考虑材料非线性与温度依赖性,可显著提升热致动器设计性能。
On the Importance of Geometric Nonlinearity and Temperature-Dependent Properties in Multi-Material Thermo-Mechanical Topology Optimization

- 引入基于对数应变的非线性本构模型与温度相关材料参数
- 温度越高,线性模型误差越大,尤其在依赖旋转的结构中
- 全物理模型设计出更坚固、更抗温变的器件,适合高温应用
热力弹性柔性器件通常基于小变形线性弹性与温度无关材料属性设计,尽管其工作温度可能远高于环境温度,此时两类假设均不成立。本文量化了多材料拓扑优化中每项假设的影响与代价。提出一种物理信息驱动的同步分析-设计框架:(i)采用有限应变二次Hencky(对数应变)本构模型,其各向同性热本征应变可在对数应变空间中精确分离;(ii)为钛-铜-钢材料体系引入温度依赖的导热率、热膨胀系数与弹性模量。在三个设计温度下,分别以基线模型与完整物理模型优化热致动器与热夹持器,受质量与可制造性约束。所有收敛设计均通过验证过的非线性有限元求解器,在全部组合的本构律与物性模型下重新评估。结果表明,本构模型是决定性因素:这些器件作为连杆机构运行,线性运动学将旋转误判为压缩应变,误差随温度升高而增大,并集中在最依赖旋转的布局上。线性优化器因回避高旋转结构而掩盖此偏差,导致模型看似可信。采用完整物理模型的设计在设计成本小幅增加的情况下,始终产出更强、更耐温变的器件。
原文摘要 · Abstract (English)
Thermo-mechanical compliant devices are commonly designed with small-strain linear elasticity and temperature-independent material properties, even though they might operate hundreds of kelvin above ambient where both assumptions are questionable. In this work, we quantify the effect and cost of each assumption in multi-material topology optimization of thermally actuated compliant devices. To this end, we introduce a physics-informed, simultaneous analysis-and-design framework with (i) a finite-strain quadratic-Hencky (logarithmic-strain) constitutive model whose isotropic thermal eigenstrain admits an exact additive split in log-strain space, and (ii) temperature-dependent conductivity, thermal expansion, and elastic moduli for a titanium--copper--steel material system. We optimize a thermal actuator and a thermal gripper at three design temperatures under both a baseline model and the full physics, subject to mass and manufacturability constraints. Every converged design is re-evaluated by verified nonlinear finite element solvers in the full factorial of constitutive law and property model. The comparison between the two factors reveals that the constitutive law is the decisive modeling choice: These devices work as linkages where linear kinematics mistakes rotation for compressive strain; its error therefore grows with the design temperature and concentrates on the very layouts that exploit rotation best. Because a linear optimizer also steers away from the rotation-rich mechanisms that would expose this bias, the model can deceptively appear trustworthy when validated against its own designs. Designing with the full physics yields consistently stronger and more temperature-robust devices at a modest increase in design-time cost.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。