A boundary element approach for topology optimization problem using the level set method

2006 ◽  
Vol 23 (5) ◽  
pp. 405-416 ◽  
Author(s):  
Kazuhisa Abe ◽  
Shunsuke Kazama ◽  
Kazuhiro Koro
Keyword(s):  
Topology Optimization ◽  
Boundary Element ◽  
Level Set Method ◽  
Level Set ◽  
Optimization Problem ◽  
Topology Optimization Problem ◽  
Element Approach

A Variational Binary Level Set Method for Structural Topology Optimization

2013 ◽  
Vol 13 (5) ◽  
pp. 1292-1308 ◽  
Author(s):  
Xiaoxia Dai ◽  
Peipei Tang ◽  
Xiaoliang Cheng ◽  
Minghui Wu
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Fast Algorithm ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Structural Topology ◽  
Piecewise Constant ◽  
Topology Optimization Problem ◽  
And Topology

AbstractThis paper proposes a variational binary level set method for shape and topology optimization of structural. First, a topology optimization problem is pre-sented based on the level set method and an algorithm based on binary level set method is proposed to solve such problem. Considering the difficulties of coordination between the various parameters and efficient implementation of the proposed method, we present a fast algorithm by reducing several parameters to only one parameter, which would substantially reduce the complexity of computation and make it easily and quickly to get the optimal solution. The algorithm we constructed does not need to re-initialize and can produce many new holes automatically. Furthermore, the fast algorithm allows us to avoid the update of Lagrange multiplier and easily deal with constraints, such as piecewise constant, volume and length of the interfaces. Finally, we show several optimum design examples to confirm the validity and efficiency of our method.

An isogeometric boundary element approach for topology optimization using the level set method

2020 ◽  
Vol 84 ◽  
pp. 536-553 ◽  
Author(s):  
Hugo Luiz Oliveira ◽  
Heider de Castro e Andrade ◽  
Edson Denner Leonel
Keyword(s):  
Topology Optimization ◽  
Boundary Element ◽  
Level Set Method ◽  
Level Set ◽  
Element Approach

scholarly journals Stiffness optimization of geometrically nonlinear structures and the level set based solution

2016 ◽  
Vol 7 ◽  
pp. A3 ◽  
Author(s):  
Qi Xia ◽  
Tielin Shi
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Optimization Problem ◽  
Two Dimensions ◽  
Geometrically Nonlinear ◽  
Nonlinear Structures ◽  
Element Analysis ◽  
Topology Optimization Problem ◽  
Stiffness Optimization ◽  
Ks Function

Load-normalized strain energy increments between consecutive load steps are aggregated through the Kreisselmeier-Steinhauser (KS) function, and the KS function is proposed as a stiffness criterion of geometrically nonlinear structures. A topology optimization problem is defined to minimize the KS function together with the perimeter of structure and a volume constraint. The finite element analysis is done by remeshing, and artificial weak material is not used. The topology optimization problem is solved by using the level set method. Several numerical examples in two dimensions are provided. Other criteria of stiffness, i.e., the end compliance and the complementary work, are compared.

1502 A topology optimization for 2D acoustics with the boundary element method and the level set method

2015 ◽  
Vol 2015.25 (0) ◽  
pp. _1502-1_-_1502-10_
Author(s):  
Moemi HANADA ◽  
Hiroshi ISAKARI ◽  
Toru TAKAHASHI ◽  
Toshiro MATSUMOTO
Keyword(s):  
Topology Optimization ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Level Set Method ◽  
Level Set ◽  
Element Method

Level Set-Based Topology Optimization of Hinge-Free Compliant Mechanisms Using a Two-Step Elastic Modeling Method

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Benliang Zhu ◽  
Xianmin Zhang ◽  
Sergej Fatikow
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Optimization Algorithm ◽  
Computational Efficiency ◽  
Efficient Algorithm ◽  
Optimization Problem ◽  
Compliant Mechanisms ◽  
Alternative Formulation ◽  
Numerical Examples

This paper presents a two-step elastic modeling (TsEM) method for the topology optimization of compliant mechanisms aimed at eliminating de facto hinges. Based on the TsEM method, an alternative formulation is developed and incorporated with the level set method. An efficient algorithm is developed to solve the level set-based optimization problem for improving the computational efficiency. Two widely studied numerical examples are performed to demonstrate the validity of the proposed method. The proposed formulation can prevent hinges from occurring in the resulting mechanisms. Further, the proposed optimization algorithm can yield fewer design iterations and thus it can improve the overall computational efficiency.

scholarly journals Stochastic topology optimization based on level-set method

2014 ◽  
Vol 33 (6) ◽  
pp. 1904-1919
Author(s):  
Yuki Hidaka ◽  
Takahiro Sato ◽  
Kota Watanabe ◽  
Hajime Igarashi
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Present Method ◽  
Design Methodology ◽  
Optimization Problem ◽  
Local Optima ◽  
Content Type ◽  
Numerical Examples ◽  
Dimensional Optimization

Purpose – Conventional level-set method tends to fall into local optima because optimization is conducted based on gradient method. The purpose of this paper is to develop a novel topology optimization in which simulated annealing (SA) is introduced to overcome the difficulties in level-set method. Design/methodology/approach – Level-set based topology optimization for two-dimensional optimization problem. Findings – It is shown in the numerical examples, where conventional and present methods are applied to shape optimization of ferrite inductor and Interior Permanent Magnetic (IPM)-motor, the present method can find solutions with better performance than those obtained by the conventional method. Originality/value – SA is introduced to improve the search performances of level-set method.

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