钢管混凝土拱极限承载力分析的共旋坐标法

Co-rotational procedure of ultimate bearing capacity analysis for concrete filled steel tubular arch

摘要:

为提高钢管混凝土拱极限承载力分析的精度和效率,基于共旋坐标法建立了考虑材料和几何非线性的钢管混凝土拱数值分析模型．首先基于共旋坐标系下应变和消除刚体位移后的变形为线性关系,利用虚功原理无须迭代就可直接计算出该坐标系下完全粘结钢管混凝土梁单元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,最终获得其在结构坐标系中考虑几何与材料双非线性的切线刚度矩阵,不平衡力完全是基于全量来计算.算例结果表明,该算法具有减少计算量、不累积误差和精度高等优点．

Abstract:

To improve calculation efficiency and accuracy of ultimate bearing capacity analysis for concrete filled steel tube arch, based on co-rotational procedure, a numerical model considering material and geometrical nonlinear analysis for concrete filled steel tube beam element is developed. Firstly, based on a linear relationship of strain in co-rotational coordinate system and deformation excluding displace of rigid body, by means of virtue work, a tangent stiffness matrix for material nonlinearity of perfectly-bonded concrete filled steel tube beam element is derived in co-rotational coordinate system without iteration. 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 concrete filled steel tube beam element is developed considering geometric and material nonlinearity, and unbalanced forces are calculated based on total relations. A comparison between the results in this paper and those from existed references demonstrates that the algorithm in this paper is highly efficient and accurate with many advantages such as non-cumulative calculation errors and reduction in computation.