- 學位論文
力法式有限纖維元素模式之二維纖維初步研究
Study on 2-D Fibers for Force-based Finite Fiber Element Model
摘要
在鋼筋混凝土梁柱構件及構架的非線性有限元素分析上，應用力法式有限纖維元素模式配合一組迭代演算流程，僅需要較少的元素自由度，就可以將鋼筋混凝土梁柱構件以及構架的撓曲行為，以很穩定的演算流程模擬出來，並得到高準確度與穩定性的分析結果。由美國加州大學柏克萊分校的太平洋地震工程研究中心所開發的物件導向式有限元素分析軟體OpenSees，即內建有力法式有限纖維元素類別。對於鋼筋混凝土梁柱構件及構架在靜力、動力分析上，使用OpenSees中單軸材料模組與力法式梁柱元素模組，能有效的反映出材料的正向應力應變行為。然而，由於剪力效應的複雜性，此分析方法目前並未考慮剪力效應，因此仍無法反映如pinching effect等剪力行為。當分析需包含剪力效應時，至少需考慮雙軸之應力應變行為。 本論文依據力法式有限纖維元素模式建立一可包含剪力效應之二維纖維元素數學組成模式，並將此模式配合美國休士頓大學所提出的軟化薄膜模式與反覆軟化薄膜模式，推導鋼筋混凝土二維纖維材料組成模式與纖維剖面勁度矩陣；除此之外，另將二維纖維元素數學組成模式配合古典塑性力學理論中的von Mises降伏準則與Prandtl-Reuss塑性流法則，推導彈塑性二維纖維材料組成模式與纖維剖面勁度矩陣，並將其實作為OpenSees軟體架構下的PlasticPlaneStree類別，以探討此分析方法應用於靜力與動力分析時所能反映的剪力效應。
並列摘要
The force-based finite fiber element model with an iterative element state determination procedure has been regarded as one of the most promising simulation methods for reinforced concrete (RC) frames subjected to cyclic-static or dynamic excitations. Compared to the conventional displacement-based approach, the force-based method can accurately simulate the flexural behavior of RC frames with robust computational stability. The OpenSees software framework developed at UC Berkeley has built-in the force-based finite fiber element model. This force-based method, however, does not incorporate the trickier shear effect due to the use of uniaxial fibers and thus is unable to reflect the shear behavior of RC frames. To reflect the shear effect, the fibers sub-dividing the cross sections need to take into account at least the bi-axial or 2-D stress state. Hence, the objective of this thesis is developing a 2-D fiber suitable for the force-based finite fiber element model. In this thesis, the general formulation of 2-D fibers for both RC sections and elasto-plastic sections is presented. The sectional tangent stiffnesses of these two types of sections are derived. The elasto-plastic fiber using the von Mises yielding criteria and the Prandtl-Reuss flow rule is implemented in OpenSees and analyses using the 2-D elasto-plastic fibers are conducted to verify the newly proposed formulation. The analytical results of the static-monotonic, static-cyclic, and dynamic analyses of a cantilever beam basically verify the feasibility of the formulation of 2-D elasto-plastic fibers proposed in this thesis.