Symbolic Calculations in Non-Linear Continuum Mechanics

A.N. Papusha
Department of Theoretical Mechanics
Murmansk State Technical University
Sportivnay, 13, 183010, Murmansk, Russia

A new symbolic technique in Continuum Mechanics is presented by using tensor calculation features of Mathematica.

We describe deriving of deformation equations and static equations of stresses in the non-linear theory of elasticity of an elastic body. The equations are expressed in any orthonormal basis of a curved line. In our notebook we develop the non-linear equations of balance. Our approach differs from the well known and widely used methods described earlier in the famous TextBooks on the theory of elasticity [1,2].

1. Green A.E., Adkins J.E. Large Elastic Deformations and Non-Linear Continuum Mechanics. Oxford, Clarendon Press, 1960, 457 p.
2. Truesdell I.C. The mechanical foundations of elastisity and fluid dynamics. Journal of Rational Mechanics and Analysis. 1952, v.1, pp.125-134.
3. Papusha A.N. Mathematica in Non-Linear Elasticity Theory. Innovations in Mathematics. Proceedings of Second International Mathematica Symposium. Computational Mechanics Publication, Southampton, Boston, 1997, pp. 383-390.