空间梁单元的理论研究及其在桥梁中的应用

发布时间：2018-03-14 00:51

本文选题：空间梁单元　切入点：刚度矩阵　出处：《长沙理工大学》2014年硕士论文　论文类型：学位论文

【摘要】：梁结构作为桥梁的重要承重结构,在工程中受到了十分广泛的应用。因此,对其进行准确合理的计算分析是十分必要的。本文以梁单元为主要研究对象,对梁单元理论及其在桥梁中的应用作了较为深入的研究,对今后处理相关的计算分析问题具有一定的积极意义。主要研究内容包括以下几个方面：首先,构造出了一种同时考虑轴向拉伸以及两个方向弯曲的局部坐标系下三结点空间梁单元。采用使用五次的Hermite插值函数及二次的Lagrange插值函数得到其横向及纵向位移场,创建出新型的局部坐标系下的空间梁单元。并基于有限元等相关理论,详细推导了该新型局部坐标系下的空间梁单元刚度矩阵,并得出其显示表达式。其次,基于局部坐标系下的空间梁单元,利用坐标转换矩阵,得到了整体坐标系下的梁单元刚度矩阵及相关表达式,然后利用能量法对多种常见外荷载形式进行了结点等效并得到了其相应的结点等效荷载。同时总结归纳了常见边界条件的处理方式等,并应用该新型空间梁单元进行了算例验证,结果表明该空间梁单元在计算上是可行的。最后,利用有限元软件ANSYS的二次开发功能,基于其UPFs二次开发工具,将理论推导的梁单元形式通过用户自定义单元的手段,修改相关的子程序,实现在ANSYS中定义与其具有相同结点数及相同自有度的新的单元类型,并利用该新单元对某一桥梁实例进行了分析验证,同时采用桥梁专用软件Midas Civil进行辅助判定,说明了该新单元类型在实际分析中是可行的。
[Abstract]:Beam structure, as an important bearing structure of bridge, has been widely used in engineering. Therefore, it is necessary to calculate and analyze it accurately and reasonably. In this paper, the theory of beam element and its application in bridges are studied in depth, which has a certain positive significance for dealing with related computational and analytical problems in the future. The main research contents include the following aspects: first, In this paper, a three-node spatial beam element in a local coordinate system considering both axial stretching and two directions bending is constructed. The transverse and longitudinal displacement fields are obtained by using the Hermite interpolation function of the fifth degree and the Lagrange interpolation function of the quadratic degree. A new space beam element in local coordinate system is established. Based on the theory of finite element, the stiffness matrix of space beam element in this new local coordinate system is derived in detail, and the display expression is obtained. Based on the spatial beam element in the local coordinate system, the stiffness matrix and the related expressions of the beam element in the global coordinate system are obtained by using the coordinate transformation matrix. Then the energy method is used to calculate the nodal equivalent load and the corresponding nodal equivalent load is obtained. At the same time, the treatment methods of common boundary conditions are summarized. The results show that the spatial beam element is feasible in calculation. Finally, using the secondary development function of finite element software ANSYS, based on the second development tool of UPFs, a new type of space beam element is developed. By means of user-defined unit, the theoretically derived beam element form is modified to realize the definition of a new type of unit with the same number of nodes and the same degree of ownership in ANSYS. An example of a bridge is analyzed and verified by using the new element, and the bridge special software Midas Civil is used to judge the bridge. It is shown that the new unit type is feasible in practical analysis.
【学位授予单位】：长沙理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：U441

【相似文献】