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In an earlier study [16] the nonlinear behaviour of unimodular laminated plates was studied. This paper, following the previous study, concerns a large deflection analysis of moderately thick rectangular plates having arbitrary boundary conditions and finite thickness shear moduli. The plates are manufactured in bimodular materials and constructed in a cross-ply fashion or in a single layer with arbitrary fibre direction angle. Numerical results are obtained by a finite element technique in which...
We propose, analyze, and compare several numerical methods for the computation of the deformation of a pressurized martensitic thin film. Numerical results have been obtained for the hysteresis of the deformation as the film transforms reversibly from austenite to martensite.
We propose, analyze, and compare several numerical methods for the
computation of the deformation of a pressurized martensitic thin
film. Numerical results have been obtained for the hysteresis of
the deformation as the film transforms reversibly from austenite to
martensite.
The following possibilities of reduction of dimension in the computational analysis of strain and stresses transferred to the subsoil massive are available: i) coming from the effective subsoil model by Kolář & Němec (1989), based on the assumptions of the Pasternak's model (1954), where the pair of material parameters of a surface model is evaluated from the energy equivalence, ii) reducing a large sparse matrix of soil massive stiffness to a smaller one, using Schur's complement technique....
The Signorini problem with friction in quasi-coupled linear thermo-elasticity (the 2D-case) is discussed. The problem is the model problem in the geodynamics. Using piecewise linear finite elements on the triangulation of the given domain, numerical procedures are proposed. The finite element analysis for the Signorini problem with friction on the contact boundary of a polygonal domain is given. The rate of convergence is proved if the exact solution is sufficiently regular.
In this paper the solution of a finite element approximation of a linear obstacle plate problem is investigated. A simple version of an interior point method and a block pivoting algorithm have been proposed for the solution of this problem. Special purpose implementations of these procedures are included and have been used in the solution of a set of test problems. The results of these experiences indicate that these procedures are quite efficient to deal with these instances and compare favourably...
A mathematical model of the equilibrium problem of elastic sandwich plates is established. Using the theory of inequalities of Korn's type for a general class of elliptic systems the existence and uniqueness of a variational solution is proved.
In the present paper the convergence of the finite element method to the solution of the problem of a plate with ribs which are stiff against torsion in the sense of Vlasov is studied. According to the conclusions of a paper by the author and J. Haslinger it suffices to prove a density theorem (Theorem 2.1).
A class of contact problems with friction in elastostatics is considered. Under a certain restriction on the friction coefficient, the convergence of the two-step iterative method proposed by P.D. Panagiotopoulos is proved. Its applicability is discussed and compared with two other iterative methods, and the computed results are presented.
The contact between two membranes can be described by a system of variational
inequalities, where the unknowns are the displacements of the membranes and the
action of a membrane on the other one. We first perform the analysis of this
system. We then propose a discretization, where the displacements are
approximated by standard finite elements and the action by a
local postprocessing. Such a discretization admits an equivalent mixed
reformulation. We prove the well-posedness of the discrete problem...
This article presents the principal results of the doctoral thesis “Direct Operational Methods
in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of
mathematics and Informatics, BAS), successfully defended before the Specialised Academic
Council for Informatics and Mathematical Modelling on 23 March, 2009.The presented research is related to the operational calculus
approach and its representative applications. Operational methods are considered,
as well as their...
We deal with an optimal control problem for variational inequalities, where the monotone operators as well as the convex sets of possible states depend on the control parameter. The existence theorem for the optimal control will be applied to the optimal design problems for an elasto-plastic beam and an elastic plate, where a variable thickness appears as a control variable.
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