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.

scholarly journals Efficient Local Level Set Method without Reinitialization and Its Appliance to Topology Optimization

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Wenhui Zhang ◽  
Yaoting Zhang
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Computational Efficiency ◽  
Numerical Stability ◽  
Local Level ◽  
Band Model ◽  
Numerical Process ◽  
Local Level Set ◽  
Narrow Band Model

The local level set method (LLSM) is higher than the LSMs with global models in computational efficiency, because of the use of narrow-band model. The computational efficiency of the LLSM can be further increased by avoiding the reinitialization procedure by introducing a distance regularized equation (DRE). The numerical stability of the DRE can be ensured by a proposed conditionally stable difference scheme under reverse diffusion constraints. Nevertheless, the proposed method possesses no mechanism to nucleate new holes in the material domain for two-dimensional structures, so that a bidirectional evolutionary algorithm based on discrete level set functions is combined with the LLSM to replace the numerical process of hole nucleation. Numerical examples are given to show high computational efficiency and numerical stability of this algorithm for topology optimization.

A Study on Basis Functions of the Parameterized Level Set Method for Topology Optimization of Continuums

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Peng Wei ◽  
Yang Yang ◽  
Shikui Chen ◽  
Michael Yu Wang
Keyword(s):  
Topology Optimization ◽  
Radial Basis Functions ◽  
Level Set Method ◽  
Level Set ◽  
Computational Efficiency ◽  
Basis Functions ◽  
The Finite Element Method ◽  
Radial Basis ◽  
Commercial Applications ◽  
2D And 3D

Abstract In recent years, the parameterized level set method (PLSM), which rests on radial basis functions in most early work, has gained growing attention in structural optimization. However, little work has been carried out to investigate the effect of the basis functions in the parameterized level set method. This paper examines the basis functions of the parameterized level set method, including radial basis functions, B-spline functions, and shape functions in the finite element method (FEM) for topology optimization of continuums. The effects of different basis functions in the PLSM are examined by analyzing and comparing the required storage, convergence speed, computational efficiency, and optimization results, with the benchmark minimum compliance problems subject to a volume constraint. The linear basis functions show relatively satisfactory overall performance. Besides, several schemes to boost computational efficiency are proposed. The study on examples with unstructured 2D and 3D meshes can also be considered as a tentative investigation of prospective possible commercial applications of this method.

Topology Optimization of Compliant Mechanisms Using Level Set Method without Re-Initialization

2011 ◽  
Vol 130-134 ◽  
pp. 3076-3082 ◽  
Author(s):  
Ben Liang Zhu ◽  
Xian Min Zhang
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Signed Distance Function ◽  
Optimal Process ◽  
Level Set Function ◽  
New Formulation ◽  
Set Function

In this paper, a new level set method for topology optimization of compliant mechanisms is presented. A new formulation is developed and built in the traditional level set method to force the level set function to be close to a signed distance function during the optimal process. The validity of the method is illustrated by topology optimization of a widely studied compliant mechanism.

Optimal Synthesis of Compliant Mechanisms Using a Connectivity Preserving Level Set Method

2005 ◽  
Author(s):  
Shikui Chen ◽  
Michael Yu Wang ◽  
Shengyin Wang ◽  
Qi Xia
Keyword(s):  
Topology Optimization ◽  
Optimal Design ◽  
Level Set Method ◽  
Level Set ◽  
Compliant Mechanisms ◽  
Structural Connectivity ◽  
Optimal Synthesis ◽  
Optimization Process ◽  
Connected Components

We present a level set based method for optimal design of compliant mechanisms. The focus of the investigation is on how to preserve the structural connectivity in the optimization process of the level set method. By introducing an extra constraint using the connected components labeling technique, the structural connectivity of the design is well maintained during the topology optimization process.

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.

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