On the economical solution method for a system of linear algebraic equations.
On the existence of a weak solution of the boundary value problem for the equilibrium of a shallow shell reinforced with stiffening ribs
The existence and the unicity of a weak solution of the boundary value problem for a shallow shell reinforced with stiffening ribs is proved by the direct variational method. The boundary value problem is solved in the space , on which the corresponding bilinear form is coercive. A finite element method for numerical solution is introduced. The approximate solutions converge to a weak solution in the space .
On the frictionless unilateral contact of two viscoelastic bodies.
On the Mixed Finite Element Approximation for the Buckling of Plates.
On the nonlinear behaviour of bimodular multilayer ed plates.
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...
On the Numerical Analysis of the Von Karman Equations : Mixed Finite Element Approximation and Continuation Techniques.
On the numerical modeling of deformations of pressurized martensitic thin films
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.
On the Numerical Modeling of Deformations of Pressurized Martensitic Thin Films
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.
On the numerical solution of plate bending problems by hybrid methods
On the solution of a finite element approximation of a linear obstacle plate problem
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...
On the solution of a plate with ribs
On the solution of one problem of the plate with ribs
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).
On the Unilateral Contact Between Membranes. Part 1: Finite Element Discretization and Mixed Reformulation
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...
Operator-splitting schemes for solving elasticity problems.
Optimal error estimates for FEM approximations of dynamic nonlinear shallow shells
Optimal error estimates for FEM approximations of dynamic nonlinear shallow shells
Finite element semidiscrete approximations on nonlinear dynamic shallow shell models in considered. It is shown that the algorithm leads to global, optimal rates of convergence. The result presented in the paper improves upon the existing literature where the rates of convergence were derived for small initial data only [19].
Optimal L...-Error Estimates for Nonconforming and Mixed Finite Element Methods of Lowest Order.
Optimization of the shape of axisymmetric shells
Axisymmetric thin elastic shells of constant thickness are considered and the meridian curves of their middle surfaces taken for the design variable. Admissible functions are smooth curves of a given length, which are uniformly bounded together with their first and second derivatives, and such that the shell contains a given volume. The loading consists of the hydrostatic pressure of a liquid, the shell's own weight and the internal or external pressure. As the cost functional, the integral of the...
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