Filter the shape sensitivity in level set-based topology optimization methods

2014 ◽  
Vol 51 (5) ◽  
pp. 1035-1049 ◽  
Author(s):  
Benliang Zhu ◽  
Xianmin Zhang ◽  
Sergej Fatikow
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Optimization Methods ◽  
Shape Sensitivity

Topology Optimization of a Turbomachinery Casing Structure Using the Level Set Method

2020 ◽  
Author(s):  
Lei Li ◽  
Andreas Neofytou ◽  
Ricardo Paiva ◽  
Akin Keskin ◽  
H. Alicia Kim
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Complex Loading ◽  
Optimization Methods ◽  
Pressure System ◽  
Linear Elastic ◽  
Boundary Definition ◽  
Minimum Stress ◽  
Problem Formulations

Abstract A turbomachinery casing structure provides the necessary support to many crucial systems and components in an aeroengine such as the combustion chamber, compressors, and turbines. A competitive casing structure should be stiff and durable while minimizing weight. This work investigates the possibilities and potential of using topology optimization to design a turbomachinery casing structure to achieve certain design requirements. As the casing structure is in a high pressure system that undergoes complex mechanical loading conditions, the level set method is employed in contrast to the common density-based topology optimization methods, which could lead to physically uninterpretable gray elements for a complex loading environment. This paper describes the basic concept of the level set method and demonstrates the benefits in terms of boundary definition, speed, and applicability to engineering problems. Topology optimization with a linear-elastic analysis based on an axisymmetric finite element solver is employed in this study. Both minimum compliance and minimum stress problem formulations are considered, and a series of optimum designs are presented and discussed.

A Velocity Predictor–Corrector Scheme in Level Set-Based Topology Optimization to Improve Computational Efficiency

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Benliang Zhu ◽  
Xianmin Zhang ◽  
Sergej Fatikow
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Velocity Field ◽  
Level Set Method ◽  
Level Set ◽  
Velocity Fields ◽  
Shape Sensitivity ◽  
Shape Sensitivity Analysis ◽  
Predictor Corrector ◽  
Mean Compliance

This paper presents an optimization method for solving level set-based topology optimization problems. A predictor–corrector scheme for constructing the velocity field is developed. In this method, after the velocity fields in the first two iterations are calculated using the shape sensitivity analysis, the subsequent velocity fields are constructed based on those obtained from the first two iterations. To ensure stability, the velocity field is renewed based on the shape sensitivity analysis after a certain number of iterations. The validity of the proposed method is tested on the mean compliance minimization problem and the compliant mechanisms synthesis problem. This method is quantitatively compared with other methods, such as the standard level set method, the solid isotropic microstructure with penalization (SIMP) method, and the discrete level set method.

scholarly journals Designing Conformal Ferromagnetic Soft Actuators Using Extended Level Set Methods (X-LSM)

2020 ◽  
Author(s):  
Jiawei Tian ◽  
Xuanhe Zhao ◽  
Xianfeng David Gu ◽  
Shikui Chen
Keyword(s):  
Topology Optimization ◽  
Objective Function ◽  
Level Set ◽  
Time Derivative ◽  
Level Set Methods ◽  
Soft Materials ◽  
Shape Sensitivity ◽  
Soft Robots ◽  
Soft Actuators ◽  
Material Layout

Abstract Ferromagnetic soft materials (FSM) can generate flexible movement and shift morphology in response to an external magnetic field. They have been engineered to design products in a variety of promising applications, such as soft robots, compliant actuators, or bionic devices, et al. By using different patterns of magnetization in the soft elastomer matrix, ferromagnetic soft matters can achieve various shape changes. Although many magnetic soft robots have been designed and fabricated, they are limited by the designers’ intuition. Topology optimization (TO) is a systematically mathematical method to create innovative structures by optimizing the material layout within a design domain without relying on the designers’ intuition. It can be utilized to architect ferromagnetic soft active structures. Since many of these ‘soft machines’ exist in the form of thin-shell structures, in this paper, the extended level set method (X-LSM) and conformal mapping theory are employed to carry out topology optimization of the ferromagnetic soft actuator on manifolds. The objective function consists of a sub-objective function for the kinematics requirement and a sub-objective function for minimum compliance. Shape sensitivity analysis is derived using the material time derivative and adjoint variable method. Two examples, including a circular shell actuator and a flytrap structure, are studied to demonstrate the effectiveness of the proposed framework.

PDE-Driven Level Sets and Shape Sensitivity for Structural Topology Optimization

2004 ◽  
Author(s):  
Michael Yu Wang ◽  
Xiaoming Wang
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Scalar Function ◽  
Natural Setting ◽  
Structural Topology ◽  
Shape Sensitivity ◽  
Structural Shape ◽  
And Topology ◽  
Global Representation

This paper addresses the problem of structural shape and topology optimization. A level set method is adopted as an alternative approach to the popular homogenization based methods. The paper focuses on four areas of discussion: (1) The level-set model of the structure’s shape is characterized as a region and global representation; the shape boundary is embedded in a higher-dimensional scalar function as its “iso-surface.” Changes of the shape and topology are governed by a partial differential equation (PDE). (2) The velocity vector of the Hamilton-Jacobi PDE is shown to be naturally related to the shape derivative from the classical shape variational analysis. Thus, the level set method provides a natural setting to combine the rigorous shape variations into the optimization process. Finally, the benefit and the advantages of the developed method are illustrated with several 2D examples that have been extensively used in the recent literature of topology optimization, especially in the homogenization based methods.

scholarly journals An efficient approach to reliability-based topology optimization for the structural lightweight design of planar continuum structures

2021 ◽  
Vol 37 ◽  
pp. 270-281
Author(s):  
Fangfang Yin ◽  
Kaifang Dang ◽  
Weimin Yang ◽  
Yumei Ding ◽  
Pengcheng Xie
Keyword(s):  
Topology Optimization ◽  
Lightweight Design ◽  
Integrated Design ◽  
Optimization Methods ◽  
Filter Function ◽  
Continuum Structures ◽  
Performance Indexes ◽  
Reliability Method ◽  
Economic Indexes ◽  
The Impact

Abstract In order to solve the application restrictions of deterministic-based topology optimization methods arising from the omission of uncertainty factors in practice, and to realize the calculation cost control of reliability-based topology optimization. In consideration of the current reliability-based topology optimization methods of continuum structures mainly based on performance indexes model with a power filter function. An efficient probabilistic reliability-based topology optimization model that regards mass and displacement as an objective function and constraint is established based on the first-order reliability method and a modified economic indexes model with a composite exponential filter function in this study. The topology optimization results obtained by different models are discussed in relation to optimal structure and convergence efficiency. Through numerical examples, it can be seen that the optimal layouts obtained by reliability-based models have an increased amount of material and more support structures, which reveals the necessity of considering uncertainty in lightweight design. In addition, the reliability-based modified model not only can obtain lighter optimal structures compared with traditional economic indexes models in most circumstances, but also has a significant advantage in convergence efficiency, with an average increase of 44.59% and 64.76% compared with the other two reliability-based models. Furthermore, the impact of the reliability index on the results is explored, which verifies the validity of the established model. This study provides a theoretical reference for lightweight or innovative feature-integrated design in engineering applications.

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