scholarly journals Parametric Level Set-Based Multimaterial Topology Optimization of Heat Conduction Structures

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Yadong Shen ◽  
Jianhu Feng
Keyword(s):  
Topology Optimization ◽  
Heat Conduction ◽  
Objective Function ◽  
Level Set ◽  
Heat Dissipation ◽  
Adjoint Method ◽  
Basis Functions ◽  
Expansion Coefficients ◽  
Quadratic Temperature ◽  
Moving Asymptotes

This paper presents a parametric level set-based method (PLSM) for multimaterial topology optimization of heat conduction structures with volume constraints. A parametric level set-based optimization model of heat conduction structures is built with multimaterial level set (MM-LS) model, which describes the boundaries of different materials by the combination of all level set functions. The heat dissipation efficiency which means the quadratic temperature gradient is conducted as the objective function. The adjoint method is utilized to calculate the sensitivities of the objective function with respect to expansion coefficients of the compactly supported radial basis functions (CSRBFs). The optimal configuration is achieved by updating the expansion coefficients gradually with the method of moving asymptotes (MMA). Several numerical examples are discussed to demonstrate effectiveness of the proposed method for multimaterial topology optimization of heat conduction structures.

2009 A level-set based topology optimization for 2D heat conduction problems using BEM

2013 ◽  
Vol 2013.26 (0) ◽  
pp. _2009-1_-_2009-3_
Author(s):  
Guoxian JING ◽  
Toshiro MATSUMOTO ◽  
Toru TAKAHASHI ◽  
Hiroshi ISAKARI ◽  
Takayuki YAMADA
Keyword(s):  
Topology Optimization ◽  
Heat Conduction ◽  
Level Set

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 for Diffusive Heat Transfer in a Domain with Internal Heat Generation using Optimality Criteria

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
T. Anupkumar ◽  
Noble Sharma ◽  
A. Srinath ◽  
G. Satya Dileep
Keyword(s):  
Heat Transfer ◽  
Topology Optimization ◽  
Objective Function ◽  
Heat Dissipation ◽  
Heat Conduction Problem ◽  
Internal Heat ◽  
Computation Time ◽  
Optimality Criteria ◽  
Gradient Field ◽  
Optimal Topology

The standard volume to point heat conduction problem is used to determine the optimal topology that maximises the heat transfer. Unlike the constructed theory, the present investigation considers heat dissipation potential function as the objective function, whose gradient field is taken as the criterion for allocation of the limited amount of high conductivity material over the domain. The considered domain is rectangular in geometry, where all its sides are insulated except a centrally located patch on one of the sides, which is maintained at a constant temperature. FEM is used to compute the temperature and it is supplied to the topology optimization algorithm to determine the distribution of material with varied thermal conductivity over the domain. Grid independency is performed for five different grid sizes varying from 10x10 to 90x90. The variation of computation time and objective function with mesh refinement is reported.

Minimizing the quadratic mean temperature gradient for the heat-conduction problem using the level-set method

2007 ◽  
Vol 221 (2) ◽  
pp. 235-248 ◽  
Author(s):  
C G Zhuang ◽  
Z H Xiong ◽  
H Ding
Keyword(s):  
Heat Conduction ◽  
Temperature Gradient ◽  
Objective Function ◽  
Level Set Method ◽  
Level Set ◽  
Heat Conduction Problem ◽  
Shape Sensitivity ◽  
Material Derivative ◽  
Quadratic Mean ◽  
Mean Temperature

This paper presents a numerical algorithm for minimizing the quadratic mean temperature gradient for the heat-conduction problem on the basis of the shape derivative for an elliptical system and the level-set method for a propagating surface. The level-set method as an implicit boundary model is employed to represent the optimal boundaries of heat transfer material. The objective function of the optimization problem is the quadratic mean temperature gradient. The shape of physical domain is treated as the design variable. The material derivative theory of the continuum mechanics and the adjoint method are used to implement the shape sensitivity analysis of the objective function. Since the level-set approach itself cannot generate new holes in the material region, as a remedy, the topological derivative of the elliptic equations that generates new holes to suppress the topological dependence of initialization is introduced. Numerical examples demonstrate that the proposed method is an effective technique for the optimal design of the heat-conduction problem.

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