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...
Original title unknown
Padesát let metody konečných prvků
Parallel solution of elasticity problems using overlapping aggregations
The finite element (FE) solution of geotechnical elasticity problems leads to the solution of a large system of linear equations. For solving the system, we use the preconditioned conjugate gradient (PCG) method with two-level additive Schwarz preconditioner. The preconditioning is realised in parallel. A coarse space is usually constructed using an aggregation technique. If the finite element spaces for coarse and fine problems on structural grids are fully compatible, relations between elements...
Preconditioning discrete approximations of the Reissner-Mindlin plate model
Preconditioning of nonsymmetric saddle point systems as arising in modelling of viscoelastic problems.
Problèmes soulevés par la programmation de la méthode des éléments finis
Processes in concrete during fire
Paper deals with hydro-thermal performance of concrete exposed to a fire. It is introduced mathematical model, numerical approach and some results provided by the model.
Punktweise Konvergenz der Methode der finiten Elemente beim Plattenproblem.
Quadratic finite elements with non-matching grids for the unilateral boundary contact
We analyze a numerical model for the Signorini unilateral contact, based on the mortar method, in the quadratic finite element context. The mortar frame enables one to use non-matching grids and brings facilities in the mesh generation of different components of a complex system. The convergence rates we state here are similar to those already obtained for the Signorini problem when discretized on conforming meshes. The matching for the unilateral contact driven by mortars preserves then the proper...
Reissner-Mindlin model for plates of variable thickness. Solution by mixed-interpolated elements
Hard clamped and hard simply supported elastic plate is considered. The mixed finite element analysis combined with some interpolation, proposed by Brezzi, Fortin and Stenberg, is extended to the case of variable thickness and anisotropic material.