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Notes on stresses for manifolds. (English) Zbl 1162.74321
Summary: The geometric structure of stress theory on differentiable manifolds is considered. Mechanics is assumed to take place on an \(m\)-dimensional and no additional metric or parallelism structure is assumed. Two different approaches are described. The first is a generalisation of the traditional Cauchy approach where the resulting stresses are represented mathematically as vector valued \((m- 1)\)-forms. The second approach is variational and stresses are represented by densities valued in the dual of the first jet bundle. It is shown how a variational stress induces a Cauchy stress.
MSC:
74A10 Stress
58A05 Differentiable manifolds, foundations
58Z05 Applications of global analysis to the sciences
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