中文摘要 本研究主要探討向量式有限元素法模擬空間剛架大變位的能力。傳統的幾何非線性有限元素法大多採用能量法或虛功原理配合元素節點位移增量的形狀函數建立相應的彈性和幾何勁度矩陣,再用預測-迭代方式求解。不同於傳統幾何非線性有限元,向量式有限元素法以構件和節點為基礎,將結構離散成一群構件點和構件元的組合,利用牛頓運動定律預測構件點運動,使複雜問題簡化成一組向量方程式求解。向量式有限元素法利用虛擬逆向運動扣除結構元的剛體平移和轉動進而估算構件元的節點變形,再用主軸座標定義構件元的應變並以能對應力觀念求節點對應的內力,最後用顯式時間積分法解構件點運動方程式,可精確、有效的計算多個連續體大剛體轉動和幾何大變位行為,同時該方法也可以直接推廣至其它元素組成的結構。
ABSTRACT In this paper, the vector form intrinsic finite element (VFIFE) method is applied to simulate the geometrically nonlinear behaviors of space frame structures. In the conventional geometrically nonlinear finite element method, energy method or principle of virtual work depend on shape function of element incremental displacement is used to establish the elasticity stiffness matrix and the geometry stiffness matrix. Then, we use prediction-iteration to find the answer. Different from conventional finite element method, the VFIFE method models analyzed domain to be composed by finite particles and Newton’s second law is applied to describe each particle’s motion. Thus, the calculation of VFIFE method becomes the equation which is uncoupled vector. In the analysis of VFIFE method, the Inverse kinematic of virtual is used to deduct the rigid body translational and rotation, which estimates particle’s deformation of structured element, the deformation coordinate is used to find strain of structured element and particle’s internal force. After combining it with explicit time integration scheme, the VFIFE method can simulate the dynamic behaviors effectively of multi-bodies system having large rigid body motion and deformation. Besides, the method can be extended to structures of the other elements.