Search results for "shape optimization"

Shape optimization of elasto-plastic bodies under plane strains: Sensitivity analysis and numerical implementation

1992

Optimal shape design problems for an elastic body made from physically nonlinear material are presented. Sensitivity analysis is done by differentiating the discrete equations of equilibrium. Numerical examples are included.

Multidisciplinary shape optimization in aerodynamics and electromagnetics using genetic algorithms

1999

SUMMARY A multiobjective multidisciplinary design optimization (MDO) of two-dimensional airfoil is presented. In this paper, an approximation for the Pareto set of optimal solutions is obtained by using a genetic algorithm (GA). The first objective function is the drag coefficient. As a constraint it is required that the lift coefficient is above a given value. The CFD analysis solver is based on the finite volume discretization of the inviscid Euler equations. The second objective function is equivalent to the integral of the transverse magnetic radar cross section (RCS) over a given sector. The computational electromagnetics (CEM) wave field analysis requires the solution of a two-dimensi…

Non-linear optimization of track layouts in loop-sorting-systems

2013

Optimization used for enhancing geometric structures iswell known. Applying obstacles to the shape optimization problemis on the other hand not very common. It requires a fast contact search algorithmand an exact continuous formulation to solve the problem robustly. This paper focuses on combining shape optimization problemswith collision avoidance constraints by which a collision detection algorithmis presented. The presentedmethod is tested against the commercial loop-sorting-system used for sorting of medium sized items. The objective is to minimize price and footprint of the system whilemaintaining its functionality. Contact constraints are in this context important to include as variou…

Fixed domain approaches in shape optimization problems

2012

This work is a review of results in the approximation of optimal design problems, defined in variable/unknown domains, based on associated optimization problems defined in a fixed ?hold-all? domain, including the family of all admissible open sets. The literature in this respect is very rich and we concentrate on three main approaches: penalization?regularization, finite element discretization on a fixed grid, controllability and control properties of elliptic systems. Comparison with other fixed domain approaches or, in general, with other methods in shape optimization is performed as well and several numerical examples are included.

A New Distributed Optimization Approach for Solving CFD Design Problems Using Nash Game Coalition and Evolutionary Algorithms

2013

For decades, domain decomposition methods (DDM) have provided a way of solving large-scale problems by distributing the calculation over a number of processing units. In the case of shape optimization, this has been done for each new design introduced by the optimization algorithm. This sequential process introduces a bottleneck.

Distributed multi-objective optimization methods for shape design using evolutionary algorithms and game strategies

2012

Remark on a nonlocal isoperimetric problem

2017

Abstract We consider isoperimetric problem with a nonlocal repulsive term given by the Newtonian potential. We prove that regular critical sets of the functional are analytic. This optimal regularity holds also for critical sets of the Ohta–Kawasaki functional. We also prove that when the strength of the nonlocal part is small the ball is the only possible stable critical set.

Free surfaces: shape sensitivity analysis and numerical methods

1999

On the numerical solution of axisymmetric domain optimization problems by dual finite element method

1994

Shape optimization of an axisymmetric three-dimensional domain with an elliptic boundary value state problem is solved. Since the cost functional is given in terms of the cogradient of the solution, a dual finite element method based on the minimum of complementary energy principle is used. © 1994 John Wiley & Sons, Inc.

Existence for shape optimization problems in arbitrary dimension

2002

We discuss some existence results for optimal design problems governed by second order elliptic equations with the homogeneous Neumann boundary conditions or with the interior transmission conditions. We show that our continuity hypotheses for the unknown boundaries yield the compactness of the associated characteristic functions, which, in turn, guarantees convergence of any minimizing sequences for the first problem. In the second case, weaker assumptions of measurability type are shown to be sufficient for the existence of the optimal material distribution. We impose no restriction on the dimension of the underlying Euclidean space.