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- W4367299060 abstract "Abstract In Continuum Mechanics a widely cited formula, due to Nanson (Mess Math 7:182–185, 1878), contributes the relation between the product of area and unit normal vectors relevant to corresponding surfaces in two configurations of a 3D body. A geometric treatment provides equivalent expressions of Nanson formula by direct elaborations on Euler – Jacobi volume change formula. Meaning and limits of Nanson formula are underlined. In the literature this formula has been improperly assumed to be expedient for attempts of imposing equilibrium in a reference shape of the body. A critical revision shows recourse to scaling and parallel transport of surface and bulk forces is impassable in assessing alleged referential equilibrium. A variational formulation of evolutive equilibrium in spacetime is developed and finite step elastic problems guided by control algorithms in computational procedures are illustrated. Step-by-step iterative methods of solution of nonlinear structural problems and simple counterexamples should help in convincing referential equilibria are not conceivable in Nonlinear Continuum Mechanics." @default.
- W4367299060 created "2023-04-29" @default.
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- W4367299060 date "2023-04-28" @default.
- W4367299060 modified "2023-09-30" @default.
- W4367299060 title "Spacetime evolutive equilibrium in Nonlinear Continuum Mechanics" @default.
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- W4367299060 doi "https://doi.org/10.1007/s00161-023-01213-z" @default.
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