scholarly journals A Multiphase Shape Optimization Problem for Eigenvalues: Qualitative Study and Numerical Results

2016 ◽  
Vol 54 (1) ◽  
pp. 210-241 ◽  
Author(s):  
Beniamin Bogosel ◽  
Bozhidar Velichkov
Keyword(s):  
Qualitative Study ◽  
Shape Optimization ◽  
Optimization Problem ◽  
Numerical Results ◽  
Shape Optimization Problem

scholarly journals Algorithmes hybrides pour l’optimisation globale

2008 ◽  
pp. 303-322
Author(s):  
Abderrahmane Habbal ◽  
Lionel Fourment ◽  
Tien Tho Do
Keyword(s):  
Shape Optimization ◽  
Total Energy ◽  
Energy Cost ◽  
Optimization Problem ◽  
Surrogate Models ◽  
Numerical Results ◽  
Interpolation Scheme ◽  
Shape Optimization Problem ◽  
Clustering Technique

We introduce two evolutionnary hybrid optimizers, based on surrogate models which use a limited prescribed number of exact evaluations of the criterion and its gradient. The first algorithm uses a discontinuous ansatz with a clustering technique. The second one uses a Liszka-Orkisz interpolation scheme, and keeps memory of the exactly evaluated individuals of previous generations. These two methods are applied to a 3D forging shape optimization problem. The considered objective combines the total energy cost and a defect criterion. We present numerical results which illustrate the efficiency of the developped algorithms.

scholarly journals Hypervolume scalarization for shape optimization to improve reliability and cost of ceramic components

2021 ◽  
Author(s):  
Johanna Schultes ◽  
Michael Stiglmayr ◽  
Kathrin Klamroth ◽  
Camilla Hahn
Keyword(s):  
Shape Optimization ◽  
Optimization Problem ◽  
Mechanical Stability ◽  
Adjoint Equation ◽  
Tensile Load ◽  
Problem Formulation ◽  
State Equation ◽  
Efficient Solutions ◽  
Volume Stability ◽  
Shape Optimization Problem

AbstractIn engineering applications one often has to trade-off among several objectives as, for example, the mechanical stability of a component, its efficiency, its weight and its cost. We consider a biobjective shape optimization problem maximizing the mechanical stability of a ceramic component under tensile load while minimizing its volume. Stability is thereby modeled using a Weibull-type formulation of the probability of failure under external loads. The PDE formulation of the mechanical state equation is discretized by a finite element method on a regular grid. To solve the discretized biobjective shape optimization problem we suggest a hypervolume scalarization, with which also unsupported efficient solutions can be determined without adding constraints to the problem formulation. FurthIn this section, general properties of the hypervolumeermore, maximizing the dominated hypervolume supports the decision maker in identifying compromise solutions. We investigate the relation of the hypervolume scalarization to the weighted sum scalarization and to direct multiobjective descent methods. Since gradient information can be efficiently obtained by solving the adjoint equation, the scalarized problem can be solved by a gradient ascent algorithm. We evaluate our approach on a 2 D test case representing a straight joint under tensile load.

scholarly journals A constrained shape optimization problem in Orlicz-Sobolev spaces

2019 ◽  
Vol 267 (9) ◽  
pp. 5493-5520 ◽  
Author(s):  
João Vitor da Silva ◽  
Ariel M. Salort ◽  
Analía Silva ◽  
Juan F. Spedaletti
Keyword(s):  
Shape Optimization ◽  
Sobolev Spaces ◽  
Optimization Problem ◽  
Shape Optimization Problem
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