大跨度扁平钢箱梁精细化模拟的一维有限元方法研究

Although to date many theoretical models are available for analyzing thin-walled steel box girder, none of them are of general interests to fit all practical needs: shell/solid element models are too mathematical intensive and time consuming to fulfill routine design tasks,whereas most simplified or semi-analytical methods though implemented with low costs can not accurately capture the deformational and load-bearing behaviour of box girder under arbitrary support and load conditions. As a result, the present investigation starts from regarding the spatial deformation of the box girder as a combination of rigid displacements and local deformations of each slab component; The restraint stiffness parameters of stiffening members will be determined by the method of structural mechanics or numerical analysis, and its effects on the local deformation of stiffened slab are taken into account by deriving the differential equations for the transverse elementary strip of unit width and the undetermined constants involved are specified as functions of displacement parameters of a typical box girder segment. Therefore, an one-dimensional finite segment model is putforward that can predict the interactions among different deformation modes of slab components and stiffening members. The effects of residual stresses and inelastic zone expansion on structural behavior are considered by reformulating the local deformations of inelastic slab components, and meanwhile an explicit elasto-plastic stiffness matrix for the extened beam model is established. In the presence of initial imperfections, the interactions between local buckling modes of slabs and stiffening members are properly simulated and an initial stress approach based on the proposed extended beam segment formulation shall be developed to reliably account for the phenomenon of local-overall interaction buckling. Based on the foregoing research results, a computer program will be written for an efficient numerical simulation of the complex multiple interaction behavior of flat steel box girder. The theoretical model and numerical procedures are subject to error checking and necessary revisions through numerical validations and scaled model tests.This investigation aims to discover the complex mechanism of deformation and internal force distribution within slab components and stiffening members and to present an one-dimensional finite element formulation for a refined, yet computational efficient modeling of the complex full-range behavior of the long-span flat steel box girder.

尽管现有多种钢箱梁计算模型，板壳/实体单元模型太复杂不便于工程应用，而简化模型无法准确描述任意支撑与荷载条件下箱梁实际变形与受力状态。本课题通过叠加板件刚性位移和局部变形来描述大跨度扁平钢箱梁空间位移；基于结构力学理论和数值方法，确定加劲构件的约束刚度，导出单位宽度横向框架条带变形微分方程，确定变形解析解待定常数与梁段位移参数间的关系；建立反映板件与加劲构件变形相互影响的一维梁段有限元模型；提出考虑残余应力及塑性区发展影响的箱梁板件局部变形重构方法以及梁段弹塑性割线刚度列式方法；提出初始几何缺陷影响下板件与加劲构件局部屈曲耦合分析方法以及局部与整体相关屈曲分析的梁段初应力方法。基于上述研究成果，编制扁平钢箱梁高效数值模拟程序；通过数值算例与模型试验，修正理论模型和分析软件。本课题旨在揭示箱梁板件及加劲构件变形与内力分配机理，提出大跨度扁平钢箱梁受力全过程精细化、高效分析的一维有限元方法。

扁平钢箱梁具有较高双向抗弯及抗扭刚度且能节省钢材，是大跨度钢桥主梁主要形式。然而，截面薄壁板件面内和面外刚度显著差别及加劲构件的局部约束，使其呈现出复杂的局部－整体相关受力特征。高效、准确地评估钢箱梁稳定极限承载力是优化结构设计的关键。二维板壳元模型尽管能准确模拟结构受力特征，但数据存储量大且计算效率低，给计算和结果分析带来不便；梁-壳混合单元模型中梁壳结合部在任意荷载及约束条件下的演变规律有待深入研究。为此，本研究提出扁平钢箱梁受力全过程精细化、高效分析的一维有限元方法，已开展的工作和取得的成果如下：.（1）将扁平钢箱梁空间位移分解为截面刚性假定引起的整体位移和考虑板件面外柔性产生的附加变形。附加变形由两部分组成，一是通过施加假想约束，排除箱梁横向框架刚体位移后，由荷载产生的板件变形，二是撤除约束而引起的板件变形。推导了板件位移显式表达式，建立了一维梁段单元模型。与板壳元模型相比，显著减少求解规模，提高计算效率；与混合元模型相比，能模拟任意荷载与约束条件下梁段整体及局部变形特征，具有较好适应性。 .（2）基于一维梁段位移模型，推导了考虑加劲构件约束的扁平钢箱梁内力势能表达式。通过刚性运动检验，得到了基于有限变形理论的势能修正项，确保在扁平钢箱梁受力全过程分析中，内力势能能反映梁段刚度变化。.（3）推导了反映梁段空间转动及梁段各板件局部转动的显式几何刚度矩阵；按弹性及弹塑性区分段建立描述梁段广义位移沿梁长变化的插值函数，推导梁段弹塑性刚度矩阵，有效缩减非线性有限元分析规模。.（4）基于梁段单元刚度矩阵和结构平衡路径临界点识别算法，探明结构最不利变形模式，追踪板件局部屈曲后扁平钢箱梁平衡路径，避免板件缺陷敏感性差异组合分析难题。.（5）编制了扁平钢箱梁一维有限元程序。通过算例分析和实桥稳定承载力分析，发现板件塑化控制结构稳定承载力，说明本研究提出理论、方法和程序的正确性及工程应用价值。