	Jinchuan Zhou, Naihua Xiu, Jein-Shan Chen. Solution properties and error bounds for semi-infinite complementarity problems. Journal of Industrial and Management Optimization, 2013, 9 (1) : 99-115. doi: 10.3934/jimo.2013.9.99
[18]	Masaru Ikehata, Mishio Kawashita. An inverse problem for a three-dimensional heat equation in thermal imaging and the enclosure method. Inverse Problems and Imaging, 2014, 8 (4) : 1073-1116. doi: 10.3934/ipi.2014.8.1073
[19]	Rentsen Enkhbat, Evgeniya A. Finkelstein, Anton S. Anikin, Alexandr Yu. Gornov. Global optimization reduction of generalized Malfatti's problem. Numerical Algebra, Control and Optimization, 2017, 7 (2) : 211-221. doi: 10.3934/naco.2017015
[20]	Toyohiko Aiki. A free boundary problem for an elastic material. Conference Publications, 2007, 2007 (Special) : 10-17. doi: 10.3934/proc.2007.2007.10

2021 Impact Factor: 1.865

Tools

Metrics

Other articles
by authors

on AIMS
Emilian Bulgariu Ionel-Dumitrel Ghiba
on Google Scholar
Emilian Bulgariu Ionel-Dumitrel Ghiba

[Back to Top]