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An adaptive strategy for nonlinear finite-element analysis, based on the combination of error estimation and h-remeshing, is presented. Its two main ingredients are a residual-type error estimator and an unstructured quadrilateral mesh generator. The error estimator is based on simple local computations over the elements and the so-called patches. In contrast to other residual estimators, no flux splitting is required. The adaptive strategy is illustrated by means of a complex nonlinear problem:...
Here we present an approximation method for a rather broad class of first order
variational problems in spaces of piece-wise constant functions over
triangulations of the base domain. The convergence of the method is based on an
inequality involving norms obtained by Nečas and on the general
framework of Γ-convergence theory.
Development of user-friendly and flexible scientific programs is a key to their usage, extension and maintenance. This paper presents an OOP (Object-Oriented Programming) approach for design of finite element analysis programs. General organization of the developed software system, called FER/SubDomain, is given which includes the solver and the pre/post processors with a friendly GUI (Graphical User Interfaces). A case study with graphical representations illustrates some functionalities of the...
Development of user-friendly and flexible scientific programs is a key to their usage, extension and maintenance. This paper presents an OOP (Object-Oriented Programming) approach for design of finite element analysis programs. General organization of the developed software system, called FER/SubDomain, is given which includes the solver and the pre/post processors with a friendly GUI (Graphical User Interfaces). A case study with graphical representations illustrates some functionalities of the...
We consider linear elliptic systems which arise in coupled elastic continuum mechanical models. In these systems, the strain tensor εP := sym (P-1∇u) is redefined to include a matrix valued inhomogeneity P(x) which cannot be described by a space dependent fourth order elasticity tensor. Such systems arise naturally in geometrically exact plasticity or in problems with eigenstresses. The tensor field P induces a structural change of the elasticity equations. For such a model the FETI-DP method is...
We consider linear elliptic systems which arise
in coupled elastic continuum mechanical models. In these systems, the strain
tensor εP := sym (P-1∇u) is redefined to include a
matrix valued inhomogeneity P(x) which cannot be described by a space
dependent fourth order elasticity tensor. Such systems arise naturally in
geometrically exact plasticity or in problems with eigenstresses.
The tensor field P induces a structural change of the elasticity equations. For
such a model the FETI-DP method is...
A unilateral contact problem with a variable coefficient of friction is solved by a simplest variant of the finite element technique. The coefficient of friction may depend on the magnitude of the tangential displacement. The existence of an approximate solution and some a priori estimates are proved.
Free material optimization solves an important problem of structural engineering, i.e. to find the stiffest structure for given loads and boundary conditions. Its mathematical formulation leads to a saddle-point problem. It can be solved numerically by the finite element method. The convergence of the finite element method can be proved if the spaces involved satisfy suitable approximation assumptions. An example of a finite-element discretization is included.
This paper deals with a finite element method to solve fluid-structure
interaction problems.
More precisely it concerns the numerical computation of harmonic
hydroelastic vibrations under gravity.
It is based on a displacement formulation for both the fluid and the solid.
Gravity effects are included on the free surface of the fluid as well
as on the liquid-solid interface.
The pressure of the fluid is used as a variable for the theoretical
analysis leading to a well posed mixed linear eigenvalue...
The plane Signorini problem is considered in the cases, when there exist non-trivial rigid admissible displacements. The existence and uniqueness of the solution and the convergence of piecewise linear finite element approximations is discussed.
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