本研究主旨在發展預力混凝土(Pre-stressed Concrete)的數值分析法。了解預力混凝土的力學行為，再藉由向量式有限元素法(Vector Form Intrinsic Finite Element Method , 以下簡稱VFIFE)來模擬混凝土構建配置鋼筋、鋼鍵的幾何非線性與材料非線性行為。VFIFE分析的流程與傳統有限元素法概念截然不同，是一種向量式的運算模式，以質點運動、途徑單元內的逆向剛體位移且不需要解矩陣為其最大優點。為了精確的計算預力混凝土元素的內力，本文將VFIFE均質材料剛架元內力計算延伸至複合材料剛架元內力計算。 複合材料斷面分析為了滿足斷面平面保持平面假定(斷面諧和條件)，引入纖維斷面法(Fiber Cross Section Method)與迭代法來計算預力混凝土複合斷面的軸力、彎矩，再與加拿大多倫多大學(University of Toronto)所開發的斷面計算軟體Response2000，比對彎矩-曲率(Moment-Curvature)，藉以驗證內力程式正確性，並加入VFIFE進行結構分析。本研究的結果可供學界與工程界模擬分析預力構件施工、測量、設計等參考。 ;The purpose of this thesis is to develop a new element that can analyze the pre-stressed concrete frame based on VFIFE. Simulate the nonlinear material and nonlinear geometry behavior of pre-stressed concrete or reinforced concrete. VFIFE is a vector form analysis method that is different to traditional finite element method. Advantages of VFIFE are point describe, inverse rigid body motion in each path element and no need to solve the matrices. This thesis based on VFIFE frame element extend to composite material section frame element for calculate the pre-stressed concrete internal forces.
For section strain distribution must be satisfy the assumption plane remain plane, pre-stressed concrete Internal forces program quotes Fiber Cross Section Method and iteration method to calculate the axial force and moment, and compare with software Response2000 which is developed by University of Toronto, verify internal force program by the Moment-Curvature diagram. Internal force program add in VFIFE method to do structure analysis. Finally, Results of this thesis provide some information of pre-stressed problem to Academic and Engineering.
