Application of adaptive virtual element method to thermodynamic topology optimization

IF 2.7 3区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY International Journal for Numerical Methods in Engineering Pub Date : 2024-08-07 DOI:10.1002/nme.7575
Mertcan Cihan, Robin Aichele, Dustin Roman Jantos, Philipp Junker
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Abstract

In this work, a low-order virtual element method (VEM) with adaptive meshing is applied for thermodynamic topology optimization with linear elastic material for the two-dimensional case. VEM has various significant advantages compared to other numerical discretization techniques, for example the finite element method (FEM). One advantage is the flexibility to use arbitrary shaped elements including the possibility to add nodes on the fly during simulation, which opens a new variety of application fields. The latter mentioned feature is used in this publication to propose an adaptive mesh-refinement strategy during the thermodynamic optimization procedure and investigate its feasibility. The thermodynamic topology optimization (TTO) includes a efficient gradient-enhanced approach to regularization of the otherwise ill-posed density based topology optimization approach and was already applied to various material models in combination with finite elements. However, the special numerical treatment leading to efficiency of the regularization approach within the TTO has to be modified to be applicable to VEM, which is presented in the publication. We show the performance of this framework by investigating several numerical results on benchmark problems.

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自适应虚拟元素法在热力学拓扑优化中的应用
本研究采用自适应网格划分的低阶虚拟元素法(VEM)对二维情况下的线性弹性材料进行热力学拓扑优化。与有限元法(FEM)等其他数值离散技术相比,虚元法具有多种显著优势。其中一个优势是可以灵活使用任意形状的元素,包括在模拟过程中即时添加节点的可能性,从而开辟了新的应用领域。本出版物利用后者的特点,在热力学优化过程中提出了一种自适应网格细化策略,并对其可行性进行了研究。热力学拓扑优化(TTO)包括一种有效的梯度增强方法,用于对基于密度的拙劣拓扑优化方法进行正则化,并已结合有限元应用于各种材料模型。然而,TTO 中导致正则化方法效率的特殊数值处理方法必须进行修改才能适用于 VEM,这将在本出版物中介绍。我们通过对几个基准问题的数值结果进行研究,展示了这一框架的性能。
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来源期刊
CiteScore
5.70
自引率
6.90%
发文量
276
审稿时长
5.3 months
期刊介绍: The International Journal for Numerical Methods in Engineering publishes original papers describing significant, novel developments in numerical methods that are applicable to engineering problems. The Journal is known for welcoming contributions in a wide range of areas in computational engineering, including computational issues in model reduction, uncertainty quantification, verification and validation, inverse analysis and stochastic methods, optimisation, element technology, solution techniques and parallel computing, damage and fracture, mechanics at micro and nano-scales, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, and error estimation and mesh generation. It is emphasized that this is by no means an exhaustive list, and particularly papers on multi-scale, multi-physics or multi-disciplinary problems, and on new, emerging topics are welcome.
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