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Computational Feasibility of Simulta...

O'Connor, Justin.

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Computational Feasibility of Simultaneous Analysis and Design in Interior Point Topology Optimization.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Computational Feasibility of Simultaneous Analysis and Design in Interior Point Topology Optimization./
Author:	O'Connor, Justin.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2023,
Description:	113 p.
Notes:	Source: Dissertations Abstracts International, Volume: 85-02, Section: A.
Contained By:	Dissertations Abstracts International85-02A.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30316497
ISBN:	9798380121347

Computational Feasibility of Simultaneous Analysis and Design in Interior Point Topology Optimization.
O'Connor, Justin.

Computational Feasibility of Simultaneous Analysis and Design in Interior Point Topology Optimization. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 113 p.

Source: Dissertations Abstracts International, Volume: 85-02, Section: A.

Thesis (Ph.D.)--Colorado State University, 2023.

This item must not be sold to any third party vendors.

Topology optimization is a class of algorithms designed to optimize a design or structure to accomplish some goal. It is part of a process of computer generated design that allows engineers to design better products faster. One such algorithm that has piqued the imagination of developers is called Simultaneous Analysis and Design (SAND), especially in the context of Interior Point Optimization (IPO). This method is known to generate extremely optimal designs, and is good at avoiding local minima. However, this method is not used in practice, due to its computational cost. This thesis examines the SAND IPO method, and develops an effective algorithm to generate a design using it. I begin by discussing nonlinear optimization algorithms, selecting pieces that work together for this problem, to generate a cohesive algorithm for the whole process. Inside this developed algorithm, as with most nonlinear optimization algorithms, the most expensive part is a linear solve. In my case, it is a linear solve of a block system. I develop and implement a multi-tier preconditioning approach to solve this system in a reasonable amount of time. Finally, I present a large topology optimization problem presented in three dimensions that has been solved using IPO and SAND, demonstrating the usability of the implemented algorithm.

ISBN: 9798380121347Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Simultaneous Analysis and Design

Computational Feasibility of Simultaneous Analysis and Design in Interior Point Topology Optimization.
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245 1 0 $a Computational Feasibility of Simultaneous Analysis and Design in Interior Point Topology Optimization.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2023
300 $a 113 p.
500 $a Source: Dissertations Abstracts International, Volume: 85-02, Section: A.
500 $a Advisor: Bangerth, Wolfgang.
502 $a Thesis (Ph.D.)--Colorado State University, 2023.
506 $a This item must not be sold to any third party vendors.
520 $a Topology optimization is a class of algorithms designed to optimize a design or structure to accomplish some goal. It is part of a process of computer generated design that allows engineers to design better products faster. One such algorithm that has piqued the imagination of developers is called Simultaneous Analysis and Design (SAND), especially in the context of Interior Point Optimization (IPO). This method is known to generate extremely optimal designs, and is good at avoiding local minima. However, this method is not used in practice, due to its computational cost. This thesis examines the SAND IPO method, and develops an effective algorithm to generate a design using it. I begin by discussing nonlinear optimization algorithms, selecting pieces that work together for this problem, to generate a cohesive algorithm for the whole process. Inside this developed algorithm, as with most nonlinear optimization algorithms, the most expensive part is a linear solve. In my case, it is a linear solve of a block system. I develop and implement a multi-tier preconditioning approach to solve this system in a reasonable amount of time. Finally, I present a large topology optimization problem presented in three dimensions that has been solved using IPO and SAND, demonstrating the usability of the implemented algorithm.
590 $a School code: 0053.
650 4 $a Mathematics. $3 515831
650 4 $a Mathematics education. $3 641129
650 4 $a Theoretical mathematics. $3 3173530
653 $a Simultaneous Analysis and Design
653 $a Interior Point Optimization
653 $a Cohesive algorithm
653 $a Topology optimization
690 $a 0405
690 $a 0642
690 $a 0280
710 2 $a Colorado State University. $b Mathematics. $3 1683531
773 0 $t Dissertations Abstracts International $g 85-02A.
790 $a 0053
791 $a Ph.D.
792 $a 2023
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30316497