scholarly journals A moving mesh fictitious domain approach for shape optimization problems

2000 ◽  
Vol 34 (1) ◽  
pp. 31-45 ◽  
Author(s):  
Raino A.E. Mäkinen ◽  
Tuomo Rossi ◽  
Jari Toivanen
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Moving Mesh ◽  
Fictitious Domain

FICTITIOUS DOMAINS METHODS WITH DISTRIBUTED LAGRANGE MULTIPLIERS PART II: APPLICATION TO THE SOLUTION OF SHAPE OPTIMIZATION PROBLEMS

2001 ◽  
Vol 11 (03) ◽  
pp. 549-563 ◽  
Author(s):  
JAROSLAV HASLINGER ◽  
JEAN-FRANCOIS MAITRE ◽  
LAURENT TOMAS
Keyword(s):  
Shape Optimization ◽  
Numerical Computation ◽  
Minimization Problem ◽  
Lagrange Multipliers ◽  
Optimization Problems ◽  
Fictitious Domain ◽  
Fictitious Domain Method ◽  
Numerical Example ◽  
Regularization Techniques ◽  
Locking Effect

The distributed Lagrange multipliers based fictitious domain method for the numerical computation of state problems presented in Part I is now used in the frame of shape optimization. Practical aspects of this approach are discussed. In general it is shown that the resulting minimization problem is nonsmooth, due to the locking effect. Two possible regularization techniques are described and the results of one numerical example is shown.

scholarly journals Fireshape: a shape optimization toolbox for Firedrake

2021 ◽  
Vol 63 (5) ◽  
pp. 2553-2569
Author(s):  
Alberto Paganini ◽  
Florian Wechsung
Keyword(s):  
Finite Element ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Shape Optimization ◽  
Open Source ◽  
Optimization Problems ◽  
Moving Mesh ◽  
Moving Mesh Method ◽  
Finite Element Software ◽  
Mesh Method

AbstractWe introduce Fireshape, an open-source and automated shape optimization toolbox for the finite element software Firedrake. Fireshape is based on the moving mesh method and allows users with minimal shape optimization knowledge to tackle with ease challenging shape optimization problems constrained to partial differential equations (PDEs).

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.

The mine blast algorithm for the structural optimization of electrical vehicle components

2020 ◽  
Vol 62 (5) ◽  
pp. 497-502 ◽  
Author(s):  
B. S. Yıldız
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Element Analysis ◽  
Mine Blast Algorithm ◽  
Component Design ◽  
Derivative Free ◽  
Door Hinge ◽  
Electrical Vehicles ◽  
Electrical Vehicle ◽  
Vehicle Components

Abstract The shape optimization of mechanical and automotive component plays a crucial role in the development of automotive technology. Presently, the use of derivative-free metaheuristics in combination with finite element analysis for mechanical component design is one of the most focused on topics due to its simplicity and effectiveness. In this research paper, the mine blast algorithm (MBA) is used to solve the problem of shape optimization for a vehicle door hinge to prove how the MBA can be used for solving shape optimization problems in designing electrical vehicles. The results show the advantage of the MBA for designing optimal components in the automotive industry.

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