An eigenvalue problem for tensors used in mechanics and the number of independent Saint-Venant strain compatibility conditions
- 17 Downloads
A number of questions concerning the eigenvalue problem for a tensor \(\mathop A\limits_ \approx\) ∈ ℝ4(Ω) with special symmetries are considered; here Ω is a domain of a four-dimensional (three-dimensional) Riemannian space. It is proved that a nonsingular fourth-rank tensor has no more than six (three) independent components in the case of a four-dimensional (three-dimensional) Riemannian space. It is shown that the number of independent Saint-Venant strain compatibility conditions is less than six.
Unable to display preview. Download preview PDF.
- 3.M. U. Nikabadze, “On Some Questions of Tensor Calculus with Applications to Mechanics,” in Tensor Analysis (RUDN Univ., Moscow, 2015), Vol. 55, pp. 3–194.Google Scholar
- 6.Ya. Rykhlevskii, Mathematical Structure of Elastic Bodies, Preprint No. 217 (Institute for Problems in Mechanics, Moscow, 1983).Google Scholar
- 7.N. I. Ostrosablin, Anisotropy and General Solutions of Equations in the Linear Theory of Elasticity, Doctoral Dissertation in Mathematics and Physics (Hydromechanics Inst., Novosibirsk, 2000).Google Scholar
- 9.B. E. Pobedrya, Numerical Methods in the Theory of Elasticity and Plasticity, 2nd ed. (Mosk. Gos. Univ., Moscow, 1995) [in Russian].Google Scholar
- 10.B. E. Pobedrya, S. V. Sheshenin, and T. Kholmatov, Problems in Terms of Stresses (Fan, Tashkent, 1988) [in Russian].Google Scholar