| 摘要: | 依據過去經驗，結構進入非線性時，由於計算複雜化，使整體運算曠日費時，為解決市售套裝之傳統有限元素分析曠日費時之問題，本研究引入非耦合隱式動力有限元素法(Implicit decoupled finite element method, IDFEM)求解運動方程式，並推導一系列元素進行數值分析。在模型基礎相同且分析結果一致的情況下，比較非耦合隱式動力有限元素法與傳統有限元素法運算效率及準確性。
過去進行非線性動力分析時，由於傳統有限元素法之勁度阻尼力無法依照當前狀態改變勁度，使其結構反應產生之不切實際的阻尼力。現實中若結構進入降伏，結構系統需透過更大的位移來消能，使得利用初始勁度進行分析之位移反應較實際來得小。
本研究開發三維新元素與新功能於非耦合隱式動力有限元素分析方法(Implicit decoupled finite element method , IDFEM)，新元素為彈簧元素，其中包含線性彈簧(Linear Spring)、雙線性彈簧(Bilinear Spring)、開孔拉伸塑性彈簧彈簧(Hook Plastic Spring)、開孔壓縮塑性彈簧彈簧(Gap Plastic Spring)；新功能為雙線性彈簧模擬塑鉸，將勁度變化所造之成勁度阻尼力變化加入程式內，除去不切實際的阻尼力，使分析行為更趨於實際行為。程式中可選擇利用初始勁度或是當前勁度，計算勁度阻尼力，進行非線性分析。經由算例與市售有限元素分析軟體SAP2000與ABAQUS相比，證實所發展之新元素與分析方法之正確性。
;According to past experience, when the structure comes to nonlinearity, the calculation is time-consuming, because of the complexity calculations. To solve the time-consuming problem of the traditional finite element analysis, this research introduces the Implicit decoupled finite element method (IDFEM) to solve the equation of motion and derives a series of elements for numerical analysis. In the same model basis and consistent analysis results, we compare the efficiency and accuracy between the implicit decoupled finite element method and the traditional finite element method.
In the past, when nonlinear dynamic analysis was executed, the stiffness-proportional damping force of the traditional finite element method could not change the stiffness according to the current state, which caused the structure to react to the unrealistic damping force. In reality, if the structure enters into yield, the structural system needs to dissipate energy through greater displacement, so that the displacement response of the analysis using the initial stiffness is smaller than in reality.
This research develops new three-dimensional elements and new functions in Implicit decoupled finite element method (IDFEM). The new element is link element, including linear spring and bilinear spring, hook plastic spring, gap plastic spring. The new function is using a bilinear spring to simulate a plastic hinge, which add the stiffness-proportional damping force changed by the stiffness change is added to the program to remove unrealistic damping force and make the analysis result more realistic. In the program, you can use the initial stiffness or the current stiffness to calculate the stiffness-proportional damping force for nonlinear analysis. The new element and the program’s correctness are verified by comparing calculation examples with the commercial finite element analysis software SAP2000 and ABAQUS. |
