几何非线性平面梁考虑收缩徐变的算法研究

Algorithm Study of the Geometrical Nonlinearity Plane Beam Considering Creep and Shrinkage

针对混凝土斜拉桥等大跨柔性混凝土结构同时存在的几何非线性与收缩徐变问题,基于微分法导出了随转坐标系下平面梁在大转动小应变时的几何非线性平衡方程,该方程已计入初应变效应.结合初应变法计算混凝土梁收缩徐变等效节点力有限元列式,利用节点力之间和节点位移之间全量及增量的关系,获得结构坐标系下平面梁单元几何非线性分析中考虑收缩徐变效应影响的实用算法,并给出了详细的计算步骤.对某大跨径混合梁斜拉桥混凝土桥塔进行了考虑混凝土徐变效应的几何非线性分析,计算结果表明本文提出的算法能较好解决上述问题,具有一定的工程应用价值.

As there are geometrical nonlinearity and concrete shrinkage and creep in long-span flexible structures such as concrete cable-stayed bridges,so,based on differential method,the geometrical nonlin-earity balance equation for large rotation displacement-small strain analysis was deduced under co-rota-tional coordinate system,which considered the initial strain.Combining with finite element formula for e-quivalent nodal force of shrinkage and creep by using initial strain method,then,through building total and incremental relationships derived from differential equations of nodal displacements and forces,a prac-tical algorithm for geometrical nonlinearity analysis of the plane beam considering concrete shrinkage and creep under global coordinate was obtained,and its calculation flowchart was also given.The geometrical nonlinearity analysis of the tower of long-span concrete cable-stayed bridge with hybrid girder considering concrete creep was performed.The results demonstrate that the algorithm developed can solve the above mentioned problems and has some engineering application value.