On a boundary value problem in nonlinear theory of thin elastic plates
On a contact problem for a viscoelastic von Kármán plate and its semidiscretization
We deal with the system describing moderately large deflections of thin viscoelastic plates with an inner obstacle. In the case of a long memory the system consists of an integro-differential 4th order variational inequality for the deflection and an equation with a biharmonic left-hand side and an integro-differential right-hand side for the Airy stress function. The existence of a solution in a special case of the Dirichlet-Prony series is verified by transforming the problem into a sequence of...
On a coupled problem between the plate equation and the membrane equation on polygons
On a cylindrical bending of a prismatic shell with two cusped edges under action of an incompressible viscous fluid.
On a plane heat-conductivity theory problem with mixed boundary conditions.
On Asymptotic Theory of Beams, Plates and Shells
Bases of asymptotic theory of beams, plates and shells are stated. The comparison with classic theory is conducted. New classes of thin bodies problems, for which hypotheses of classic theory are not applicable, are considered. By the asymptotic method effective solutions of these problems are obtained. The effectiveness of the asymptotic method for finding solutions of as static, as well as dynamic problems of beams, plates and shells is shown.
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 dual integral equations arising in problems of bending of anisotropic plates.
On numerical solution of a variational inequality of the 4th order by finite element method
The problem of a thin elastic plate, deflection of which is limited below by a rigid obstacle is solved. Using Ahlin's and Ari-Adini's elements on rectangles, the convergence is established and SOR method with constraints is proposed for numerical solution.
On one type of integro-differential equations.
On Signorini problem for von Kármán equations
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 solvability of one special problem of coupled thermoelasticity. I. Classical boundary conditions and steady sources
On some unilateral boundary value problems for the von Kármán equations. Part I: The coercive case
On the accuracy of asymptotic approximations for longitudinal deformation of a thin plate
On the accuracy of Reissner–Mindlin plate model for stress boundary conditions
For a plate subject to stress boundary condition, the deformation determined by the Reissner–Mindlin plate bending model could be bending dominated, transverse shear dominated, or neither (intermediate), depending on the load. We show that the Reissner–Mindlin model has a wider range of applicability than the Kirchhoff–Love model, but it does not always converge to the elasticity theory. In the case of bending domination, both the two models are accurate. In the case of transverse shear domination, the...
On the asymptotics of the spectrum of a thin plate problem of elasticity.
On the control of stability in nonlinear mechanics
On the convergence of a mixed finite element method for Reissner-Mindlin plates
On the dynamical behaviour of plates in unilateral contact with an elastic foundation: a finite element approach.
In questo lavoro viene studiato il comportamento dinamico di una piastra vincolata monolateralmente su una fondazione elastica alla Winkler. Si presentano alcuni risultati numerici ottenuti mediante discretizzazione agli elementi finiti. Tali risultati mettono in luce l'influenza di alcuni fattori tipici come le funzioni di forma, il parametro di mesh e l'ampiezza dell'intervallo con cui si realizza l'integrazione nel tempo delle equazioni del moto. Si istituiscono infine dei confronti con risultati...