Some Differential Equations of Elasticity and their Lie Point Symmetry Generators

1. Azad H., Mustafa M. T., Arif A. F. M. (2010), Analytic Solutions of Initial-Boundary-Value Problems of Transient Conduction Using Symmetries, Applied Mathematics and Computation, Vol. 215, 41324140.Search in Google Scholar

2. Bluman G. W., Cole J. D. (1974), Similarity Methods for Differential Equations, Springer-Verlag, New York, 1974.10.1007/978-1-4612-6394-4Search in Google Scholar

3. Champagne B., Hereman W., Winternitz P. (1991), The Computer Calculation of Lie Point Symmetries of Large Systems of Differential Equations, Computer Physics Communications, Vol. 66, 319-340.Search in Google Scholar

4. Drew M. S., Kloster S. (1989), Lie Group Analysis and Similarity Solutions for the Equation ∂2u∂2x2+∂2u∂2y2+∂2(eu)∂2z2=0, Nonlinear Analysis, Theory Methods Applications, Vol. 13, No. 5, 1989, 489505.Search in Google Scholar

5. Euler N., Steeb W.-H. (1992), Continuous Symmetries, Lie Algebras and Differential Equations, Brockhaus AG, Mannheim.Search in Google Scholar

6. Head A. K. (1993), LIE a PC Program for Lie Analysis of Differential Equations, Computer Physics Communications, Vol. 71, 241-248.Search in Google Scholar

7. Head A. K. (1996), Instructions for Program LIE ver. 4.5, CSIRO, Australia.Search in Google Scholar

8. Lie S. (1891), Vorlesungen iiber Differentialgleichungen mit bekannten infinitesimalen Transformationen, Teubner, Leipzig.Search in Google Scholar

9. Lie S. (1896), Geometrie der Beriihrungstransformationen, Teubner, Leipzig.Search in Google Scholar

10. Olver P. J. (1986), Applications of Lie Groups to Differential Equations, Springer-Verlag, New York.10.1007/978-1-4684-0274-2Search in Google Scholar

11. Sansour C., Bednarczyk H. (1991), Shells at Finite Rotations with Drilling Degrees of Freedom, Theory and Finite Element Formulation, In: Glowinski R., Ed., Computing Methods in Applied Sciences and Engineering, Nova Sci. Publish., New York, 163-173.Search in Google Scholar

12. Sansour C., Bednarczyk H. (1995), The Cosserat Surface as a Shell Model, Theory and Finite-Element Formulation, Computer Methods in Applied Mechanical Engineering, Vol. 120, 1-32.Search in Google Scholar

13. Sansour C., Bufler H. (1992), An Exact Finite Rotation Shell Theory, its Mixed Variational Formulation, and its Finite Element Implementation, International Journal for Numerical Methods in Engineering, Vol. 34, 73-115.Search in Google Scholar

14. Schwarz F. (1982), Symmetries of the Two-Dimensional Korteweg-de Vries Equation, Journal of the Physical Society of Japan, Vol. 51, No. 8, 2387-2388.Search in Google Scholar

15. Schwarz F. (1984), Lie Symmetries of the von Karman Equations, Computer Physics Communications, Vol. 31, 113-114.Search in Google Scholar

16. Schwarz F. (1988), Symmetries of Differential Equations from Sophus Lie to Computer Algebra. SIAM Review, Vol. 30, No. 3, 450481.Search in Google Scholar

17. Sherring J., Head A. K., Prince G. E. (1997), DIMSYM and LIE: Symmetry Determination Packages. Algorithms and Software for Symbolic Analysis of Nonlinear Systems, Mathematical and Computer Modelling, Vol. 25, No. 8-9, 153-164.10.1016/S0895-7177(97)00066-6Search in Google Scholar

18. Simo J. C., Fox D. D. (1989), On a Stress Resultant Geometrically Exact Shell Model, Part I.: Formulation and Optimal Parametrization, Computer Methods in Applied Mechanics and Engineering, Vol. 72, 267-304.10.1016/0045-7825(89)90002-9Search in Google Scholar

19. Vu K. T., Jefferson G. F., Carminati J. (2012), Finding Higher Symmetries of Differential Equations Using the MAPLE Package DESOLVII, Computer Physics Communications, Vol. 183, No. 4, 1044-1054.Search in Google Scholar