The solution of Navier equations of classical elasticity using Lie symmetry groups

Mechanics Research Communications

Volumn 30, Issue 2, 2003, Pages 193-201

  Ozer T ^a,b  

^a ISTANBUL TECHNICAL UNIVERSITY   (Turkey)

^b Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

Lie groups; Navier equations; Similarity solutions

Indexed keywords

COMPUTATIONAL METHODS; DIFFERENTIAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS; PROBLEM SOLVING;

ELASTODYNAMICS;

ELASTICITY;

EID: 0037366847     PISSN: 00936413     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0093-6413(02)00365-8     Document Type: Article

References (11)

1. Axelsson, O., Gustafsson, I., 1978. Iterative methods for solution of Navier equations of elasticity. Computer Meth. Appl. Mech. Eng. 15 (2), 241-258.
2. Bluman, G.W., Kumei, S., 1989. Symmetries and differential equations. Springer-Verlag, Berlin.
3. Charalambopoulos, A., Dassions, G., Fotiadis, D.I., Massalas, C.V., 1999. Note on eigenvector solutions of the Navier equation on cylindrical coordinates. Acta Mech. 134, 115-119.
4. Ibragimov, N.H. (Ed.), 1996. CRC Handbook of Lie Group Analysis of Differential Equations. CRC Press, Boca Raton, FL.
5. Lakes, R.S., 1983. Size effects and micromechanics of a porous solid. J. Mater. Sci. 18, 2572-2580.
6. Malvern, L.E., 1969. Introduction to the Mechanics of a Continuous Medium. Prentice-Hall, Englewood Cliffs, NJ.
7. Olver, P.J., 1993. Application of Lie groups to differential equations. Springer-Verlag, Berlin.
8. Ovsiannikov, L.V., 1982. Group properties of differential equations, Academic Press, New York.
9. Ozer, T., 1999. On the symmetry group properties of equations of nonlocal elasticity. Mech. Res. Comm. 26, 725-733.
10. Ozer, T., 2000. Solution of Boussinesq problem using Lie symmetries. Math. Comput. Appl. 5 (1), 1-11.
11. Truesdell, C., 1972. In: The Linear Theory of Elasticity in the Encyclopedia of Physics, vol. 2. Springer-Verlag, Berlin, pp. 1-296.