In the context of structural optimization via a level-set method we propose a framework to handle geometric constraints related to a notion of local thickness. The local thickness is calculated using the signed distance function to the shape. We formulate global constraints using integral functionals and compute their shape derivatives. We discuss different strategies and possible approximation...

The goal of this paper is to improve the performance of an electric motor by modifying the geometry of a specific part of the iron core of its rotor. To be more precise, the objective is to smooth the rotation pattern of the rotor. A shape optimization problem is formulated by introducing a tracking-type cost functional to match a desired rotation pattern. The magnetic field generated by perman...

In this paper, we focus on the following general shape optimization problem: min{J(Ω), Ω convex, Ω ∈ Sad}, where Sad is a set of 2-dimensional admissible shapes and J : Sad → R is a shape functional. Using a specific parameterization of the set of convex domains, we derive some extremality conditions (first and second order) for this kind of problem. Moreover, we use these optimality conditions...

the shape of wake behind a wind turbine is normally assumed to have a hat shape for the models used in wind farm layout optimization purposes; however, it is know from experimental tests and numerical simulations that this is not a real assumption. in reality, the results of actual measurements and detailed numerical simulation show that the velocity in wake region has a s-shape profile. the pr...

An embedding domain method for mixed boundary value problems is derived and applied to a class of shape optimization problems. The derivative of the cost with respect to the shape is characterized in terms of the Lagrange multipliers for the pri-mal and the adjoint problem. Numerical results illustrating the eeciency of the method which is related to a mixed nite element method are presented.

Article history: Received 26 November 2009 Received in revised form 22 April 2010 Accepted 8 June 2010 Available online xxxx

In recent years, it has become obvious that deterministic optimization of structures no longer is appropriate. Increasing demands with respect to safety, reliability and quality in structural engineering require the integration of probabilistic phenomena as well as the consideration of real-world stochastic processes induced in the structures. Within the present contribution two distinct resear...

A practical three-dimensional shape optimization for aerodynamic design of a transonic wing has been performed using Evolutionary Algorithms (EAs). Because EAs coupled with aerodynamic function evaluations require enormous computational time, Numerical Wind Tunnel (NWT) located at National Aerospace Laboratory in Japan has been utilized based on the simple master-slave concept. Parallel process...

In this paper, we are interested in the application to video segmentation of the discrete shape optimization problem

We consider a non-local shape optimization problem, which is motivated by a simple model for swarming and other self-assembly/aggregation models, and prove the existence of different phases. A technical key ingredient, which we establish, is that a strictly subharmonic function cannot be constant on a set of positive measure.