Conservation properties for plane deformations of anisotropic linearly elastic curved strips (Q1805165)

The plane deformation problem is considered for a curved strip \(R=\{ (r,\theta) \mid a< r< b\), \(0< \theta< \theta^*\}\) composed of an homogeneous cylindrically anisotropic linearly elastic material. The strip is supposed to be in equilibrium under the action of end loads keeping the lateral sides traction-free. Generalizing previously known results in the case of rectangular strip [see \textit{J. N. Flavin} and \textit{R. J. Knops} in Z. Angew. Math. Phys. 39, No. 2, 166-176 (1988; Zbl 0644.73025) and \textit{C. O. Horjan} in Q. Appl. Math. 47, 147-157 (1989; Zbl 0692.35010)], the author establishes two conservation properties for certain cross-sectional stress measure. Conservation properties of this kind are useful in assessing the influence of material anisotropy on Saint-Venant's principle, as well as in establishing convexity properties for cross-sectional stress measures. In the author's opinion, such results should be useful in determining the extent of edge effects in the testing of anisotropic and composite curved strips.