AI 中文总结
研究考虑非线性蠕变的热结构拓扑优化问题，引入可微框架，用诺顿模型结合自动微分进行灵敏度分析，通过向后欧拉格式求解瞬态响应，在二维基准验证并用于三维涡轮叶片成分设计，凸显高温蠕变感知设计的必要。
AI 中文摘要
蠕变是高温下金属部件的主要寿命限制机制，即使应力低于屈服强度，在持续载荷下也会产生永久变形。将蠕变纳入拓扑优化（TO）仍未解决，因为其响应是非线性、历史依赖且热机械耦合的，以往工作常依赖线性粘弹性模型，无法捕捉金属在高温下的行为。为弥补这一差距，我们引入了一个可微的热结构TO框架。该方法使用诺顿模型考虑蠕变变形，并利用JAX的自动微分进行伴随灵敏度分析，通过向后欧拉格式求解规定使用寿命内的瞬态材料响应。我们的目标是在体积约束下最小化蠕变变形。首先在标准二维基准上验证框架，结果表明与仅针对弹性刚度优化的设计相比，该公式显著降低了永久变形。然后提出一个具有挑战性的问题，即对三维梯度材料涡轮叶片进行成分设计，其中两种候选合金的局部混合比例被优化。这个具有挑战性的问题展示了框架的全部能力，包括瞬态非线性蠕变、耦合热载荷、三维几何形状和基于梯度的多材料设计，突出了高温应用中蠕变感知设计的必要性。
英文摘要
Creep is a primary life-limiting mechanism for metallic components operating at high temperature, producing permanent deformation under sustained loads even when stresses remain below yield. The design of structures to minimize this deformation is critical to extending the service life of components. Incorporating creep into topology optimization (TO) remains open because the response is nonlinear, history-dependent, and thermomechanically coupled, and prior work often relies on linear viscoelastic models, which do not capture the behavior of metals at high temperatures. To bridge this gap, we introduce a differentiable thermo-structural TO framework. The approach considers creep deformation using the Norton model and leverages JAX's automatic differentiation to perform adjoint sensitivity analysis, enabling efficient gradient-based optimization. The transient material response is solved via a backward Euler scheme over a prescribed service life. Our objective is to minimize creep deformation subject to a volume constraint. We first demonstrate the framework on canonical two-dimensional benchmarks, showing that the proposed formulation significantly reduces permanent deformation compared to designs optimized solely for elastic stiffness. We then pose, as a challenge problem, the compositional design of a three-dimensional graded material turbine blade in which the local mixture of two candidate alloys is optimized. This challenge problem exercises the full capability of the framework, including transient nonlinear creep, coupled thermal loading, three-dimensional geometry, and gradient-based multi-material design, highlighting the need for creep-aware design in high-temperature applications.
CommentsSubmitted to Structural and Multidisciplinary Optimization
