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.

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.

Multi-Stage Design Method for Practical Compliant Mechanisms by Topology and Shape Optimizations and Shape Conversion Method Utilizing Level Set Method

2008 ◽  
Author(s):  
Masakazu Kobayashi ◽  
Shinji Nishiwaki ◽  
Masatake Higashi
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Design Method ◽  
Stage Design ◽  
Conversion Method ◽  
Multi Stage

This paper proposes a multi-stage design method for a design of practical compliant mechanisms. The proposed method consists of topology and shape optimizations and a shape conversion method that incorporates two optimizations. In the 1st stage, an initial and conceptual compliant mechanism is created by topology optimization. In the 2nd stage, an initial model of shape optimization is created from the result of topology optimization by the shape conversion method based on the level set method. In the 3rd stage, the shape optimization yields a detailed shape of the compliant mechanism by considering non-linear deformation and stress concentration. Execution of the shape optimization after the topology optimization enables evaluation of stress concentration and large deformation effect that are normally difficult for the traditional topology optimization. On the other side, the precise conversion from the model by topology optimization to the one for the shape optimization becomes possible by the shape conversion method that is utilizing the level set method. Using the proposed multi-stage method, a practical compliant mechanism can be designed with the designer’s minimum efforts that are indications of design conditions of the topology and shape optimizations and several parameters and threshold values of the shape conversion 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.

Topology optimization of rotor poles in a permanent-magnet machine using level set method and continuum design sensitivity analysis

2014 ◽  
Vol 33 (3) ◽  
pp. 711-728 ◽  
Author(s):  
Piotr Putek ◽  
Piotr Paplicki ◽  
Ryszard Pałka
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Permanent Magnet ◽  
Level Set Method ◽  
Level Set ◽  
Numerical Approach ◽  
Design Sensitivity ◽  
Optimization Process ◽  
Content Type ◽  
Rotor Poles

Purpose – In this paper, a numerical approach to the topology optimization is proposed to design the permanent magnet excited machines with improved high-speed features. For this purpose the modified multi-level set method (MLSM) was proposed and applied to capture the shape of rotor poles on the fixed mesh using FE analysis. The paper aims to discuss these issues. Design/methodology/approach – This framework is based on theories of topological and shape derivative for the magnetostatic system. During the iterative optimization process, the shape of rotor poles and its evolution is represented by the level sets of a continuous level set function f. The shape optimization of the iron and the magnet rotor poles is provided by the combining continuum design sensitivity analysis with level set method. Findings – To obtain an innovative design of the rotor poles composed of different materials, the modified MLSM is proposed. An essential advantage of the proposed method is its ability to handle a topology change on a fixed mesh by the nucleating a small hole in design domain that leads to more efficient computational scheme then standard level set method. Research limitations/implications – The proposed numerical approach to the topology design of the 3D model of a PM machine is based on the simplified 2D model under assumption that the eddy currents in both the magnet and iron parts are neglected. Originality/value – The novel aspect of the proposed method is the incorporation of the Total Variation regularization in the MLSM, which distribution is additionally modified by the gradient derivative information, in order to stabilize the optimization process and penalize oscillations without smoothing edges.

Parametric Structural Shape and Topology Optimization With a Variational Distance-Regularized Level Set Method

2016 ◽  
Author(s):  
Long Jiang ◽  
Shikui Chen
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Optimization Process ◽  
Signed Distance ◽  
Level Set Function ◽  
Distance Property ◽  
Initialization Scheme ◽  
Set Function ◽  
Distance Regularization

In conventional level set methods, the slope of the level set function needs to be well controlled to maintain the numerical stability during the topology optimization process. One common solution is to regularize the level set function to be a signed distance function, which is usually achieved by periodically implementing the so called re-initialization scheme to force the level set function to gain the desired signed distance property. However, the re-initialization scheme will bring some unwanted drawbacks to the optimization process, such as zero level set drifting, time consuming etc. In addition, re-initialization is usually implemented outside the optimization loop, which will cause convergence issues. In this paper, a distance regularization functional is introduced to the structural topology optimization objective functional to ensure the signed distance property of the level set function near the structure boundaries. This functional can also keep the level set function to be constant-value at positions far away from the structural boundaries. The radial basis function (RBF) based parameterization technique together with the mathematical programming are utilized to improve the potential capability of handling multiple constraints for the topology optimization. The combination of these two techniques makes the level set based topology optimization be capable of handling complicated multi-constrained problems with higher numerical efficiency, leaving no compromise to multiple drawbacks. To demonstrate the validity of the proposed scheme, benchmark examples on minimum compliance structural optimization are employed. This type of problem is computed by the conventional level set method with the introduced distance regularization functional, the RBF based parametric level set and at last, the distance regularized RBF based parametric level set separately to demonstrate their differences.

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