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Article
Acceleration of shape optimization analysis using model order reduction by Karhunen-Loève expansion
This paper presents a method to reduce the computational time required to solve shape optimization problems. A volume minimization problem under the mean compliance constraint is chosen as an example of the sh...
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Article
A second-order shape optimization algorithm for solving the exterior Bernoulli free boundary problem using a new boundary cost functional
The exterior Bernoulli problem is rephrased into a shape optimization problem using a new type of objective function called the Dirichlet-data-gap cost function which measures the \(L^2\) L 2 -distance betwe...
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Article
Shape optimization of running shoes with desired deformation properties
The present paper describes a shape optimization procedure for designing running shoes, focusing on two mechanical properties, namely, the shock absorption and the stability kee** the right posture. These pr...
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Chapter
Basics of Optimization Theory
Chapter 1 investigated explicit optimal design problems and illustrated different approaches for obtaining optimality conditions. Terminology and results utilized in optimization theory were also used. This ch...
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Chapter
Basics of Variational Principles and Functional Analysis
In last chapters, we looked at the theory of solutions relating to optimization problems in finite-dimension. From this chapter onward, we shall consider optimization problems where the design variables are of...
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Chapter
Fundamentals of Numerical Analysis
In Chap. 5, covering several boundary value problems of elliptic partial differential equations, we saw that the existence of their unique solutions could be guaranteed using solutions of the weak form. These ...
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Chapter
Topology Optimization Problems of Density Variation Type
From this chapter, we finally examine shape optimization problems in continua. Firstly, let us think about a problem seeking the appropriate arrangement of holes in a domain where the boundary value problem of...
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Chapter
Basics of Optimal Design
The main topic of this book is optimal design. In order to understand the mathematical structures involved in our study, we will begin by examining two simple problems. Upon finishing this book, the reader sho...
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Chapter
Basics of Mathematical Programming
In Chap. 2, we discussed the conditions satisfied by a local minimum point (the required conditions of a local minimum point) and the conditions which guarantee it to be a minimum point (sufficient conditions ...
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Chapter
Boundary Value Problems of Partial Differential Equations
As seen in Chap. 1, optimal design problems are optimization problems whose state equations are considered as equality constraints. In Chap. 1, we have considered design variables and state variables as ele...
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Chapter
Abstract Optimum Design Problem
We have seen in Chaps. 5 and 6 how boundary problems of partial differential equations are constructed and how they are solved. If we compare them to the optimum design problems looked at in Chap. 1, the...
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Chapter
Shape Optimization Problems of Domain Variation Type
In Chap. 8 we looked at problems for obtaining the optimal topologies of continua with the densities of continua set to be the design variable. In this chapter, we shall look at the type of shape optimization ...
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Article
An improved shape optimization formulation of the Bernoulli problem by tracking the Neumann data
We propose a new shape optimization formulation of the Bernoulli problem by tracking the Neumann data. The associated state problem is an equivalent formulation of the Bernoulli problem with a Robin condition....
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Article
Shape optimization approach to defect-shape identification with convective boundary condition via partial boundary measurement
We aim to identify the geometry (i.e., the shape and location) of a cavity inside an object through the concept of thermal imaging. More precisely, we present an identification procedure to determine the geome...
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Article
Topology optimization of density type for a linear elastic body by using the second derivative of a KS function with respect to von Mises stress
This study demonstrates the use of Newton method to solve topology optimization problems of density type for linear elastic bodies to minimize the maximum von Mises stress. We use the Kreisselmeier–Steinhauser...
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Chapter and Conference Paper
Second Derivatives of Cost Functions and \(H^1\) Newton Method in Shape Optimization Problems
We derive the second-order shape derivatives (shape Hessians) of cost functions for shape optimization problems of domains in which boundary value problems of partial differential equations are defined, and pr...
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Chapter and Conference Paper
Solution of Shape Optimization Problem and Its Application to Product Design
In this paper, we define shape optimization problems as problems of finding the shapes of domains in which boundary value problems of partial differential equations are defined. A domain map** from an initia...
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Chapter and Conference Paper
Shape Optimization Approach by Traction Method to Inverse Free Boundary Problems
The importance of the optimal shape design has been increasing in the present industrial design due to the request to make their production more efficient.
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Article
Shape optimization of an electrostatic capacitive sensor
This paper describes the shape optimization of an electrostatic capacitive sensor used to detect fingers. We consider two state determination problems. The first is a basic electrostatic field problem consisti...
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Article
Shape optimization of flow field improving hydrodynamic stability
This paper presents a solution of a shape optimization problem of a flow field for delaying transition from a laminar flow to a turbulent flow. Map** from an initial domain to a new domain is chosen as the d...
