The behaviour of solutions to fourth order problems is studied through the decomposition into a system of second order ones, which leads to relaxed formulations with the introduction of measure terms. This allows to solve a shape optimization problem for a simply supported thin plate. Ref. S.I.S.S.A. 32/97/M (March 97) Asymptotic behaviour of solutions of fourth order Dirichlet problems 1

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.

Using gradient-based optimization combined with numerical solutions of the Helmholtz equation, we design an acoustic device with high transmission efficiency and even directivity throughout a two-octave-wide frequency range. The device consists of a horn, whose flare is subject to boundary shape optimization, together with an area in front of the horn, where solid material arbitrarily can be di...

Shape optimization problem for a nonlinear elastic plate governed by von Karman equation is considered. Using material derivative method, sensitivity analysis of the solution to the von Karman system with respect to the variation of the domain is performed and a necessary optimality condition is derived.

This paper is devoted to the analysis of multiphase shape optimization problems, which can formally be written as min { g ( (F1(Ω1), . . . , Fh(Ωh) ) +m ∣∣ h ⋃ i=1 Ωi ∣∣ : Ωi ⊂ D, Ωi ∩ Ωj = ∅}, where D ⊆ R is a given bounded open set, |Ωi| is the Lebesgue measure of Ωi and m is a positive constant. For a large class of such functionals, we analyse qualitative properties of the cells and the int...

This chapter presents an approach to organizational-self design (OSD), a method of designing organizations at run-time in which the agents are responsible for generating their own organizational structures. OSD is especially suitable for environments that are dynamic, albeit slowly changing. Such environments preclude the use of static, design-time generated, organizational structures, and yet ...

We intend to propose a framework to handle the problem of mesh deformation in the context of shape optimization. The main idea is to combine the level set method with meshing tools specialized to deal with implicitly-defined geometries. The proposed method is then as well a topology optimization as a geometric optimization method.

Contents List of figures x List of tables xi Notation xii Kurzfassung xv 1 Introduction 1 1.

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. Th...