多材料热机械拓扑优化中几何非线性与温度相关特性的重要性

中文摘要 AI 辅助

热机械柔顺器件通常采用小应变线弹性理论和温度无关的材料特性进行设计，即便它们可能在高于环境温度数百开尔文的环境中工作，此时这两个假设均存在问题。本研究量化了热致动柔顺器件多材料拓扑优化中每个假设的影响与代价。为此，我们引入了一种物理信息驱动的同步分析-设计框架，该框架包含：(i) 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实现精确加性分解；(ii) 钛-铜-钢材料系统的温度相关电导率、热膨胀系数和弹性模量。我们针对热致动器和热夹持器，在三个设计温度下，分别采用基线模型和全物理模型进行优化，优化过程需满足质量和可制造性约束。每个收敛的设计都通过经过验证的非线性有限元求解器，在本构定律和特性模型的全因子组合下重新评估。对两个因素的比较表明，本构定律是决定性的建模选择：这些器件作为连杆机构工作，线性运动学将旋转误认为压缩应变；因此其误差随设计温度升高而增大，并集中在最能利用旋转的布局上。由于线性优化器也会避开富含旋转的机制（这些机制会暴露其偏差），因此该模型在针对自身设计进行验证时，可能会产生虚假的可信度。采用全物理模型进行设计，可得到强度更高、温度鲁棒性更强的器件，仅需适度增加设计时间成本。

英文摘要

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.

发表机构

• University of California, Irvine（加利福尼亚大学欧文分校）

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