zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Magneto-thermoelastic problem in rotating non-homogeneous orthotropic hollow cylinder under the hyperbolic heat conduction model. (English) Zbl 1258.74055
Summary: We proposed a model of generalized magneto-thermoelastic for orthotropic hollow cylinder whose surfaces are subjected to a thermal relaxation under the effect of rotation with one relaxation time. The system of fundamental equations is solved by using an implicit finite-difference scheme. A numerical method is used to calculate the temperature, displacement and the components of stresses with time and through the radial of the cylinder. Numerical results are given and illustrated graphically for each case considered. The results indicate that the effect of rotation, inhomogeneity and magnetic field are very pronounced. Comparison made with the results predicted by the theory of generalized magneto-thermoelasticity with one relaxation time in the absence of rotation.
74F05Thermal effects in solid mechanics
74S20Finite difference methods in solid mechanics
[1]Lord H, Shulman Y (1967) A generalized dynamical theory of thermoelasticity. J Mech Phys Solids 15:299–309 · Zbl 0156.22702 · doi:10.1016/0022-5096(67)90024-5
[2]Green AE, Lindsay KA (1972) Thermoelasticity. J Elast 2:1–7 · Zbl 0775.73063 · doi:10.1007/BF00045689
[3]Green AE, Nagdhi PM (1991) A re-examination of the basic postulate of thermo mechanics. Proc R Soc Lond 432:171–194 · Zbl 0726.73004 · doi:10.1098/rspa.1991.0012
[4]Green AE, Nagdhi PM (1992) On undamped heat wave in an elastic solid. J Therm Stresses 15:253–264 · doi:10.1080/01495739208946136
[5]Green AE, Nagdhi PM (1993) Thermoelasticity without energy dissipation. J Elast 31:189–208 · Zbl 0784.73009 · doi:10.1007/BF00044969
[6]Das NC, Bhakta PC, Datta S (1988) Eigenfunction expansion method to thermoelastic and magneto-thermoelastic problems. Indian J Pure Appl Math 19:697–712
[7]Zibdeh HS, Al Farran JM (1995) Stress analysis in composite hollow cylinders due to an symmetric temperature distribution. J Press Vessel Technol 117:59–65 · doi:10.1115/1.2842091
[8]Noda N, Ashida F (1986) A three-dimensional treatment of transient thermal stresses semi-infinite circular subjected to an symmetric temperature on the cylindrical surface. Acta Mech 58:175–191 · Zbl 0578.73017 · doi:10.1007/BF01176598
[9]Tsai YM (1993) Thermal stress in a transversely isotropic medium containing a penny-shaped crack. ASME J Appl Mech 50:24–28 · Zbl 0511.73005 · doi:10.1115/1.3167012
[10]Chandrasekharaiah DS, Keshavan HR (1991) Thermoelastic plane waves in a transversely isotropic body. Acta Mech 87:11–22 · Zbl 0729.73813 · doi:10.1007/BF01177168
[11]El-Naggar AM, Abd-Alla AM, Fahmy MA, Ahmed SM (2002) Thermal stresses in a rotating non-homogeneous orthotropic hollow cylinder. J Heat Mass Transfer 39:41–46 · doi:10.1007/s00231-001-0285-4
[12]Misra JC, Samanta SC, Chakrabarty AK, Misra SC (1991) Magnetothermoelastic inter-action in an infinite elastic continuum with a cylindrical hole subjected to ramp-type heating. Int J Eng Sci 29:1505–1514 · Zbl 0763.73048 · doi:10.1016/0020-7225(91)90122-J
[13]Misra JC, Samanta SC, Chakrabarty AK (1991) Magneto-thermoelastic interaction in an aeolotropic solid cylinder subjected to a ramp-type heating. Int J Eng Sci29:1065–1075 · Zbl 0761.73096 · doi:10.1016/0020-7225(91)90112-G
[14]Abd-Alla AM, Abd-Alla AN, Zeidan NA (2000) Thermal stresses in a non-homogeneous orthotropic elastic multilayered cylinder. J Therm Stresses 23:413–428 · doi:10.1080/014957300403914
[15]Abd-Alla AM, El-Naggar AM, Fahmy MA (2003) Magneto-thermoelastic problem in non-homogeneous isotropic cylinder. J Heat Mass Transfer 39:625–629 · doi:10.1007/s00231-002-0370-3
[16]Ding DJ, Wang HM, Chen WQ (2003) A solutions of a non-homogeneous orthotropic cylindrical shell for axisymmetric plane strain dynamic thermoelastic problems. J Sound Vib 263:815–829 · doi:10.1016/S0022-460X(02)01075-1
[17]Abd-El-Salam MR, Abd-Alla AM, Hosham HA (2007) A numerical solution of magneto-thermoelastic problem in non-homogeneous isotropic cylinder by the finite difference method. Appl Math Model 31:1662–1670 · Zbl 1136.78004 · doi:10.1016/j.apm.2006.05.009
[18]Abd-Alla AM, Salama AA, Abd-El-Salam MR, Hosham HA (2007) An implicit finite-difference method for solving the transient coupled thermoelastic of an annular fin. Appl Math Inf Sci 1:62–73
[19]Sadd MH (2005) Elasticity: theory, application, and numerics. Elsevier, Amsterdam
[20]Jain MK (1987) Numerical solution of differential equations, 2nd edn. Wiley, New York