本文以向量式有限元(Vector Form Intrinsic Finite Element，VFIFE，V-5)以及運動解析作為板殼結構分析之基本理論，發展板殼結構的VFIFE-DKT元素。引用運動解析理論中的概念：點值描述，途徑單元和移動基礎架構，將板殼結構的非線性運動行為，轉為可用材料力學微變形分析概念處理的小變形問題，並在元素層面引入DKT板元與CST薄膜元的分析概念，完成VFIFE-DKT元素的推導。基於運動解析的發展理念，本文著重於板殼結構運動行為的驗證與探討，在動力分析部份，本文提出兩種轉動慣量的計算方式，並以穩定的變形座標選定法則計算板殼結構的小變位振動與自由運動及動力挫屈等問題，其結果皆與文獻結果一致。在靜力問題部份則是提出一套VFIFE板殼元標準的靜力分析程序，算例結果顯示此程序穩定並具有良好的收斂性。而為了驗證板殼轉動慣量的準確性，本文亦完成一薄殼結構大變位實驗之量測與比對，結果顯示本文VFIFE-DKT元素與轉動慣量計算與所得分析實驗結果近似。最終則是依運動解析的理念，提出一個板殼元簡易的開裂分析程序，確保結構系統破壞後能夠成為獨立的運動體，且系統總能在開裂過程不會有額外的損失。 In order to simulate the large displacement of a thin shell structure, a novel shell element based on the vector form intrinsic finite element (VFIFE) method is presented. The motion of the shell structure is characterized by the motions of finite particles. Each particle is subjected to the external forces and internal forces. The motion of each particle satisfies the Law of Mechanics. In addition, three key processes of the VFIFE method such as the point value description, path element and convected material frame are adopted. A fictitious reversed rigid body motion is used to separate the rigid body motion and the deformations of the VFI-DKT element within each path element. The internal forces of the element determined in the deformation coordinate system satisfy the equilibrium equations. Through the numerical analyses of the benchmark structures undergo extremely-large displacements and rotation during motion, this novel shell element of the VFIFE method demonstrates its outstanding accuracy and efficiency.
