Currently displaying 1 – 20 of 20

Showing per page

Order by Relevance | Title | Year of publication

An elastic membrane with an attached non-linear thermoelastic rod

Werner HornJan Sokołowski — 2002

International Journal of Applied Mathematics and Computer Science

We study a thermo-mechanical system consisting of an elastic membrane to which a shape-memory rod is glued. The slow movements of the membrane are controlled by the motions of the attached rods. A quasi-static model is used. We include the elastic feedback of the membrane on the rods. This results in investigating an elliptic boundary value problem in a domain Ω ⊂ R^2 with a cut, coupled with non-linear equations for the vertical motions of the rod and the temperature on the rod. We prove the existence...

Shape Sensitivity Analysis of the Dirichlet Laplacian in a Half-Space

Cherif AmroucheŠárka NečasováJan Sokołowski — 2004

Bulletin of the Polish Academy of Sciences. Mathematics

Material and shape derivatives for solutions to the Dirichlet Laplacian in a half-space are derived by an application of the speed method. The proposed method is general and can be used for shape sensitivity analysis in unbounded domains for the Neumann Laplacian as well as for the elasticity boundary value problems.

Selfadjoint Extensions for the Elasticity System in Shape Optimization

Serguei A. NazarovJan Sokołowski — 2004

Bulletin of the Polish Academy of Sciences. Mathematics

Two approaches are proposed to modelling of topological variations in elastic solids. The first approach is based on the theory of selfadjoint extensions of differential operators. In the second approach function spaces with separated asymptotics and point asymptotic conditions are introduced, and a variational formulation is established. For both approaches, accuracy estimates are derived.

Shape and topological sensitivity analysis in domains with cracks

Alexander KhludnevJan SokołowskiKatarzyna Szulc — 2010

Applications of Mathematics

The framework for shape and topology sensitivity analysis in geometrical domains with cracks is established for elastic bodies in two spatial dimensions. The equilibrium problem for the elastic body with cracks is considered. Inequality type boundary conditions are prescribed at the crack faces providing a non-penetration between the crack faces. Modelling of such problems in two spatial dimensions is presented with all necessary details for further applications in shape optimization in structural...

On the analysis of boundary value problems in nonsmooth domains

Problems involving cracks are of particular importance in structural mechanics, and gave rise to many interesting mathematical techniques to treat them. The difficulties stem from the singularities of domains, which yield lower regularity of solutions. Of particular interest are techniques which allow us to identify cracks and defects from the mechanical properties. Long before advent of mathematical modeling in structural mechanics, defects were identified by the fact that they changed the sound...

A level set method in shape and topology optimization for variational inequalities

Piotr FulmańskiAntoine LaurainJean-Francois ScheidJan Sokołowski — 2007

International Journal of Applied Mathematics and Computer Science

The level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology...

Analysis of crack singularities in an aging elastic material

Martin CostabelMonique DaugeSergeïA. NazarovJan Sokolowski — 2006

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a quasistatic system involving a Volterra kernel modelling an hereditarily-elastic aging body. We are concerned with the behavior of displacement and stress fields in the neighborhood of cracks. In this paper, we investigate the case of a straight crack in a two-dimensional domain with a possibly anisotropic material law. We study the asymptotics of the time dependent solution near the crack tips. We prove that, depending on the regularity of the material law and the Volterra kernel,...

Topological derivatives for semilinear elliptic equations

Mohamed IguernaneSerguei A. NazarovJean-Rodolphe RocheJan SokolowskiKatarzyna Szulc — 2009

International Journal of Applied Mathematics and Computer Science

The form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in the L∞ norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.

Page 1 Next

Download Results (CSV)