Topology Optimization of Thermal Initial Value Problems Exploiting Efficient Harmonic Analysis-Reference-Cited by-同舟云学术

Topology Optimization of Thermal Initial Value Problems Exploiting Efficient Harmonic Analysis

Published:2024-05-07 Issue: Volume: Page:
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Author:

Işıklar Göktuğ¹^ORCID,Christiansen Rasmus Ellebæk¹,Sigmund Ole¹

Affiliation:

1. Technical University of Denmark: Danmarks Tekniske Universitet

Abstract

Topology optimization can be employed to manipulate transient thermal behavior for heat transfer devices. As a gradient-based approach, transient topology optimization faces challenges with the CPU cost of the associated forward and backward time-stepping procedure. This study introduces a harmonic analysis-based substitute optimization method to alleviate these computational challenges. Using an analytical solution for a one-dimensional heat conduction problem, we derive a conversion coefficient linking harmonic excitation frequency to the desired transient time instance. Applying this harmonic formulation in the topology optimization of a two-dimensional transient heat conduction problem shows a remarkable speedup, around a factor of 20 per design iteration, with less than a 5% decrease (at most) in the figure of merit compared to the transient approach. Extending the study to include heat convection displays a stable region where the proposed harmonic substitute method sustains the same computational efficiency with less than a 10% difference for objective value comparison in the worst-case scenario.

Publisher

Research Square Platform LLC

Reference30 articles.

1. Dbouk, T. (2017) {A review about the engineering design of optimal heat transfer systems using topology optimization}. Applied Thermal Engineering 112: 841--854 https://doi.org/10.1016/j.applthermaleng.2016.10.134, Conjugate heat transfer,Design,Fluid flows,Heat conduction,Topology optimization, 13594311, :C\:/Users/gokisi/Documents/articles/Dbouk_AppliedThermalEngineering_2017.pdf:pdf, Topology optimization (TO) is a promising numerical technique for designing optimal engineering designs in many industrial applications. It is expected that it might become an unavoidable engineering tool for many new rising technologies such as the additive manufacturing or metal 3D printing as addressed recently in the literature. During the last fifteen years, several TO methods have been developed for optimizing thermal systems based on conductive, convective and conjugate heat transfer. These numerical methods and tools are dispersed in the literature, and there are no enough comparisons between them which makes one doubts their real capabilities in finding really optimal designs. This paper presents a review about TO design methods that have been developed during the last 15 –20 years to design optimal heat transfer systems. Each numerical method is presented briefly with an emphasize on its advantages, disadvantages, limitations and perspectives. Finally, this review shows that TO today is not yet a robust numerical design technique for finding optimal designs of thermal systems.

2. Dems, K. and Rousselet, B. (1999) {Sensitivity analysis for transient heat conduction in a solid body - Part I: External boundary modification}. Structural Optimization 17(1): 36--45 https://doi.org/10.1007/bf01197711, 09344373, :C\:/Users/gokisi/Downloads/BF01197711.pdf:pdf, A transient hat conduction problem within a thermal anisotropic solid body is formulated. Considering an arbitrary thermal functional defined over space and time domains, its first-order sensitivities with respect to variation of structural material parameters as well as external boundary are derived using the direct and adjoint approaches. {\textcopyright} Springer-Verlag 1999.

3. Madsen, S{\o}ren and Lange, Nis P. and Giuliani, Luisa and Jomaas, Grunde and Lazarov, Boyan S. and Sigmund, Ole (2016) {Topology optimization for simplified structural fire safety}. Engineering Structures 124: 333--343 https://doi.org/10.1016/j.engstruct.2016.06.018, Length scale,Multiphysics,Robustness,Structural fire safety,Topology optimization, 18737323, :C\:/Users/gokisi/Documents/Mendeley Desktop/Madsen et al. - 2016 - Topology optimization for simplified structural fire safety.pdf:pdf, Topology optimization is applied in an idealized structural fire safety model, where the minimum compliance problem is constrained by temperature-controlled structural degradation. The constraint ensures a certain structural stiffness after a prescribed time. As this time period is extended, resulting optimized topologies tend to become thicker or introduce redundant members that can take over when structural parts near the origin of the fire lose their load carrying capability. Hence, the structural degradation model acts as an erosion operator on the topology and indirectly enforces a minimum length scale on the final designs.

4. Sigmund, Ole (2009) {Manufacturing tolerant topology optimization}. Acta Mechanica Sinica/Lixue Xuebao 25(2): 227--239 https://doi.org/10.1007/s10409-009-0240-z, Compliant mechanisms,Manufacturing constraints,Robust design,Topology optimization, 05677718, :C\:/Users/gokisi/Downloads/s10409-009-0240-z.pdf:pdf, In this paper we present an extension of the topology optimization method to include uncertainties during the fabrication of macro, micro and nano structures. More specifically, we consider devices that are manufactured using processes which may result in (uniformly) too thin (eroded) or too thick (dilated) structures compared to the intended topology. Examples are MEMS devices manufactured using etching processes, nano-devices manufactured using e-beam lithography or laser micro-machining and macro structures manufactured using milling processes. In the suggested robust topology optimization approach, under- and over-etching is modelled by image processing-based "erode" and "dilate" operators and the optimization problem is formulated as a worst case design problem. Applications of the method to the design of macro structures for minimum compliance and micro compliant mechanisms show that the method provides manufacturing tolerant designs with little decrease in performance. As a positive side effect the robust design formulation also eliminates the longstanding problem of one-node connected hinges in compliant mechanism design using topology optimization. {\textcopyright} 2009 The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH.

5. Zhuang, Chungang and Xiong, Zhenhua and Ding, Han (2013) {Topology optimization of the transient heat conduction problem on a triangular mesh}. Numerical Heat Transfer, Part B: Fundamentals 64(3): 239--262 https://doi.org/10.1080/10407790.2013.791785, 10407790, :C\:/Users/gokisi/Downloads/Topology Optimization of the Transient Heat Conduction Problem on a Triangular Mesh.pdf:pdf, Optimization design of the transient heat conduction problem is different from steady-state heat conduction because of varying temperature. This article proposes the integral of temperature gradient over a fixed time interval as an objective function. The shape sensitivity of the transient heat conduction problem is derived. The derivative information of the objective function about the element densities is used as a strategy to create holes. A narrow band on a triangular mesh is proposed to improve the computational efficiency. Numerical examples are presented to demonstrate the effectiveness of the proposed approach for optimal design of transient heat conduction problems. {\textcopyright} 2013 Copyright Taylor and Francis Group, LLC.