On a plane heat-conductivity theory problem with mixed boundary conditions.
On a type of Signorini problem without friction in linear thermoelasticity
In the paper the Signorini problem without friction in the linear thermoelasticity for the steady-state case is investigated. The problem discussed is the model geodynamical problem, physical analysis of which is based on the plate tectonic hypothesis and the theory of thermoelasticity. The existence and unicity of the solution of the Signorini problem without friction for the steady-state case in the linear thermoelasticity as well as its finite element approximation is proved. It is known that...
On Cauchy's stress theorem
In this work a new proof of the theorem of Cauchy on the existence of the stress tensor is given which does not use the tetrahedron argument.
On classical dynamics of affinely-rigid bodies subject to the Kirchhoff-Love constraints.
On Cosserat continua
On coupled thermoelastic vibration of geometrically nonlinear thin plates satisfying generalized mechanical and thermal conditions on the boundary and on the surface
The vibration problem in two variables is derived from the spatial situation (a plate as a three-dimensional body) on the basis of geometrically nonlinear plate theory (using Kármán's hypothesis) and coupled linear thermoelasticity. That leads to coupled strongly nonlinear two-dimensional equilibrium and heat conducting equations (under classical mechanical and thermal boundary conditions). For the generalized problem with subgradient conditions on the boundary and in the domain (including also...
On elastic waves in a medium with randomly distributed cylinders.
On generalized thermoelastic disturbances in an elastic solid with a spherical cavity.
On implicit constitutive theories
In classical constitutive models such as the Navier-Stokes fluid model, and the Hookean or neo-Hookean solid models, the stress is given explicitly in terms of kinematical quantities. Models for viscoelastic and inelastic responses on the other hand are usually implicit relationships between the stress and the kinematical quantities. Another class of problems wherein it would be natural to develop implicit constitutive theories, though seldom resorted to, are models for bodies that are constrained....
On internal constraints in continuum mechanics.
On Lamb's plane problem in micropolar viscoelastic half-space with stretch.
On quasistatic inelastic models of gradient type with convex composite constitutive equations
This article defines and presents the mathematical analysis of a new class of models from the theory of inelastic deformations of metals. This new class, containing so called convex composite models, enlarges the class containing monotone models of gradient type defined in [1]. This paper starts to establish the existence theory for models from this new class; we restrict our investigations to the coercive and linear self-controlling case.
On Signorini problem for von Kármán equations. The case of angular domain
The paper deals with the generalized Signorini problem. The used method of pseudomonotone semicoercive operator inequality is introduced in the paper by O. John. The existence result for smooth domains from the paper by O. John is extended to technically significant "angular" domains. The crucial point of the proof is the estimation of the nonlinear term which appears in the operator form of the problem. The substantial technical difficulties connected with non-smoothness of the boundary are overcome...
On some contact problems for bodies with elastic inclusions.
On symmetrically growing bodies.
This work presents a setting for the formulation of the mechanics of growing bodies. By the mechanics of growing bodies we mean a theory in which the material structure of the body does not remain fixed. Material points may be added or removed from the body.
On the analysis of a viscoplastic contact problem with time dependent Tresca's friction law.
On the analysis of elastic layers by a Fourier series, Green's function approach
The plane strain elastic analysis of a homogeneous and isotropic layer of constant thickness, is formulated using Fourier series expansions in the direction parallel to the layer and suitable Green's functions in the transversal direction. For each frequency the unknown distributions of the Fourier coefficients relevant to the symmetric or skew-symmetric problems are governed by one-dimensional equations which can be solved exactly. The proposed method is used to critically discuss the "transfer"...
On the anelastic evolution of second-grade materials.
On the approximation of the Signorini problem with friction
On the Cauchy Problem in Nonlinear 3-d-Thermoelasticity.