Spacetime evolutive equilibrium in Nonlinear Continuum Mechanics
نویسندگان
چکیده
Abstract In Continuum Mechanics a widely cited formula, due to Nanson (Mess Math 7:182–185, 1878), contributes the relation between product of area and unit normal vectors relevant corresponding surfaces in two configurations 3D body. A geometric treatment provides equivalent expressions formula by direct elaborations on Euler – Jacobi volume change formula. Meaning limits are underlined. literature this has been improperly assumed be expedient for attempts imposing equilibrium reference shape critical revision shows recourse scaling parallel transport surface bulk forces is impassable assessing alleged referential equilibrium. variational formulation evolutive spacetime developed finite step elastic problems guided control algorithms computational procedures illustrated. Step-by-step iterative methods solution nonlinear structural simple counterexamples should help convincing equilibria not conceivable Nonlinear Mechanics.
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ژورنال
عنوان ژورنال: Continuum Mechanics and Thermodynamics
سال: 2023
ISSN: ['0935-1175', '1432-0959']
DOI: https://doi.org/10.1007/s00161-023-01213-z