Displaying similar documents to “Singularity problems in linear elastodynamics”

On the stability of multipolar elastic materials.

N. S. Wilkes (1979)

Stochastica

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In 1964, Green and Rivlin [1, 2] proposed two non-standard theories of continua. Both papers concerned non-simple materials: the first considered deformation gradients of higher order than the first as dependent variables; and the second, which generalised the first, treated materials whose kinematic state was not completely detemined by the deformation function, but was also dependent upon some multipolar deformation functions. In both theories the existence of higher order stresses...

A note on prestressed thermoelastic bodies.

Ramón Quintanilla (1991)

Collectanea Mathematica

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This note is concerned with the ill-posed problem for prestressed thermoelastic bodies. Under suitable hypotheses for the thermoelastic coefficients, the domain and the behavior of solutions at infinity, we prove uniqueness of the solutions. We also obtain some estimates for the solutions related with the initial condition.

Stress equations of motion of Ignaczak type for the second axisymmetric problem of micropolar elastodynamics

Janusz Dyszlewicz (1997)

Applicationes Mathematicae

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A second axially-symmetric initial-boundary value problem of linear homogeneous isotropic micropolar elastodynamics in which the displacement and rotation take the forms u ̲ = ( 0 , u θ , 0 ) , φ ̲ = ( φ r , 0 , φ z ) ((r,θ,z) are cylindrical coordinates; cf. [17]) is formulated in a pure stress language similar to that of [12]. In particular, it is shown how u ̲ and φ ̲ can be recovered from a solution of the associated pure stress initial-boundary value problem, and how a singular solution corresponding to harmonic vibrations of...

Some qualitative results for the linear theory of binary mixtures of thermoelastic solids.

F. Martínez, R. Quintanilla (1995)

Collectanea Mathematica

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In this paper we study the linear thermodynamical problem of mixtures of thermoelastic solids. We use some results of the semigroup theory to obtain an existence theorem for the initial value problem with homogeneous Dirichlet boundary conditions. Continuous dependence of solutions upon the initial data and body forces is also established. We finish with a study of the asymptotic behavior of solutions of the homogeneous problem.

Some thoughts on the material mechanics of materials.

Gérard A. Maugin (1999)

Extracta Mathematicae

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This paper outlines recent developments and prospects in the application of the continuum mechanics expressed intrinsically on the material manifold itself. This includes applications to materially inhomogeneous materials, physical effects which, in this vision, manifest themselves as quasi-inhomogeneities, and the notion of thermodynamical driving force of the dissipative progress of singular point sets on the material manifold with special emphasis on fracture, shock waves and phase-transition...

Betti's reciprocal theorem for Cosserat elastic shells

Franco Pastrone (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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It is proved that, as in three-dimensional elasticity, Betti's theorem represents a criterion for the existence of a stored-energy function for a Cosserat elastic shell.