On the von Mises-Sternberg version of Saint-Venant's principle in plane linear elastostatics
The von Mises-Sternberg version of Saint-Venant's principle for a homogeneous isotropic elastic body subject to continuous surface traction fields (cf. The linear theory of elasticity, by \textit{M. E. Gurtin} [Encyclopedia of Physics Vol. VIa/2, pp. 190-196 (1972; Zbl 0277.73001)]) is extended to include a nonhomogeneous anisotropic but plane elastic body. The elasticity tensor \(\mathbb{C}\) is assumed to be bounded and measurable, so weak solutions to the governing equations are dealt with. Due to nonregularity of the first derivatives of the solutions, the strains are estimated in Morrey norms if \(\mathbb{C}\) is at most continuous, and in Hölder norms if \(\mathbb{C}\) is Hölder continuous. The estimation technique is based on a number of a priori estimates and some lemmas from functional analysis. The reviewer believes that the results obtained hold only if the problem is formulated in a dimensionless form. Otherwise, one can not calculate, for example, a norm in \(C^{0, \alpha}\) (except for \(\alpha= 0\)) in the main theorem, or use Hardy's inequality (6.2), etc. No mention is made, however, what system of units has been chosen to make the problem dimensionless.
scientific article; zbMATH DE number 754035
scientific article