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- W2022278564 abstract "The homogeneous Navier equations o2 u + yo(o· u ) = 0, (y = (u + w)/w = 1/(1-2 v ), with homogeneous boundary conditions of place or traction admit non-trivial solutions when y takes values in a set of points (lying of course outside the physical range for Poisson's ratio) called the Cosserat spectrum. The properties of the spectrum and the corresponding eigenfunctions were studied by S.G. Mikhlin who proved completeness, and orthogonality, to be reviewed here briefly. By using these properties we investigate how solutions of the equations of elasticity depend on Poisson's ratio. Furthermore we show that any eigenfunction u of the above eigenvalue problem may be visualized as displacement in an equilibrium thermoelastic problem with temperature distributions T div u . Using that the collection of the divergences of the eigenfunctions is complete in L 2 we are able to expand the solutions of the equilibrium equations of thermoelasticity under arbitrary temperature distribution in a rapidly convergent series of the eigenfunctions. We prove that the eigenfunctions can be characterized as stationary points of the Helmholtz free energy (and elastic energy) under the constraint that the thermal part of the free energy Z T 2dV is constant." @default.
- W2022278564 created "2016-06-24" @default.
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- W2022278564 date "1998-02-08" @default.
- W2022278564 modified "2023-09-26" @default.
- W2022278564 title "The Cosserat spectrum in the theory of elasticity and applications" @default.
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- W2022278564 doi "https://doi.org/10.1098/rspa.1998.0177" @default.
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