Search results for "shape optimization"
showing 10 items of 44 documents
Fixed domain approaches in shape optimization problems with Dirichlet boundary conditions
2009
Fixed domain methods have well-known advantages in the solution of variable domain problems including inverse interface problems. This paper examines two new control approaches to optimal design problems governed by general elliptic boundary value problems with Dirichlet boundary conditions. Numerical experiments are also included peerReviewed
Contact Shape Optimization
1995
Shape optimization is a branch of the optimal control theory in which the control variable is connected with the geometry of the problem. The aim is to find a shape from an a priori defined class of domains, for wich the corresponding cost functional attains its minimum. Shape optimization of mechanical systems, behaviour of which is described by equations, has been very well analyzed from the mathematical, as well as from the mechanical point of view, see [1], [2], [3] and references therein. The aim of this contribution is to extend results to the case, in which the system is described by the so called variational inequalities. There are two reasons for doing that: 1) The behavior of many…
Shape Optimization in Contact Problems. 1. Design of an Elastic Body. 2. Design of an Elastic Perfectly Plastic Body
1986
The optimal shape design of a two dimensional body on a rigid foundation is analyzed. The problem is how to find the boundary part of the body where the unilateral boundary conditions are assumed in such a way that a certain energy integral (total potential energy, for example) will be minimized. It is assumed that the material of the body is elastic. Some remarks will be given concerning the design of an elastic perfectly plastic body. Numerical examples will be given.
Shape design optimization in 2D aerodynamics using Genetic Algorithms on parallel computers
1996
Publisher Summary This chapter presents two Shape Optimization problems for two dimensional airfoil designs. The first one is a reconstruction problem for an airfoil when the velocity of the flow is known on the surface of airfoil. The second problem is to minimize the shock drag of an airfoil at transonic regime. The flow is modeled by the full potential equations. The discretization of the state equation is done using the finite element method and the resulting non-linear system of equations is solved by using a multi-grid method. The non-linear minimization process corresponding to the shape optimization problems are solved by a parallel implementation of a genetic algorithm (GA). Some n…
Sharp estimates and saturation phenomena for a nonlocal eigenvalue problem
2011
Abstract We determine the shape which minimizes, among domains with given measure, the first eigenvalue of a nonlocal operator consisting of a perturbation of the standard Dirichlet Laplacian by an integral of the unknown function. We show that this problem displays a saturation behaviour in that the corresponding value of the minimal eigenvalue increases with the weight affecting the average up to a (finite) critical value of this weight, and then remains constant. This critical point corresponds to a transition between optimal shapes, from one ball as in the Faber–Krahn inequality to two equal balls.
Wind tunnel testing, numerical analyses and shape optimization of a vertical axis wind turbine
2011
In this work the aerodynamic efficiency of a small commercial vertical axis wind turbine is investigated experimentally and numerically. The turbine is a Darrieus type with three vertical airfoil blades having helical twist of 78 degrees, height 1.45m and diameter of 1.45m. The airfoils have a chord of 222 mm and a thickness of 35 mm. The experimental studies were made in a wind tunnel where a hot-wire anemometer was used to measure the wind speed. The power curves of the turbine were extracted using a generator connected with an inverter able to vary the resistant moment applied to the turbine and to measure its resulting angular speed. The energy produced by the turbine itself at various …
On the Methods for Optimal Shape Design
1990
A short survey of the numerical methods for solving optimal shape design problems is given.
THE TOPOLOGY OPTIMIZATION IN THE PRODUCT DESIGN PROCESS
2009
The design process represents, already for a long time now, a very interesting research field for the scientific community that has tried, through its own activity of research and development, to make it faster, more reliable and efficient. Thanks to this continuous development, during the last years, the product design process has suffered a remarkable improvement, both regarding the methodological aspect, become mostly structured, objective and rational, and as regards the helping tools for the design like, for example, the software CAD, FEM, CFD, that have been improved in their efficiency and functionality. In this context, the development of more and more reliable and simple to use met…
Definition of a mutual reference shape based on information theory and active contours
2013
In this paper, we propose to consider the estimation of a reference shape from a set of different segmentation results using both active contours and information theory. The reference shape is then defined as the minimum of a criterion that benefits from both the mutual information and the joint entropy of the input segmentations. This energy criterion is here justified using similarities between information theory quantities and area measures, and presented in a continuous variational framework. This framework brings out some interesting evaluation measures such as the specificity and sensitivity. In order to solve this shape optimization problem, shape derivatives are computed for each te…
Multiobjective muffler shape optimization with hybrid acoustics modelling
2010
Shape optimization of a duct system with respect to sound transmission loss is considered. The objective of optimization is to maximize the sound transmission loss at multiple frequency ranges simultaneously by adjusting the shape of a reactive muffler component. The noise reduction problem is formulated as a multiobjective optimization problem. The sound attenuation for each considered frequency is determined by a hybrid method, which requires solving Helmholtz equation numerically by finite element method. The optimization is performed using non-dominated sorting genetic algorithm, NSGA-II, which is a multi-objective genetic algorithm. The hybrid numerical method is flexible with respect …