Discrete variable topology optimization for simplified convective heat transfer via sequential approximate integer programming with trust‐region

Yan, Xiao; Liang, Yuan; Cheng, Gengdong

doi:10.1002/nme.6775

Cited by 19 publications

(5 citation statements)

References 49 publications

(164 reference statements)

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“…Liang et al suggested a sequential approximate integer programming with a trust region framework to restrict the range of discrete design variables by linearizing the non-linear trust region constraint [139]. This provided method was also extended into 3D structures and convective heat transfer problems [140,141].…”

Section: Augmented Lagrangementioning

confidence: 99%

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

Long,

Saeed,

Zhang

et al. 2024

CMES

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This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures. These structures, commonly encountered in engineering applications, often involve complex objective and constraint functions that cannot be readily expressed as explicit functions of the design variables. As a result, sequential approximation techniques have emerged as the preferred strategy for addressing a wide array of topology optimization challenges. Over the past several decades, topology optimization methods have been advanced remarkably and successfully applied to solve engineering problems incorporating diverse physical backgrounds. In comparison to the large-scale equation solution, sensitivity analysis, graphics post-processing, etc., the progress of the sequential approximation functions and their corresponding optimizers make sluggish progress. Researchers, particularly novices, pay special attention to their difficulties with a particular problem. Thus, this paper provides an overview of sequential approximation functions, related literature on topology optimization methods, and their applications. Starting from optimality criteria and sequential linear programming, the other sequential approximate optimizations are introduced by employing Taylor expansion and intervening variables. In addition, recent advancements have led to the emergence of approaches such as Augmented Lagrange, sequential approximate integer, and non-gradient approximation are also introduced. By highlighting real-world applications and case studies, the paper not only demonstrates the practical relevance of these methods but also underscores the need for continued exploration in this area. Furthermore, to provide a comprehensive overview, this paper offers several novel developments that aim to illuminate potential directions for future research.

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Section: Augmented Lagrangementioning

confidence: 99%

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

Long,

Saeed,

Zhang

et al. 2024

CMES

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show abstract

“…In addition to the optimization techniques discussed above, a limited number of studies have investigated the Cuckoo Search Algorithm, linear programming, − finite volume method (for topology optimization), , and nonlinear least-squares error . However, justification for the applicability and usage of these techniques to different heat transfer problems has been missing in these studies, as not all optimization techniques could fit any problem, , depending on the given constraints and objectives.…”

Section: Introductionmentioning

confidence: 99%

Optimizing the Heat Loss from an Insulation Material and Boundary Layer Thickness of Airflow through a Hot Plate Using Nonlinear Least-Squares Error and Linear Programming Algorithms

Alrasheed

2023

ACS Omega

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Heat loss is a major challenge in heat transfer problems. Several researchers have minimized heat loss for different heat transfer cases, focusing on one optimization technique; however, not all optimization techniques are suitable for a given problem. A limited number of studies have compared different techniques for a given problem under boundary conditions and constraints. This review revisits basic heat transfer problems and identifies a promising technique for each problem to minimize heat loss. The paper considers three techniques: nonlinear least-squares error (LSE), interior point linear programming (IPLP), and genetic algorithm. Two cases are studied: 1. heat loss optimization from cylindrical insulating surfaces and 2. laminar airflow on a heated plate. The results are compared for each technique, and a suitable technique is recommended for each considered case. Nonlinear LSE is found to be most suitable for case 1. IPLP and GA are recommended for the Case 2 problem. The average thermal conductivity is found to be 0.081 W/mK. The average insulation thickness is found to be 213.25 mm. This research will act as a basis for future research to justify and implement suitable techniques for different heat transfer problems.

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“…However, the level set method has the disadvantage of initialization dependence; thus, the location of convection boundaries will greatly affect the optimization results. More importantly, the above studies did not consider the fact that a structure boundary might be partly convective (Hu et al, 2008;Wang and Qian, 2020;Yan et al, 2021). Hence, it is necessary to identify whether a boundary is convective, adiabatic or partly convective.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization for thermal structures considering design-dependent convection boundaries based on the bidirectional evolutionary structural optimization method

et al. 2023

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Abstract. Based on the bidirectional evolutionary structural optimization (BESO) method, the present article proposes an optimization method for a thermal structure involving design-dependent convective boundaries. Because the BESO method is incapable of keeping track of convection boundaries, virtual elements are introduced to assist in identifying the convection boundaries of the structure. In order to solve the difficult issue of element assignment under a design-dependent convection boundary, label matrixes are employed to modify the heat transfer matrix and the equivalent temperature load vector of elements over topology iterations. Additionally, the optimization objective is set to minimize the maximum temperature of the structure in order to deal with the objective reasonableness, and the p-norm method is then used to fit the objective function to calculate sensitivity. Finally, several cases, including 2D and 3D structures under various heat transfer boundary conditions, are provided to illustrate the effectiveness and good convergence of the proposed method.

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Discrete variable topology optimization for simplified convective heat transfer via sequential approximate integer programming with trust‐region

Cited by 19 publications

References 49 publications

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

Optimizing the Heat Loss from an Insulation Material and Boundary Layer Thickness of Airflow through a Hot Plate Using Nonlinear Least-Squares Error and Linear Programming Algorithms

Topology optimization for thermal structures considering design-dependent convection boundaries based on the bidirectional evolutionary structural optimization method

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