Abstract
A method is developed for a full nonlinear evaluation of all velocities and stresses represented in the Navier-Stokes equations and in the general stress tensor. The information required is essentially that for solution of linearized forms. The solution is analytical except for the calculation of the axial velocity, which requires computer assistance to step through time and space. The treatment of the problem, although directed towards solutions involving fluid flow in elastic vessels, is also adaptable to solid deformations (strain vs rate of strain) where the general stress tensor applies. A special case for the distorting ellipse is presented as well as a limited, spatially analytic, solution.
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Melbin, J., Noordergraaf, A. General solution for flow and stress phenomena in elastic vessles (Navier-Stokes). Bltn Mathcal Biology 44, 29–42 (1982). https://doi.org/10.1007/BF02459417
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DOI: https://doi.org/10.1007/BF02459417