【作者】 张俊峰；

【导师】 郝际平；

【作者基本信息】 西安建筑科技大学 ， 结构工程， 2008， 博士

【摘要】 传统的设计方法分为两个阶段,通过一阶线弹性理论分析计算结构在各种荷载作用下的内力,即结构分析;然后再将结构分析求得的内力用极限状态理论的相关方程进行逐个杆件的截面验算,即构件设计。这种设计方法有很大的缺陷:结构内力分析模式与构件承载力计算模式不一致,不能对结构进行完全的整体分析,而必须采用规范中的计算公式对单构件进行强度和稳定验算。而高等分析是一种新的分析方法,它通过精确的一次非线性分析,完善的考虑结构的二阶效应及其他因素的影响,完成目前两阶段设计所作的工作。由于它分析时能充分描述结构系统及构件的强度和稳定性,直接考虑结构的几何、材料非线性性能,从而避免对构件承载力进行逐个的安全验算,使设计更加合理,也大大简化了设计过程。本课题对高等分析理论的塑性铰法进行了比较全面的分析,分别研究了基于有限元法的集中塑性铰模型和基于梁柱法的精细塑性铰模型,对几何非线性、剪切变形、翘曲、初始缺陷和节点半刚性都进行了研究。最后根据面向对象的思想,采用C++语言编制了面向对象的空间钢框架高等分析程序ADANS,为该理论在工程中的应用提供实现途径。从理论分析到程序实现,本文立足三维空间结构,主要做了如下工作:根据连续介质力学的有限变形理论,从更新Lagrange构形的虚位移原理出发,得到了空间梁柱单元的虚功增量平衡方程;以三次插值函数为形函数,考虑剪切变形、翘曲变形、双向弯曲、扭转、轴向变形以及耦合项的影响,推导了三维空间薄壁梁柱单元的切线刚度矩阵,在塑性铰处理上根据Prandtl-Reuss理论和Drucker公式,推导了单元杆端出现塑性铰时单元的弹塑性刚度矩阵。分别对考虑初始缺陷和不考虑初始缺陷的空间梁柱单元进行了研究,推导了两种情况下考虑剪切变形影响的几何非线性空间梁柱单元刚度矩阵。对于不考虑初始缺陷的空间梁柱单元,又着重研究了残余应力,弯曲引起的渐进屈服,弯扭耦合的影响,推导了单元的弹塑性刚度矩阵。对柱弱轴顶底角钢半刚性连接节点进行了试验研究,还提出了一种新的柱弱轴半刚性连接节点形式,研究了该节点连接的性能,并与柱强轴半刚性连接进行了对比。采用单元端部附加连接弹簧的方法研究了半刚性框架的非线性性能;并对端部为铰接,刚接,半刚性的各种连接情况进行了讨论。根据面向对象的编程思想,将有限单元研究域分为:节点类(CNode)、节点管理类(CNodeMng)、单元类(CBaseElemnt)、截面特性类(CBaseElePro)、材料类(CBaseMaterial)、荷载类(CLoad)、荷载组类(CLoadGroup)以及总体结构类(CGlobalElement),并派生了基于节点类、单元类、材料类、截面特性类的派生类,算法中引入牛顿-拉夫逊迭代法和广义位移法,并对空间几何非线性的大转动,恢复力的求解,初始坐标转换以及收敛准则等问题进行了探讨。结合本文研究的空问钢结构高等分析理论,编制了面向对象的空间钢框架高等分析程序ADANS。使用本文程序对一些有代表性的钢框架结构进行了分析。实践证明本文单元具有良好的精度,每个构件通常只需用很少的单元来模拟就能够获得结构的性能。对采用ANSYS进行结构极限承载力的分析进行了研究,探讨了如何基于数据文件对ANSYS进行二次开发,在此基础上编制了外部可执行程序CRSTRESS来直接考虑残余应力,并对直接考虑残余应力的平面及空间钢框架的极限承载力进行了研究,最后对某体育馆拱形变截面,变曲率刚架进行了分析,评估了该结构的安全性能。更多还原

【Abstract】 The traditional design method consists of two stages: elastic analysis is used to determine the forces acting on each member of a structural system, whereas inelastic analysis is used to determine the strength of each member treated as an isolated component. However, despite its popular use in the past and present as a basis for design, the approach has major limitations. There is no verification of the compatibility between the isolated member and the member as part of a frame. The individual member strength equations as specified in specifications are not concerned with system compatibility. As a result, there is no explicit guarantee that all members will sustain their design loads under the geometric configuration imposed by the framework. The advanced analysis is actually a kind of second-order elasto-plastic analysis method. It refers to any method that can capture the strength and stability of a structural system and its individual members in such a manner that individual member capacity checks are not required, which simplify the design process.The simple plastic-hinge model based on the finite element theory and the refined plastic-hinge model based on the beam-column theory were derived. The geometric nonlinear, material nonlinear, shear deformation, torsional deformation, initial imperfection and semi-rigid connections were discussed in the paper. Object-oriental program ADANS based on space steel frame advanced analysis theory was compiled using C++ language. The followings were the main contents in detail.Based on the theory of continuous medium mechanics, second-order elastic stiffness matrix of a 3-D beam-column for space steel frames was derived making use of updated Lagrangian formulation, virtual displacement principle and cubic interpolation functions considering shearing effect. Nonlinear effects, such as initial imperfection, shear deformation, warping deformation, dual-direction bending, torsion and axial deformation were considered in element formulation. Based on the Prandtl-Reuss and Drucker theory, the element stiffness matrix considering plastic-hinge occurred on the ends of the element was derived.Spatial beam-column elements with and without initial imperfection were studied. And their stiffness matrixes considering shear deformation effect were derived. For element without the initial imperfection, the effects of residual stress, gradual yield reduced by bending, the couple of bending and torsion were also studied.Moment-rotation relationship of semi-rigid beam-to-column minor axis connections was researched through experimental tests. A new type connection was proposed. The performance of the connection was studied and contrasted with semi-rigid beam-to-column major axis connection.Modified beam element method was used to account for the effect of connection flexibility on the structural behavior. The pin, rigid and semi-rigid connections were discussed.Based on the object-oriented analysis and design conception, the finite element analysis domain was divided into many classes, such as CNode, CNodeMng, CBaseElement, CBaseElePro, CBaseMaterial, CLoad, CLoadGroup, CGlobalElement and lots of inherit classes. Using advanced analysis theories, the spatial steel frame analysis program was complied. Nonlinear analysis adopted Newton-Raphson and general displacement control methods. The problems about finite space rotational properties, some update methods of beam-column element transformation matrix and convergence rules were discussed. The static analytical results of proposed elements were compared fairly well with that of some representative steel frames, and only few proposed elements for each member were needed to achieve acceptable accuracy. The proposed beam-column element has excellent efficiency and will save much time in the analysis of large-scale structures compared to numerically integrated element.Through the data file, the further development of ANSYS was achieved. The program CRSTRESS considering the residual stress effect was compiled, and through which plane and spatial steel frame were studied. Finally, the ultimate strength capacities of an arch steel frame with variable curvatures and variable sectional heights were studied.更多还原