A linear theory of thin elastic shells, based on conservation of a non-normal straight line

Epstein, Marcelo; Tene, Yair

doi:10.1016/0020-7683(73)90103-0

Cited by 5 publications

(1 citation statement)

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“…For the unique determination of the tangent surface stress, one needs at least some specified vector field which is transversal to the boundary or an equivalent structure. The situation is similar to that described in Epstein and Tene (1973); Epstein and de León (1998), where shell theory is considered. Evidently, for the case of a Riemannian manifold, the unit normal vector field provides such a transversal field naturally.…”

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confidence: 70%

Geometric analysis of hyper-stresses

Segev

2017

International Journal of Engineering Science

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A. A geometric analysis of high order stresses in continuum mechanics is presented. Virtual velocity fields take their values in a vector bundle W over the n-dimensional space manifold. A stress field of order k is represented mathematically by an n-form valued in the dual of the vector bundle of k-jets of W . While only limited analysis can be performed on high order stresses as such, they may be represented by non-holonomic hyper-stresses, n-forms valued in the duals of iterated jet bundles. For non-holonomic hyperstresses, the analysis that applies to first order stresses may be iterated. In order to determine a unique value for the tangent surface stress field on the boundary of a body and the corresponding edge interactions, additional geometric structure should be specified, that of a vector field transversal to the boundary.2000 Mathematics Subject Classification. 74A10; 53Z05; 58A32 .

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confidence: 70%