计及弯扭耦合效应的空间梁杆结构计算分析方法

发布时间：2018-02-04 11:26

本文关键词： 空间梁杆结构弯扭耦合势能驻值原理有限单元法刚度矩阵高空作业车　出处：《哈尔滨工业大学》2017年硕士论文　论文类型：学位论文

【摘要】：现有的梁杆结构分析理论从平面问题扩展到空间问题时,大多情况下只是将平面理论的推导结果进行简单的线性组合与叠加来实现,忽略了各方向变形与受力之间的耦合作用,对弯曲刚度与扭转刚度较弱的大柔度空间弯扭梁杆结构而言,其计算结果往往存在较大误差。目前关于弯扭耦合效应的结构分析很少见,分析中缺乏通用的、完整的计及弯扭耦合影响的梁杆有限元模型。因此,本文以空间双向弯曲和扭转梁杆为研究对象,利用基于势能驻值原理的有限元解法,对计及弯扭耦合与压弯扭耦合效应的空间梁杆进行了研究。首先,将基于势能驻值原理的有限元法应用于平面纯弯梁杆的分析中,利用插值函数构造单元变形场,得到平面梁单元的弯曲刚度阵。继而运用二阶理论引入轴力效应,研究计及压弯耦合效应的平面梁单元,得到了单元压弯刚度阵,它由纯弯曲刚度阵和与轴力有关的几何刚度阵组成,使平面内的拉压与弯曲效应得以耦合,由此解决了平面梁杆系统小位移条件下几何非线性分析问题。然后,研究计及弯扭耦合效应的空间双向弯曲梁杆,通过分析其任意一点的应力与应变表达式,得到该点处微段的应变能,积分得到梁杆的总势能。根据势能驻值原理的有限元解法进行推导,得到了计及弯扭耦合效应的梁杆单元刚度阵,在空间上使弯曲与扭转效应得到耦合。编写了MATLAB程序以实现刚度阵的组装,并利用置一赋零法进行边界条件处理。针对本文特殊的非线性计算模型,提出一种近似的数值求解方法。运用MATLAB编程分析两个不同截面悬臂梁算例,并将结果与ANSYS分析结果对比,从多种角度证明了本文方法的先进性。最后,研究了计及压弯扭耦合效应的空间梁杆,在前述工作基础上,推导任意一点的应变与应力表达式,得到了计及压弯扭耦合效应的空间梁杆单元刚度阵,在空间上使构件的拉压、弯曲和扭转效应完整耦合起来。并通过算例证明了本文方法的适用性。以某一型号高空作业车的几何非线性分析为实例,通过MATLAB编程,求解其臂架系统的位移情况,并与ANSYS软件的计算结果进行对比,证明了本文方法在工程实践中的适用性。
[Abstract]:When the existing theory of beam-bar structure analysis is extended from plane problem to spatial problem, in most cases, the derivation results of plane theory are simply linear combination and superposition to realize. The coupling effect between deformation and force in all directions is neglected, and the bending stiffness and torsional stiffness are weak for space bending and torsional beam and bar structures with large flexibility. At present, the structural analysis of the coupling effect of bending and torsion is rare, and there is a lack of a complete finite element model of beam and rod considering the effect of bending and torsional coupling. In this paper, the spatial beam bar is studied by using the finite element method based on the potential energy standing principle, and the coupling effect between bending and torsion is studied. The finite element method based on the principle of standing value of potential energy is applied to the analysis of plane pure bending beam and the element deformation field is constructed by interpolation function. The bending stiffness matrix of the plane beam element is obtained, and then the axial force effect is introduced by using the second order theory, and the plane beam element considering the coupling effect of compression and bending is studied, and the bending stiffness matrix of the element is obtained. It is composed of pure bending stiffness matrix and geometric stiffness matrix related to axial force, which makes the tension and bending effect in plane coupled, thus solving the problem of geometric nonlinear analysis under the condition of small displacement of plane beam and bar system. By analyzing the stress and strain expressions at any point, the strain energy of the micro-segment at this point is obtained by considering the coupling effect of bending and torsion. The total potential energy of beam rod is obtained by integral, and the stiffness matrix of beam member element considering the coupling effect of bending and torsion is obtained by the finite element method of potential energy standing principle. The bending and torsion effects are coupled in space. The MATLAB program is written to assemble the stiffness matrix and the boundary conditions are processed by the method of setting a zero. The special nonlinear calculation model is presented in this paper. In this paper, an approximate numerical solution method is proposed. Two examples of cantilever beams with different sections are analyzed by MATLAB program, and the results are compared with those of ANSYS analysis. The advancement of this method is proved from various angles. Finally, the spatial beam and bar with the coupling effect of compression, bending and torsion are studied. On the basis of the above work, the strain and stress expressions at any point are derived. The stiffness matrix of spatial beam and bar element considering the coupling effect of compression, bending and torsion is obtained, which makes the members pull and compress in space. The effect of bending and torsion is completely coupled. The applicability of this method is proved by an example. Taking the geometric nonlinear analysis of a certain type of aerial vehicle as an example, the programming is carried out by MATLAB. The displacement of the boom system is solved and compared with the results of ANSYS software, which proves the applicability of this method in engineering practice.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH123

【相似文献】