本論文主要引用楊永斌教授、郭世榮教授[1]於桁架元素、剛架元素之幾何非線性推導，探討靜力情況下平面剛架於剛體運動產生幾何大變位之非線性行為，驗證剛體運動法則與力平衡兩者條件。 應用更新式推演法，表示元素於不同狀態下之物理量。以虛功法為理論基礎推導元素增量力平衡方程式，考慮剛體運動效應及Bernoulli-Euler梁因撓曲產生正向應力、正向應變、剪應力及材料本構關係，並以有限元素法概念，推導出非線性平面剛架元素內力向量。 力學分析中剛體運動法則與力平衡為必須滿足之首要條件，將非線性平面剛架元素內力向量推導結果進行剛體運動檢測，桁架元素剛體運動檢核中，在大旋轉角度下，元素初始節點力作用方向隨著元素方向改變，其值保持不變。剛架元素剛體運動檢核中，剛體平移運動對於力分量的大小並無影響，剛體旋轉運動會造成力分量的大小改變，旋轉角度大小會影響整體元素力平衡。 非線性平面剛架元素內力向量隱含高次項位移變數，因此在數值分析中將元素內力向量對每一個自由度微分得平面剛架元素切線勁度矩陣，利用增量¬－迭代法分析，需滿足每一元素結點力平衡及位移連續。 ;This paper mainly Yang, Y. B., Kuo, S. R. [1] in the geometric nonlinear derivation of truss elements and rigid frame elements, and discusses the nonlinear behavior of plane rigid frame in rigid body motion under static conditions to generate large geometric displacement, and verifies the rigid body motion law. and force balance both conditions. Apply the update green-lagrange method to express the physical quantity of the element in different states.Derive the element incremental force balance equation based on the virtual work method, consider the rigid body motion effect and the normal stress, normal strain, shear stress and material composition rate of the Bernoulli-Euler beam due to deflection, and use the finite element method concept, The internal force vector of the nonlinear plane rigid frame element is derived. In mechanical analysis, the law of rigid body motion and equation of forces are the primary conditions that must be met. The results of the derivation of the internal force vector of the nonlinear plane frame element are tested for rigid body motion to ensure that the element’s initial nodal force acts in the direction of the element after each deformation. The element direction changes, and its value remains the same. The internal force vector of the nonlinear plane frame element implies the displacement variable of the higher order term. Therefore, in the numerical analysis, the element internal force vector is differentiated for each degree of freedom to obtain the tangent stiffness matrix of the plane rigid frame element. It equation of forces and continuous displacement of each element node.
