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Forced periodic vibrations of an elastic system with elastico-plastic damping

Pavel Krejčí (1988)

Aplikace matematiky

We prove the existence and find necessary and sufficient conditions for the uniqueness of the time-periodic solution to the equations u t t - Δ x u ± F ( u ) = g ( x , t ) for an arbitrary (sufficiently smooth) periodic right-hand side g , where Δ x denotes the Laplace operator with respect to x ∈ Ω ⊂ R N , N ≥ 1 , and F is the Ishlinskii hysteresis operator. For N = 2 this equation describes e.g. the vibrations of an elastic membrane in an elastico-plastic medium.

Mixed formulation for elastic problems - existence, approximation, and applications to Poisson structures

Julian Ławrynowicz, Alain Mignot, Loucas Papaloucas, Claude Surry (1996)

Banach Center Publications

A mixed formulation is given for elastic problems. Existence and uniqueness of the discretized problem are given for conformal continuous interpolations for the stress tensor components and for the components of the displacement vector. A counterpart of the problem is discussed in the case of an even-dimensional Euclidean space with an associated Hamiltonian vector field and the Poisson structure. For conformal interpolations of the same order the question remains open.

On general boundary value problems and duality in linear elasticity. I

Rolf Hünlich, Joachim Naumann (1978)

Aplikace matematiky

The equilibrium state of a deformable body under the action of body forces is described by the well known conditions of equilibrium, the straindisplacement relations, the constitutive law of the linear theory and the boundary conditions. The authors discuss in detail the boundary conditions. The starting point is the general relation between the vectors of stress and displacement on the boundary which can be expressed in terms of a subgradient relation. It is shown that this relation includes as...

On general boundary value problems and duality in linear elasticity. II

Rolf Hünlich, Joachim Naumann (1980)

Aplikace matematiky

The present part of the paper completes the discussion in Part I in two directions. Firstly, in Section 5 a number of existence theorems for a solution to Problem III (principle of minimum potential energy) is established. Secondly, Section 6 and 7 are devoted to a discussion of both the classical and the abstract approach to the duality theory as well as the relationship between the solvability of Problem III and its dual one.

On identification of critical curves

Jaroslav Haslinger, Václav Horák (1990)

Aplikace matematiky

The paper deals with the problem of finding a curve, going through the interior of the domain Ω , accross which the flux ∂ u / ∂ n , where u is the solution of a mixed elliptic boundary value problem solved in Ω , attains its maximum.

On one mathematical model of creep in superalloys

Jiří Vala (1998)

Applications of Mathematics

In a new micromechanical approach to the prediction of creep flow in composites with perfect matrix/particle interfaces, based on the nonlinear Maxwell viscoelastic model, taking into account a finite number of discrete slip systems in the matrix, has been suggested; high-temperature creep in such composites is conditioned by the dynamic recovery of the dislocation structure due to slip/climb motion of dislocations along the matrix/particle interfaces. In this article the proper formulation of the...

On the domain of influence in thermoelasticity of bodies with voids

Marin Marin (1997)

Archivum Mathematicum

The domain of influence, proposed by Cowin and Nunziato, is extended to cover the thermoelasticity of bodies with voids. We prove that for a finite time t > 0 the displacement field u i , the temperature θ and the change in volume fraction σ generate no disturbance outside a bounded domain B t .

Currently displaying 21 – 40 of 81