On the Numerical Solution of a Shape Optimization Problem for the Heat Equation

2013 ◽  
Vol 35 (1) ◽  
pp. A104-A121 ◽  
Author(s):  
Helmut Harbrecht ◽  
Johannes Tausch
Keyword(s):  
Heat Equation ◽  
Shape Optimization ◽  
Numerical Solution ◽  
Optimization Problem ◽  
Shape Optimization Problem

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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