A finite difference scheme for magneto-thermo analysis of an infinite cylinder
Author(s)
Daoud S. Mashat
ABSTRACT
A finite different scheme as well as least-square method is presented for the magneto-thermo analysis of an infinite functionally graded hollow cylinder. The radial displacement, mechanical stresses and temperature as well as the electromagnetic stress are investigated along the radial direction of the cylinder. Material properties are assumed to be graded in the radial direction according to a novel exponential-law distribution in terms of the volume fractions of the metal and ceramic constituents. The governing second-order differential equations are derived from the equations of motion and the heat-conduction equation. The system of differential equations is solved numerically and some plots for displacement, radial stress, and temperature are presented.
A finite different scheme as well as least-square method is presented for the magneto-thermo analysis of an infinite functionally graded hollow cylinder. The radial displacement, mechanical stresses and temperature as well as the electromagnetic stress are investigated along the radial direction of the cylinder. Material properties are assumed to be graded in the radial direction according to a novel exponential-law distribution in terms of the volume fractions of the metal and ceramic constituents. The governing second-order differential equations are derived from the equations of motion and the heat-conduction equation. The system of differential equations is solved numerically and some plots for displacement, radial stress, and temperature are presented.
Cite this paper
Mashat, D. (2010) A finite difference scheme for magneto-thermo analysis of an infinite cylinder. Natural Science, 2, 1312-1317. doi: 10.4236/ns.2010.211159.
Mashat, D. (2010) A finite difference scheme for magneto-thermo analysis of an infinite cylinder. Natural Science, 2, 1312-1317. doi: 10.4236/ns.2010.211159.
References
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[1] Wang, X., Lu, G. and Guillow, S.R. (2002) Magnetothermodynamic stress and perturbation of magnetic field vector in a solid cylinder. Journal of Thermal Stresses, 25, 909-926. [2] X. Wang and H.L. Dai: Magnetothermodynamic stress and perturbation of magnetic field vector in an orthotropic thermoelastic cylinder. The International Journal of Engineering Science, 42, 539-556. [3] Wang, X. and Dai, H.L. (2004) Magneto-thermo-dynamic stress and perturbation of magnetic field vector in a hollow cylinder. Journal of Thermal Stresses, 3, 269- 288. [4] Dai, H.L. and Wang, X. (2006) Magneto-thermo-electro-elastic transient response in a piezoelectric hollow cylinder subjected to complex loadings. The International Journal of Solids and Structures, 43, 5628-5646. [5] H.L. Dai and Fu, Y.M. (2007) Magnetothermoelastic interactions in hollow structures of functionally graded material subjected to mechanical loads. The International Journal of Pressure Vessels and Piping, 84, 132-138. [6] Chen, C.K. and Yang, Y.C. (1986) Thermoelastic transient response of an infinitely long annular cylinder composed of two different materials. The International Journal of Engineering Science, 24, 569-581. [7] Jane, K.C. and Lee, Z.Y. (1999) Thermoelastic transient response of an infinitely long multilayered cylinder. Mechanics Research Communications, 26, 709-718. [8] Lee, Z.-Y. (2004) Hybrid numerical method applied to 3-D multilayers hollow cylinder with time-dependent boundary conditions. Applied Mathematics and Computation, 150, 25-43. [9] Awaji, H. and Sivakuman, R. (2001) Temperature and stress distributions in a hollow cylinder of functionally graded material: the case of temperature-dependent material properties. Journal of the American Ceramic Society, 84, 1059-1065. [10] Yang, Y.-C., Chu, S.-S., Lee, H.-L. and Lin, S.-L. (2006) Hybrid numerical method applied to transient hygrothermal analysis in an annular cylinder. International Communications in Heat and Mass Transfer, 33, 102-111. [11] Chen, Y.Z. (2000) Stress intensity factors in a finite length cylinder with a circumferential crack. International Journal of Pressure Vessels and Piping, 77, 439- 444. [12] Jane, K.C. and Lee, Z.Y. (1999) Thermoelastic transient response of an infinitely long annular multilayered cylinder. Mechanics Research Communications, 26, 709- 718.