钢筋混凝土梁单元双非线性分析的共旋坐标法

Co-rotational Procedure for the Bi-nonlinear Analysis of Reinforced Concrete Beam Element

针对已有的钢筋混凝土梁单元非线性分析模型采用较多的假定和近似从而导致计算量增大及计算精度下降的问题,基于共旋坐标法建立了考虑材料和几何非线性的任意截面钢筋混凝土梁的数值分析模型.首先利用虚功原理计算共旋坐标系下完全粘结钢筋混凝土梁考虑材料非线性的切线刚度矩阵,再通过结构坐标系与共旋坐标系下节点力之间及节点位移之间的总量关系及微分导出的增量关系,最终获得钢筋混凝土梁在结构坐标系中考虑几何与材料双重非线性的切线刚度矩阵.算例结果表明,本文算法可减少计算量、不累积误差、精度高.

Multiple assumptions and approximations in nonlinearity analysis models of existing reinforced concrete beam element result in low calculation efficiency and low calculation accuracy.In this paper,based on co-rotational procedure,a numerical model for a given section considering material and geometrical nonlinear analysis of reinforced concrete beam element was developed.Firstly,by means of virtual work,a tangent stiffness matrix for the material nonlinearity of perfectly-bonded reinforced concrete beam element was derived in co-rotational coordinate system.Then,by building total and incremental relationships derived from differential equations of nodal displacements and forces between global coordinate system and co-rotational coordinate system,respectively,tangent stiffness in global coordinate system reinforced concrete beam element was developed by considering geometric and material nonlinearity.A comparison between the results in this paper and those from existing references has demonstrated that the algorithm developed is highly efficient and accurate with many advantages,such as non-cumulative calculation errors and reduction in computation.