On the algebra of two-point tensors and their applications. (English) Zbl 0894.15017
The authors point out that the definition of the transpose of two-point tensors of F. G. Kollmann and H.-P. Hackenberg [Z. Angew. Math. Mech. 73, No. 11, 307-314 (1993; Zbl 0793.15021)] is well known in the mathematical literature, and is called the adjoint of two-point tensors. A short discussion on the use of the adjoint of two-point tensors in nonlinear continuum mechanics is also provided.
Reviewer: V.L.Popov (Moskva)
MSC:
| 15A72 | Vector and tensor algebra, theory of invariants |
| 74A99 | Generalities, axiomatics, foundations of continuum mechanics of solids |
| 53A45 | Differential geometric aspects in vector and tensor analysis |
| 70G45 | Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics |
Citations:
Zbl 0793.15021References:
| [1] | : Continuum mechanics, John Wiley & Sons, New York 1976. · Zbl 0329.73003 |
| [2] | ; : Applicable differential geometry. Cambridge University Press, New York 1988. |
| [3] | Kollmann, Z. Angew. Math. Mech. 73 pp 307– (1993) |
| [4] | : Introduction to the mechanics of a continuous medium. Prentice-Hall, Inc., Englewood Cliffs, New Jersey 1969. |
| [5] | ; : Mathematical foundations of elasticity. Prentice-Hall, New Jersey 1983. · Zbl 0545.73031 |
| [6] | : Lecture notes on geometrically-exact shell theory. University of Florida, Gainesville, FL 32511, USA 1990. |
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