Geodesic
Restrictions on stress components in the vertices of regular triangular and quadrangular pyramids embedded in elastic body
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 62 (2019), pp. 119-134

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In the framework of continuous model of deformable bodies, each point of the continuum is associated with an elementary volume. The concepts of continuum mechanics regarding material properties and state parameters (stresses, strains) are applicable to this volume. In the paper, this statement extends to singular points which are the vertices of triangular and quadrangular pyramids embedded in an elastic body. The restrictions on the stress components at the considered points are studied. It is shown that the number of restrictions determines a non-classical formulation of the problem of mechanics of a deformable body. The dependences for material constants of the bonded elements, which lead to an unlimited increase in the stresses in the vertices of triangular and quadrangular pyramids immersed in an elastic medium, are found to be the same. Moreover, these dependences coincide with those known for a circular cone and a spatial edge. The investigation results will find application in the mechanics of composite materials when studying the samples by indentation or interaction with prismatic cantilevers.
Keywords: internal singular point, non-classical problem, elementary volume.
Mots-clés : stress concentration 
@article{VTGU_2019_62_a9,
     author = {V. M. Pestrenin and I. V. Pestrenina and L. V. Landik},
     title = {Restrictions on stress components in the vertices of regular triangular and quadrangular pyramids embedded in elastic body},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {119--134},
     publisher = {mathdoc},
     number = {62},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2019_62_a9/}
}
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V. M. Pestrenin; I. V. Pestrenina; L. V. Landik. Restrictions on stress components in the vertices of regular triangular and quadrangular pyramids embedded in elastic body. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 62 (2019), pp. 119-134. http://geodesic.mathdoc.fr/item/VTGU_2019_62_a9/