考慮不確定性於熱固耦合機械尖峰反應之解析力學研究

Abstract

本論文針對熱固耦合結構於不確定熱邊界條件下所產生之機械極值響應進行深入探討，首創一套具解析能力的熱載響應關聯預測方法（Thermal load response correlation,TLRC）。此方法突破傳統以大量數值模擬或實驗數據採集才能估算極值區間的限制，建立一套可直接預測結構關鍵自由度最大熱致變形與內部應力分佈的高效率解法，兼具解析性、可重現性與工程實用性，為熱固耦合結構之安全設計與可靠度評估提供全新技術典範。 本研究首度將 TLRC 方法系統性應用於一維與二維二力桿件 (Truss) 架構中，並結合隨機熱邊界建模與有限元素法進行統計驗證。透過與大規模採集數值樣本比對，證實本方法不僅在極值預測上具高準確性，其對結構內部應力集中區域之定位亦顯著優於傳統手段。研究同時深入分析在極端熱擾動下之應力回應特徵，評估結構是否面臨塑性破壞風險，展現方法於熱致安全性診斷上的關鍵價值。 本論文架構涵蓋五大核心章節：第一章說明研究動機與背景脈絡；第二章推導熱固耦合有限元素理論與座標轉換機制；第三章提出 TLRC 模型與數學化極值預測策略；第四章以多組實例（包含太陽能支架、高功率導線、微機電橋式元件等）進行應用驗證，具體展現方法的跨尺度適用性與工程意義；第五章綜合研究成果並針對未來應用與理論延伸提出具體建議。 綜上所述，本研究不僅建立一個兼具物理保真性與數值效率的預測架構，更有效解決熱場不確定性對結構設計帶來的風險預測瓶頸，為熱固耦合問題的極值解析開啟一條具高度前瞻性的研究新路徑。

This thesis presents a novel analytical methodology for predicting the peak mechanical responses of thermo-solid coupled structures under uncertain thermal boundary conditions. A Thermal load response correlation (TLRC) framework is proposed to efficiently estimate the critical thermal deformation and internal stress response without relying on large-scale numerical sampling. This framework breaks through the traditional limitations of data-acquisition-based uncertainty quantification by offering a high-fidelity, computationally efficient, and physically transparent alternative, laying a robust foundation for reliable structural design under thermal uncertainty. The TLRC method is systematically implemented on both 1D and 2D Truss-based structural systems and rigorously verified through finite element simulations incorporating random thermal boundary conditions. The predicted peak displacements and stress distributions are benchmarked against data-acquisition results, demonstrating excellent agreement and confirming the accuracy and robustness of the proposed method. Furthermore, the internal stress behavior under extreme thermal loads is thoroughly investigated to assess potential material failure risks and stress concentration zones. This work is structured into five core chapters. Chapter 1 introduces the research motivation and contextual background. Chapter 2 provides a comprehensive derivation of the thermo-mechanical finite element formulation and coordinate transformation mechanisms. Chapter 3 details the theoretical development of the TLRC model and its peak prediction capability. Chapter 4 validates the methodology through various practical case studies, including solar panel aluminum frames, high-power conductor wires, and MEMS-based microbridge structures, showcasing the wide applicability and engineering relevance of the method. Finally, Chapter 5 summarizes the findings and discusses future directions for extending the theory and broadening its applications. In conclusion, this study offers a significant advancement in peak response prediction under thermal uncertainty. It establishes an efficient and generalizable framework that not only improves analytical insight into thermo-mechanical behaviors but also provides practical tools for structural safety assessment and reliability engineering.