论文标题
具有非对称组件的热导率张量的免费材料优化
Free material optimization of thermal conductivity tensors with asymmetric components
论文作者
论文摘要
自由材料优化（FMO）是拓扑优化的一个分支，其中设计变量是完整的本构张量，可以提供设计问题的最通用形式。考虑到由各向同性材料组成的微观结构，本构张量仍然是积极的和对称的。另一方面，据报道，通过考虑其他物理现象，可以在外观上打破这种构张张量的对称性。在本研究中，我们关注热霍尔效应，当将磁场应用于固体时，它被解释为诱导温度梯度正交到给定温度梯度的现象。这种效果使导热性张量不对称，并证明将本构张量的空间扩展为不对称结构域。我们提出了非对称本构张量的FMO，从而参数化设计空间，以便可以自然满足物理上可用的属性。提供了几个数值实验，以显示该方法的有效性和实用性。
Free Material Optimization (FMO), a branch of topology optimization, in which the design variables are the full constitutive tensors, can provide the most general form of the design problems. Considering the microstructure composed of isotropic materials, the constitutive tensors are yet positive definite and symmetric. On the other hand, it has been reported that the symmetry of this constitutive tensor can be broken in appearance by considering other physical phenomena. In the present study, we focus on the thermal Hall effect, which is explained as the phenomena that induces the temperature gradient orthogonal to a given temperature gradient across a solid when a magnetic field is applied to the solid. This effect makes the thermal conductivity tensor asymmetric and justifies extending the space of the constitutive tensors to be an asymmetric domain. We propose the FMO for asymmetric constitutive tensors, parameterizing the design space so that the physically available property could be naturally satisfied. Several numerical experiments are provided to show the validity and the utility of the proposed method.
