scholarly journals Numerical Solution for Min-Max Shape Optimization Problems. (Minimum Design of Maximum Stress and Displacement).

1998 ◽  
Vol 41 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Masatoshi SHIMODA ◽  
Hideyuki AZEGAMI ◽  
Toshiaki SAKURAI
Keyword(s):  
Shape Optimization ◽  
Numerical Solution ◽  
Maximum Stress ◽  
Optimization Problems

scholarly journals Numerical solution to shape optimization problems for non-stationary Navier-Stokes problems

JSIAM Letters ◽  
2010 ◽  
Vol 2 (0) ◽  
pp. 37-40 ◽  
Author(s):  
Yutaro Iwata ◽  
Hideyuki Azegami ◽  
Taiki Aoyama ◽  
Eiji Katamine
Keyword(s):  
Shape Optimization ◽  
Numerical Solution ◽  
Optimization Problems ◽  
Navier Stokes ◽  
Stokes Problems

scholarly journals Relaxed gradient projection algorithm for constrained node-based shape optimization

2021 ◽  
Author(s):  
Ihar Antonau ◽  
Majid Hojjat ◽  
Kai-Uwe Bletzinger
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Design Parameters ◽  
Active Set ◽  
Physical Constraints ◽  
Original Algorithm ◽  
Gradient Projection Algorithm ◽  
Non Linear

AbstractIn node-based shape optimization, there are a vast amount of design parameters, and the objectives, as well as the physical constraints, are non-linear in state and design. Robust optimization algorithms are required. The methods of feasible directions are widely used in practical optimization problems and know to be quite robust. A subclass of these methods is the gradient projection method. It is an active-set method, it can be used with equality and non-equality constraints, and it has gained significant popularity for its intuitive implementation. One significant issue around efficiency is that the algorithm may suffer from zigzagging behavior while it follows non-linear design boundaries. In this work, we propose a modification to Rosen’s gradient projection algorithm. It includes the efficient techniques to damp the zigzagging behavior of the original algorithm while following the non-linear design boundaries, thus improving the performance of the method.

Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows

2013 ◽  
Vol 60 (3) ◽  
pp. 537-563 ◽  
Author(s):  
Francesco Ballarin ◽  
Andrea Manzoni ◽  
Gianluigi Rozza ◽  
Sandro Salsa
Keyword(s):  
Shape Optimization ◽  
Numerical Solution ◽  
Existence Results ◽  
Free Form ◽  
Stokes Flows ◽  
Free Form Deformation
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