A condition number-based numerical stabilization method for geometrically nonlinear topology optimization

IF 2.7 3区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
Lennart Scherz, Benedikt Kriegesmann, Claus B. W. Pedersen
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Abstract

The current paper introduces a new stabilization scheme for void and low-density elements for geometrical nonlinear topology optimization. Frequently, certain localized regions in the geometrical nonlinear finite element analysis of the topology optimization have excessive artificial distortions due to the low stiffness of the void and low-density elements. The present stabilization applies a hyperelastic constitutive material model for the numerical stabilization that is associated with the condition number of the deformation gradient and thereby, is associated with the numerical conditioning of the mapping between current configuration and reference configuration of the underlying continuum mechanics on a constitutive material model level. The stabilization method is independent upon the topology design variables during the optimization iterations. Numerical parametric studies show that the parameters for the constitutive hyperelasticity material of the new stabilization scheme are governed by the stiffness of the constitutive model of the initial physical system. The parametric studies also show that the stabilization scheme is independently upon the type of constitutive model of the physical system and the element types applied for the finite element modeling. The new stabilization scheme is numerical verified using both academic reference examples and industrial applications. The numerical examples show that the number of optimization iterations is significantly reduced compared to the stabilization approaches previously reported in the literature.

Abstract Image

基于条件数的几何非线性拓扑优化数值稳定方法
本文为几何非线性拓扑优化引入了一种新的空洞和低密度元素稳定方案。在拓扑优化的几何非线性有限元分析中,由于空隙和低密度元素的刚度较低,某些局部区域经常出现过大的人为变形。本稳定方法采用超弹性材料构成模型进行数值稳定,该模型与变形梯度的条件数相关联,因此与构成材料模型层面上底层连续介质力学的当前配置与参考配置之间映射的数值调节相关联。在优化迭代过程中,稳定方法与拓扑设计变量无关。数值参数研究表明,新稳定方案的构成超弹性材料参数受制于初始物理系统构成模型的刚度。参数研究还表明,稳定方案与物理系统构成模型的类型和有限元建模所采用的元素类型无关。新的稳定方案通过学术参考实例和工业应用进行了数值验证。数值实例表明,与之前文献中报道的稳定方法相比,优化迭代次数明显减少。
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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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