Search results for "Shape optimization"
showing 10 items of 44 documents
Numerical methods for acoustics and noise control
2010
Artikkeliväitöskirja. Sisältää yhteenveto-osan ja viisi artikkelia. Article dissertation. Contains an introduction part and five articles. This dissertation considers numerical methods for wave propagation modelling and noise control. The first part of the dissertation discusses an efficient method for solving time-harmonic wave equations in acoustic (the Helmholtz equation) and elastic domains (the Navier equation). The solver is based on preconditioning a Krylov subspace method, such as GMRES, with approximations of damped variants of the corresponding wave equations. An algebraic multigrid method is used in approximating the inverse of damped operators. The method can be used in complex …
Optimal Shape Design in Contact Problems
1989
From the mathematical point of view, optimal shape design (or optimum design, optimization of the domain, structural optimization) is a branch of the calculus of variations and especially of optimal control where study is devoted to the problem of finding the optimal shape for an object. In an optimal shape design process the objective is to optimize certain criteria involving the solution of a partial differential equation with respect to its domain of definition, [2, 3, 5].
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…
Surrogate-assisted evolutionary multiobjective shape optimization of an air intake ventilation system
2017
We tackle three different challenges in solving a real-world industrial problem: formulating the optimization problem, connecting different simulation tools and dealing with computationally expensive objective functions. The problem to be optimized is an air intake ventilation system of a tractor and consists of three computationally expensive objective functions. We describe the modeling of the system and its numerical evaluation with a commercial software. To obtain solutions in few function evaluations, a recently proposed surrogate-assisted evolutionary algorithm K-RVEA is applied. The diameters of four different outlets of the ventilation system are considered as decision variables. Fr…
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 optimization utilizing consistent sensitivities
2010
Optimization of the domain in elliptic variational inequalities
1988
This paper is concerned with a nonsmooth shape optimization problem for the Signorini unilateral boundary-value problem. The necessary optimality conditions are derived. The results of computations are presented.
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 …
Katsaus muodon optimoinnin menetelmiin
2017
Tutkielma esittelee muodon optimoinnin menetelmiä sekä niiden historiaa luoden katsauksen menetelmien kehittymiseen sekä niiden keskinäisiin suhteisiin. Tällaisia ovat esimerkiksi menetelmän matemaattisen teorian “kehittyneisyys” ja ratkaisemisen tehokkuus tai soveltuvuus. Tarkoituksena on muodostaa yleiskuva siitä, mitä menetelmiä muodon optimointiin on jo kehitetty, selvittää, miten ajankohtaisia eri menetelmät ovat, miten menetelmät vertautuvat toisiinsa ja selvittää, mihin eri menetelmät soveltuvat. Lukijan odotetaan selvittävän tarvittavat taustatiedot, sillä tutkielma ei juurikaan esittele muodon optimoinnin matematiikkaa. This thesis presents shape optimization methods, their history…