Two solutions for the BVP of a rotating variable-thickness solid disk
ABSTRACT
This paper presents the analytical and numerical solutions for a rotating variable-thickness solid disk. The outer edge of the solid disk is considered to have free boundary conditions. The governing equation is derived from the basic equations of the rotating solid disk and it is solved analytically or numerically using finite difference algorithm. Both analytical and numerical results for the distributions of stress function and stresses of variable-thickness solid disks are obtained. Finally, the distributions of stress function and stresses are presented and the appropriate comparisons and discussions are made at the same angular velocity.
This paper presents the analytical and numerical solutions for a rotating variable-thickness solid disk. The outer edge of the solid disk is considered to have free boundary conditions. The governing equation is derived from the basic equations of the rotating solid disk and it is solved analytically or numerically using finite difference algorithm. Both analytical and numerical results for the distributions of stress function and stresses of variable-thickness solid disks are obtained. Finally, the distributions of stress function and stresses are presented and the appropriate comparisons and discussions are made at the same angular velocity.
Cite this paper
Zenkour, A. and Al-Ahmadi, S. (2011) Two solutions for the BVP of a rotating variable-thickness solid disk. Natural Science, 3, 145-153. doi: 10.4236/ns.2011.32021.
Zenkour, A. and Al-Ahmadi, S. (2011) Two solutions for the BVP of a rotating variable-thickness solid disk. Natural Science, 3, 145-153. doi: 10.4236/ns.2011.32021.
References
[1] Timoshenko, S.P. and Goodier, J.N. (1970) Theory of elasticity. McGraw-Hill, New York. [2] Ugural, S.C. and Fenster, S.K. (1987) Advanced strength and applied elasticity. Elsevier, New York. [3] Gamer, U. (1984) Elastic-plastic deformation of the rotating solid disk. Ingenieur-Archiv, 54, 345-354. doi:10.1007/BF00532817 [4] Gamer, U. (1985) Stress distribution in the rotating elastic-plastic disk. ZAMM, 65, T136-137. [5] Eraslan, A.N. (2000) Inelastic deformation of rotating variable thickness solid disks by Tresca and Von Mises criteria. International Journal of Computational Engineering Science, 3, 89-101. doi:10.1142/S1465876302000563 [6] Eraslan, A.N. and Orcan, Y. (2002) On the rotating elastic-plastic solid disks of variable thickness having concave profiles. International Journal of Mechanical Sciences, 44, 1445-1466. doi:10.1016/S0020-7403(02)00038-3 [7] Eraslan, A.N. (2005) Stress distributions in elastic-plastic rotating disks with elliptical thickness profiles using Tresca and von Mises criteria. ZAAM, 85, 252-266. [8] Zenkour, A.M. and Allam, M.N.M. (2006) On the rotating fiber-reinforced viscoelastic composite solid and annular disks of variable thickness. International Journal for Computational Methods in Engineering Science, 7, 21-31. doi:10.1080/155022891009639 [9] Zienkiewicz, O.C. (1971) The finite element method in engineering science. McGraw-Hill, London. [10] Banerjee, P.K. and Butterfield, R. (1981) Boundary element methods in engineering science. McGraw-Hill, New York. [11] You, L.H., Tang, Y.Y., Zhang, J.J. and Zheng, C.Y. (2000) Numerical analysis of with elastic-plastic rotating disks arbitrary variable thickness and density. The International Journal of Solids and Structures, 37, 7809-7820. doi:10.1016/S0020-7683(99)00308-X [12] Zenkour, A.M. and Mashat, D.S. (2010), Analytical and numerical solutions for a rotating disk of variable thickness. Applied Mathematics, 1, 430-437. doi:10.4236/am.2010.15057
[1] Timoshenko, S.P. and Goodier, J.N. (1970) Theory of elasticity. McGraw-Hill, New York. [2] Ugural, S.C. and Fenster, S.K. (1987) Advanced strength and applied elasticity. Elsevier, New York. [3] Gamer, U. (1984) Elastic-plastic deformation of the rotating solid disk. Ingenieur-Archiv, 54, 345-354. doi:10.1007/BF00532817 [4] Gamer, U. (1985) Stress distribution in the rotating elastic-plastic disk. ZAMM, 65, T136-137. [5] Eraslan, A.N. (2000) Inelastic deformation of rotating variable thickness solid disks by Tresca and Von Mises criteria. International Journal of Computational Engineering Science, 3, 89-101. doi:10.1142/S1465876302000563 [6] Eraslan, A.N. and Orcan, Y. (2002) On the rotating elastic-plastic solid disks of variable thickness having concave profiles. International Journal of Mechanical Sciences, 44, 1445-1466. doi:10.1016/S0020-7403(02)00038-3 [7] Eraslan, A.N. (2005) Stress distributions in elastic-plastic rotating disks with elliptical thickness profiles using Tresca and von Mises criteria. ZAAM, 85, 252-266. [8] Zenkour, A.M. and Allam, M.N.M. (2006) On the rotating fiber-reinforced viscoelastic composite solid and annular disks of variable thickness. International Journal for Computational Methods in Engineering Science, 7, 21-31. doi:10.1080/155022891009639 [9] Zienkiewicz, O.C. (1971) The finite element method in engineering science. McGraw-Hill, London. [10] Banerjee, P.K. and Butterfield, R. (1981) Boundary element methods in engineering science. McGraw-Hill, New York. [11] You, L.H., Tang, Y.Y., Zhang, J.J. and Zheng, C.Y. (2000) Numerical analysis of with elastic-plastic rotating disks arbitrary variable thickness and density. The International Journal of Solids and Structures, 37, 7809-7820. doi:10.1016/S0020-7683(99)00308-X [12] Zenkour, A.M. and Mashat, D.S. (2010), Analytical and numerical solutions for a rotating disk of variable thickness. Applied Mathematics, 1, 430-437. doi:10.4236/am.2010.15057