Shape optimization problems in control form

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.

Reduction of the Adjoint Gradient Formula for Aerodynamic Shape Optimization Problems

AIAA Journal ◽

10.2514/2.6830 ◽

2003 ◽

Vol 41 (11) ◽

pp. 2114-2129 ◽

Cited By ~ 34

Author(s):

Antony Jameson ◽

Sangho Kim

Keyword(s):

Shape Optimization ◽

Optimization Problems ◽

Aerodynamic Shape Optimization ◽

Aerodynamic Shape ◽

Adjoint Gradient

On the Bernoulli free boundary problem and related shape optimization problems

Interfaces and Free Boundaries ◽

10.4171/ifb/30 ◽

2001 ◽

pp. 1-13 ◽

Cited By ~ 5

Author(s):

Mohammed Hayouni ◽

Antoine Henrot ◽

Nadia Samouh

Keyword(s):

Free Boundary ◽

Shape Optimization ◽

Boundary Problem ◽

Free Boundary Problem ◽

Optimization Problems ◽

Bernoulli Free Boundary

Approximation in shape optimization problems

10.1063/1.3546088 ◽

2011 ◽

Author(s):

Dan Tiba

Keyword(s):

Shape Optimization ◽

Optimization Problems

Numerical Solution of 2D Contact Shape Optimization Problems Involving a Solution-Dependent Coefficient of Friction

Lecture Notes in Computational Science and Engineering - Optimization with PDE Constraints ◽

10.1007/978-3-319-08025-3_1 ◽

2014 ◽

pp. 1-24

Author(s):

Petr Beremlijski ◽

Jaroslav Haslinger ◽

Jiří Outrata ◽

Róbert Pathó

Keyword(s):

Shape Optimization ◽

Numerical Solution ◽

Coefficient Of Friction ◽

Optimization Problems ◽

Contact Shape

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

Materials Testing ◽

10.1515/mt-2020-620510 ◽

2020 ◽

Vol 62 (5) ◽

pp. 497-502 ◽

Cited By ~ 5

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.

Second Derivatives of Cost Functions and $$H^1$$ Newton Method in Shape Optimization Problems

Mathematical Analysis of Continuum Mechanics and Industrial Applications II - Mathematics for Industry ◽

10.1007/978-981-10-6283-4_6 ◽

2017 ◽

pp. 61-72

Author(s):

Hideyuki Azegami

Keyword(s):

Shape Optimization ◽

Newton Method ◽

Optimization Problems ◽

Cost Functions ◽

Second Derivatives ◽

Derivatives Of

Shape Optimization Problems

Optimal Control of Partial Differential Equations - Applied Mathematical Sciences ◽

10.1007/978-3-030-77226-0_11 ◽

2021 ◽

pp. 373-421

Author(s):

Andrea Manzoni ◽

Alfio Quarteroni ◽

Sandro Salsa

Keyword(s):

Shape Optimization ◽

Optimization Problems

Development of an Optimization Framework for Parameter Identification and Shape Optimization Problems in Engineering

International Journal of Manufacturing Materials and Mechanical Engineering ◽

10.4018/ijmmme.2011010105 ◽

2011 ◽

Vol 1 (1) ◽

pp. 57-79 ◽

Cited By ~ 2

Author(s):

A. Andrade-Campos

Keyword(s):

Inverse Problems ◽

Shape Optimization ◽

Parameter Identification ◽

Optimization Problems ◽

Optimization Methods ◽

Optimum Shape ◽

Optimization Framework ◽

Search Optimization ◽

Initial Geometry

The use of optimization methods in engineering is increasing. Process and product optimization, inverse problems, shape optimization, and topology optimization are frequent problems both in industry and science communities. In this paper, an optimization framework for engineering inverse problems such as the parameter identification and the shape optimization problems is presented. It inherits the large experience gain in such problems by the SiDoLo code and adds the latest developments in direct search optimization algorithms. User subroutines in Sdl allow the program to be customized for particular applications. Several applications in parameter identification and shape optimization topics using Sdl Lab are presented. The use of commercial and non-commercial (in-house) Finite Element Method codes to evaluate the objective function can be achieved using the interfaces pre-developed in Sdl Lab. The shape optimization problem of the determination of the initial geometry of a blank on a deep drawing square cup problem is analysed and discussed. The main goal of this problem is to determine the optimum shape of the initial blank in order to save latter trimming operations and costs.