基于混合单元法的预应力混凝土梁非线性分析

利用共旋坐标法提出了一种预应力钢筋混凝土梁非线性分析的混合单元模型，在随转坐标系内，采用分层梁单元来模拟混凝土结构，带初应变的杆单元来模拟预应力钢筋，预应力钢筋杆元和混凝土梁元的变形协调则通过非线性刚臂来实现，通过刚臂单元两端节点位移和力的关系形成预应力钢筋对混合单元刚度矩阵的贡献，从而导出随转坐标系下预应力混凝土梁考虑材料非线性的切线刚度矩阵，几何非线性则由单元随转坐标系到结构坐标系的转换矩阵及其微分来体现，从而获得结构坐标系下混合单元模型的几何与材料双非线性切线刚度矩阵。数个钢筋混凝土及预应力钢筋混凝土梁非线性分析算例表明:所提出的混合单元模型能较好地分析预应力钢筋混凝土梁非线性性能，具有一定的实用价值。

NONLINEAR ANALYSIS OF PRESTRESSED CONCRETE BEAM BASED ON HYBRID ELEMENT METHOD

A nonlinear hybrid element model has been developed for a prestressed concrete beam, based on co-rotational procedure. A concrete structure was simulated by a layered beam and a prestressed reinforcement was regarded as a truss element with an initial strain in a co-rotational coordinate system, and the nodes of a beam and a truss in the same side were linked by a rigid arm, which can ensure a deformation coordination. The contribution of a prestressed reinforcement for a hybrid element stiffness matrix was acquired by the relation of node displacements and forces in both rigid arm ends, and the hybrid element tangent stiffness for matrix material nonlinearity was derived in a co-rotational coordinate system, through the node displacement and force amount and the incremental relationship between a global coordinate system and a co-rotational coordinate system. The hybrid element geometric and material nonlinearity tangent stiffness in a global coordinate system was proposed. Three examples are solved to verify the reliability and correctness of the proposed hybrid element formulation.