Optimum design and thermal modeling for 2D and 3D natural convection problems incorporating level set‐based topology optimization with body‐fitted mesh†

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.

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J122025 A study of the optimum design of the locally resonant sonic materials using the level set based-topology optimization method

The Proceedings of Mechanical Engineering Congress Japan ◽

10.1299/jsmemecj.2012._j122025-1 ◽

2012 ◽

Vol 2012 (0) ◽

pp. _J122025-1-_J122025-2

Author(s):

Takayuki YAMADA ◽

Toshiro MATSUMOTO

Keyword(s):

Topology Optimization ◽

Optimum Design ◽

Level Set ◽

Optimization Method ◽

Topology Optimization Method

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

Journal of Mechanical Design ◽

10.1115/1.4047900 ◽

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.

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