scholarly journals Two Dimensional Topology Optimization of Heat Exchangers with the Density and Level-Set Methods

2021 ◽  
Author(s):  
M. Troya ◽  
D. Tortorelli ◽  
V. Beck
Keyword(s):  
Topology Optimization ◽  
Heat Exchanger ◽  
Level Set ◽  
Volume Fraction ◽  
Level Set Methods

scholarly journals Level set band method: A combination of density-based and level set methods for the topology optimization of continuums

2020 ◽  
Vol 15 (3) ◽  
pp. 390-405
Author(s):  
Peng Wei ◽  
Wenwen Wang ◽  
Yang Yang ◽  
Michael Yu Wang
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Level Set Methods ◽  
Boundary Representation ◽  
Structural Topology ◽  
Topology Changes ◽  
Practical Engineering ◽  
Band Method ◽  
2D And 3D ◽  
Level Set Framework

Abstract The level set method (LSM), which is transplanted from the computer graphics field, has been successfully introduced into the structural topology optimization field for about two decades, but it still has not been widely applied to practical engineering problems as density-based methods do. One of the reasons is that it acts as a boundary evolution algorithm, which is not as flexible as density-based methods at controlling topology changes. In this study, a level set band method is proposed to overcome this drawback in handling topology changes in the level set framework. This scheme is proposed to improve the continuity of objective and constraint functions by incorporating one parameter, namely, level set band, to seamlessly combine LSM and density-based method to utilize their advantages. The proposed method demonstrates a flexible topology change by applying a certain size of the level set band and can converge to a clear boundary representation methodology. The method is easy to implement for improving existing LSMs and does not require the introduction of penalization or filtering factors that are prone to numerical issues. Several 2D and 3D numerical examples of compliance minimization problems are studied to illustrate the effects of the proposed method.

Parametric Shape and Topology Optimization: A New Level Set Approach Based on Cardinal Kernel Functions

2017 ◽  
Author(s):  
Long Jiang ◽  
Shikui Chen ◽  
Xiangmin Jiao
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Material Property ◽  
Kernel Function ◽  
Level Set Methods ◽  
Level Set Function ◽  
Set Function ◽  
Distance Regularization ◽  
Parametric Level Set Method

The parametric level set method is an extension of the conventional level set methods for topology optimization. By parameterizing the level set function, conventional levels let methods can be easily coupled with mathematical programming to achieve better numerical robustness and computational efficiency. Furthermore, the parametric level set scheme not only can inherit the original advantages of the conventional level set methods, such as clear boundary representation and high topological changes handling flexibility but also can alleviate some un-preferred features from the conventional level set methods, such as needing re-initialization. However, in the RBF-based parametric level set method, it was difficult to determine the range of the design variables. Moreover, with the mathematically driven optimization process, the level set function often results in significant fluctuations during the optimization process. This brings difficulties in both numerical stability control and material property interpolation. In this paper, an RBF partition of unity collocation method is implemented to create a new type of kernel function termed as the Cardinal Basis Function (CBF), which employed as the kernel function to parameterize the level set function. The advantage of using the CBF is that the range of the design variable, which was the weight factor in conventional RBF, can be explicitly specified. Additionally, a distance regularization energy functional is introduced to maintain a desired distance regularized level set function evolution. With this desired distance regularization feature, the level set evolution is stabilized against significant fluctuations. Besides, the material property interpolation from the level set function to the finite element model can be more accurate.

Topology optimization of hinge-free compliant mechanisms using level set methods

2013 ◽  
Vol 46 (5) ◽  
pp. 580-605 ◽  
Author(s):  
Benliang Zhu ◽  
Xianmin Zhang ◽  
Nianfeng Wang ◽  
Sergej Fatikow
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Compliant Mechanisms ◽  
Level Set Methods

Level Set Based Robust Shape and Topology Optimization Under Random Field Uncertainties

2009 ◽  
Author(s):  
Shikui Chen ◽  
Sanghoon Lee ◽  
Wei Chen
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Uncertainty Propagation ◽  
Level Set Methods ◽  
Random Variable ◽  
Shape And Topology Optimization ◽  
Extended Space ◽  
And Topology ◽  
Material Uncertainties ◽  
Gauss Type

A level-set-based method for robust shape and topology optimization (RSTO) is proposed in this work with consideration of uncertainties that can be represented by random variables or random fields. Uncertainty, such as those associated with loading and material, is introduced into shape and topology optimization as a new dimension in addition to space and time, and the optimal geometry is sought in this extended space. The level-set-based RSTO problem is mathematically formulated by expressing the statistical moments of a response as functionals of geometric shapes and loading/material uncertainties. Spectral methods are employed for reducing the dimensionality in uncertainty representation and the Gauss-type quadrature formulae is used for uncertainty propagation. The latter strategy also helps transform the RSTO problem into a weighted summation of a series of deterministic topology optimization subproblems. The above-mentioned techniques are seamlessly integrated with level set methods for solving RSTO problems. The method proposed in this paper is generic, which is not limited to problems with random variable uncertainties, as usually reported in other existing work, but is applicable to general RSTO problems considering uncertainties with field variabilities. This characteristic uniquely distinguishes the proposed method from other existing approaches. Preliminary 2D and 3D results show that RSTO can lead to designs with different shapes and topologies and superior robustness compared to their deterministic counterparts.

A Meshless Level Set Method for Shape and Topology Optimization

2011 ◽  
Vol 308-310 ◽  
pp. 1046-1049 ◽  
Author(s):  
Yu Wang ◽  
Zhen Luo
Keyword(s):  
Topology Optimization ◽  
Free Boundary ◽  
Level Set Method ◽  
Level Set ◽  
Level Set Methods ◽  
Discrete Level ◽  
Shape And Topology Optimization ◽  
Level Set Function ◽  
And Topology ◽  
Set Function

This paper proposes a meshless Galerkin level set method for structural shape and topology optimization of continua. To taking advantage of the implicit free boundary representation scheme, structural design boundary is represented through the introduction of a scalar level set function as its zero level set, to flexibly handle complex shape fidelity and topology changes by maintaining concise and smooth interface. Compactly supported radial basis functions (CSRBFs) are used to parameterize the level set function and also to construct the shape functions for mesh free function approximation. The meshless Galerkin global weak formulation is employed to implement the discretization of the state equations. This provides a pathway to simplify two numerical procedures involved in most conventional level set methods in propagating the discrete level set functions and in approximating the discrete equations, by unifying the two different stages at two sets of grids just in terms of one set of scattered nodes. The proposed level set method has the capability of describing the implicit moving boundaries without remeshing for discontinuities. The motion of the free boundary is just a question of advancing the discrete level set function by finding the design variables of the size optimization in time. One benchmark example is used to demonstrate the effectiveness of the proposed method. The numerical results showcase that this method has the ability to simplify numerical procedures and to avoid numerical difficulties happened in most conventional level set methods. It is straightforward to apply the present method to more advanced shape and topology optimization problems.

Level-set methods for structural topology optimization: a review

2013 ◽  
Vol 48 (3) ◽  
pp. 437-472 ◽  
Author(s):  
N. P. van Dijk ◽  
K. Maute ◽  
M. Langelaar ◽  
F. van Keulen
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Level Set Methods ◽  
Structural Topology Optimization ◽  
Structural Topology

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.

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