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A structural optimization method based on the level set method using a new geometry‐based re‐initialization scheme
Author(s) -
Yamasaki Shintaro,
Nishiwaki Shinji,
Yamada Takayuki,
Izui Kazuhiro,
Yoshimura Masataka
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2874
Subject(s) - initialization , level set method , mathematical optimization , maximization , set (abstract data type) , finite element method , level set (data structures) , function (biology) , mathematics , algorithm , scheme (mathematics) , topology optimization , computer science , optimization problem , artificial intelligence , mathematical analysis , engineering , structural engineering , segmentation , evolutionary biology , image segmentation , biology , programming language
Structural optimization methods based on the level set method are a new type of structural optimization method where the outlines of target structures can be implicitly represented using the level set function, and updated by solving the so‐called Hamilton–Jacobi equation based on a Eulerian coordinate system. These new methods can allow topological alterations, such as the number of holes, during the optimization process whereas the boundaries of the target structure are clearly defined. However, the re‐initialization scheme used when updating the level set function is a critical problem when seeking to obtain appropriately updated outlines of target structures. In this paper, we propose a new structural optimization method based on the level set method using a new geometry‐based re‐initialization scheme where both the numerical analysis used when solving the equilibrium equations and the updating process of the level set function are performed using the Finite Element Method. The stiffness maximization, eigenfrequency maximization, and eigenfrequency matching problems are considered as optimization problems. Several design examples are presented to confirm the usefulness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.