Shape optimization in contact problems. Approximation and numerical realization
Shape optimization in contact problems based on penalization of the state inequality
The paper deals with the approximation of optimal shape of elastic bodies, unilaterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established.
Shape optimization in two-dimensional elasticity by the dual finite element method
Shape optimization of an elasto-perfectly plastic body
Within the range of Prandtl-Reuss model of elasto-plasticity the following optimal design problem is solved. Given body forces and surface tractions, a part of the boundary, where the (two-dimensional) body is fixed, is to be found, so as to minimize an integral of the squared yield function. The state problem is formulated in terms of stresses by means of a time-dependent variational inequality. For approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant...
Shape optimization of an elasto-plastic body for the model with strain- hardening
The state problem of elasto-plasticity (for the model with strain-hardening) is formulated in terms of stresses and hardening parameters by means of a time-dependent variational inequality. The optimal design problem is to find the shape of a part of the boundary such that a given cost functional is minimized. For the approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant triangular elements for the stress and the hardening parameter, and backward differences...
Shape optimization of elastic axisymmetric bodies
The shape of the meridian curve of an elastic body is optimized within a class of Lipschitz functions. Only axisymmetric mixed boundary value problems are considered. Four different cost functionals are used and approximate piecewise linear solutions defined on the basis of a finite element technique. Some convergence and existence results are derived by means of the theory of the appropriate weighted Sobolev spaces.
Shape optimization of elasto-plastic axisymmetric bodies
A minimization of a cost functional with respect to a part of a boundary is considered for an elasto-plastic axisymmetric body obeying Hencky's law. The principle of Haar-Kármán and piecewise linear stress approximations are used to solve the state problem. A convergence result and the existence of an optimal boundary is proved.
Shape optimization of elastoplastic bodies obeying Hencky's law
A minimization of a cost functional with respect to a part of the boundary, where the body is fixed, is considered. The criterion is defined by an integral of a yield function. The principle of Haar-Kármán and piecewise constant stress approximations are used to solve the state problem. A convergence result and the existence of an optimal boundary is proved.
Simulation and design of extraction and separation fluidic devices
We present the combination of a state control and shape design approaches for the optimization of micro-fluidic channels used for sample extraction and separation of chemical species existing in a buffer solution. The aim is to improve the extraction and identification capacities of electroosmotic micro-fluidic devices by avoiding dispersion of the extracted advected band.
Simulation and design of extraction and separation fluidic devices
We present the combination of a state control and shape design approaches for the optimization of micro-fluidic channels used for sample extraction and separation of chemical species existing in a buffer solution. The aim is to improve the extraction and identification capacities of electroosmotic micro-fluidic devices by avoiding dispersion of the extracted advected band.
Simulation of anisotropic motion by mean curvature -- comparison of phase field and sharp interface approaches.
Singular Perturbations For Heart Image Segmentation Tracking
In this note we give a result of convergence when time goes to infinity for a quasi static linear elastic model, the elastic tensor of which vanishes at infinity. This method is applied to segmentation of medical images, and improves the 'elastic deformable template' model introduced previously.
Singular solutions of a transmission problem in plane linear elasticity for wedge-shaped regions.
Singularity problems in linear elastodynamics
Slab analogy in theory and practice of conforming equilibrium stress models for finite element analysis of plane elastostatics
The fundamental problem in the application of the principle of complementary energy is the construction of suitable subsets that approximate the set of all statically admissible fields satisfying both the conditions of equilibrium inside the body and the static boundary conditions. The notion “slab analogy” is motivated and the interface conditions for the Airy stress function are established at the contact of two domains. Some spaces of types of conforming equilibrium stress elements, which can...
Solutions stables d'un problème simplifié de coque élastique
Some Equilibrium Finite Element Methods for Two- Dimensional Elasticity Problems.
Some methods for calculating stiffness properties of periodic structures
We present a general numerical method for calculating effective elastic properties of periodic structures based on the homogenization method. Some concrete numerical examples are presented.
Some new technics regarding the parallelisation of ZéBuLoN, an object oriented finite element code for structural mechanics
A finite element code, called ZéBuLoN was parallelised some years ago. This code is entirely written using an object oriented framework (C++ is the support language). The aim of this paper is to present some problems which arose during the parallelization, and some innovative solutions. Especially, a new concept of message passing is presented which allows to take into account SMP machines while still using the parallel virtual machine abstraction.
Some new technics regarding the parallelisation of ZéBuLoN, an object oriented finite element code for structural mechanics
A finite element code, called ZéBuLoN was parallelised some years ago. This code is entirely written using an object oriented framework (C++ is the support language). The aim of this paper is to present some problems which arose during the parallelization, and some innovative solutions. Especially, a new concept of message passing is presented which allows to take into account SMP machines while still using the parallel virtual machine abstraction.