Variational Formulation of a Model Free-Boundary Problem

Formulation of a Model Free-boundary Problem

The purpose of this work is to present an error analysis of the numerical approximation by a finite element method of a free-surface problem. The analysis has been done in an abstract model which has many of the features of a free-surface problem for a viscous liquid. We study in this paper how the numerical approximation of the free boundary affects the approximation of the other variables of ...

Variational Iteration Method for Free Vibration Analysis of a Timoshenko Beam under Various Boundary Conditions

In this paper, a relatively new method, namely variational iteration method (VIM), is developed for free vibration analysis of a Timoshenko beam with different boundary conditions. In the VIM, an appropriate Lagrange multiplier is first chosen according to order of the governing differential equation of the boundary value problem, and then an iteration process is used till the desired accuracy ...

A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids

A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids is presented. The coupled thermo-mechanical boundary-value problem under consideration consists of the equilibrium problem for a deformable, inelastic and dissipative solid with the heat conduction problem appended in addition. The variational formulation allows for general dissipati...

Free and constrained equilibrium states in a variational problem on a surface

We study the equilibrium states for an energy functional with a parametric force field on a region of a surface. Consideration of free equilibrium states is based on Lyusternik - Schnirelman's and Skrypnik's variational methods. Consideration of equilibrium states under a constraint of geometrical character is based on an analog of Skrypnik's method, described in [P. Vyridis, {it Bifurcation in...

Variational Modeling of Parabolic Free Boundary Problems