Reformulation of Navier equations for solving three-dimensional elasticity problems with applications to thick plate analysis

Acta Mechanica

Volumn 208, Issue 3-4, 2009, Pages 227-235

  Saidi, A R ^a   Atashipour, S R ^a   Jomehzadeh, E ^a  

^a SHAHID BAHONAR UNIVERSITY OF KERMAN   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

CLOSED FORM SOLUTIONS; CO-ORDINATE SYSTEM; DECOUPLED EQUATION; DISPLACEMENT COMPONENTS; ELASTO-DYNAMICS; NAVIER EQUATIONS; NUMERICAL RESULTS; ROTATION COMPONENTS; THICK PLATE; THICK RECTANGULAR PLATES; THREE-DIMENSIONAL ELASTICITY; THREE-DIMENSIONAL ELASTOSTATICS;

ELASTICITY; NUMERICAL ANALYSIS; ROTATION; THREE DIMENSIONAL;

EQUATIONS OF MOTION;

EID: 75549088566     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00707-009-0147-6     Document Type: Article

References (19)

1. Nosier, A., Reddy, J.N.: On vibration and buckling of symmetric laminated plates according to shear deformation theories: Part I. Acta Mech. 94, 123-144 (1992)
2. Nosier, A., Reddy, J.N.: On vibration and buckling of symmetric laminated plates according to shear deformation theories: Part II. Acta Mech. 94, 145-169 (1992)
3. Nosier, A., Reddy, J.N.: On boundary layer and interior equations for higher-order theories of plates. ZAMM 72, 657-666 (1992)
4. Nosier, A., Yavari, A., Sarkani, S.: A study of the edge-zone equation of Mindlin-Reissner plate theory in bending of laminated rectangular plates. Acta Mech. 146, 227-238 (2001)
5. Nosier, A., Yavari, A., Sarkani, S.: On a boundary layer phenomenon in Mindlin-Reissner plate theory for laminated circular sector plates. Acta Mech. 151, 149-161 (2001)
6. Nosier, A., Fallah, F.: Reformulation of Mindlin-Reissner governing equations of functionally graded circular plates. Acta Mech. 198, 209-233 (2008)
7. Jomehzadeh, E., Saidi, A.R.: Analytical solution for free vibration of transversely isotropic sector plates using a boundary layer function. Thin Wall Struct. 47, 82-88 (2009)
8. Jomehzadeh, E., Saidi, A.R.: Accurate natural frequencies of transversely isotropic moderately thick annular sector plates. J. Mech. Eng. Sci. 222. doi:10.1243/09544062JMES1199
9. Plevako, V.P.: On the theory of elasticity of inhomogeneous media. J. Appl. Math. Mech. 35, 806-813 (1971)
10. Charalambopoulos, A., Dassions, G., Fotiadis, D.I., Massalas, C.V.: Note on eigenvector solutions of the Navier equation on cylindrical coordinates. Acta Mech. 134, 115-119 (1999)
11. Poullikkas, A., Karageorghis, A., Georgiou, G.: The method of fundamental solutions in three-dimensional elastostatics. In: International conference on parallel processing and appliedmathematics, vol.2328, pp. 747-755, Leczow, Poland (2001)
12. Ozer, T.: The solution of Navier equations of classical elasticity using Lie symmetry groups. Mech. Res. Commun. 30, 193-201 (2003)
13. Levinson, M.: The simply supported rectangular plate: an exact three-dimensional linear elasticity solution. J. Elast. 15, 283-291 (1985)
14. Levinson, M.: Free vibrations of a simply supported rectangular plate, an exact elasticity solution. J Sound Vib. 98, 289-298 (1985)
15. Tsai, C.C.: Themethod of fundamental solutions for three-dimensional elastostatic problems of transversely isotropic solids. Eng. Anal. Bound. Elem. 31, 586-594 (2007)
16. Civalek, O.: Three-dimensional vibration, buckling and bending analyses of thick rectangular plates based on discrete singular convolution method. Int. J. Mech. Sci. 49, 752-765 (2007)
17. Demasi, L.: Three-dimensional closed form solutions and exact thin plate theories for isotropic plates. Compos. Struct. 80, 183-195 (2007)
18. Srinivas, S., Rao, A.K.: Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. Int. J. Solid Struct. 6, 1463-1481 (1970)
19. Vel, S.S., Batra, R.C.: Three-dimensional exact solution for the vibration of functionally graded rectangular plates. J. Sound Vib. 272, 703-730 (2004)