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1.
文颖  曾庆元 《计算力学学报》2013,30(6):796-801,814
几何刚度矩阵的推演是结构几何非线性有限元分析的重点和难点之一。推导几何刚度矩阵显式解析表达式成为简化非线性有限元列式,提高分析效率的关键。本文在协同转动法框架下,基于刚体运动法则对四节点二十四自由度的平板壳单元几何刚度矩阵显式解析式进行了推导和讨论;分析了悬臂梁大转动、不同壁厚条件下简支圆柱形屋顶空间大变位两个经典算例。研究结果表明:(1)几何刚度矩阵的显式计算公式不仅为板壳结构几何非线性列式提供了方便而且具有良好的精度;(2)推导的几何刚度矩阵适用于各类型四边形二十四自由度平板壳单元模型;(3)与数值积分相比,采用解析形式的几何刚度矩阵可以显著提高非线性响应计算效率。  相似文献   

2.
共旋坐标法(C.R法)具有在局部坐标系考虑材料非线性,通过局部坐标系与结构坐标系之间内力和切线刚度矩阵的转换矩阵来考虑几何非线性,从而实现两种非线性脱耦的优点,C.R法相对于其它非线性有限元列式而言较少运用于商业程序。本文利用ANSYS平台提供的单元二次开发工具——用户可编程特性(UPFs),开发了基于C.R法的几何非线性平面梁单元,给出了详细的算法及流程,通过多个算例对本文算法及程序进行了验证。研究表明:该方法能有效利用共旋法非线性单元和ANSYS商业程序的优点,对于方框架在对边中点受一对集中力的算例1,采用二次开发的用户梁单元与beam3梁单元在每个荷载步下收敛所需的迭代次数分别为3次和6次;对于预应力钢筋混凝土悬臂梁发生大变形的算例2,上述两种单元模型进行非线性计算能收敛的预应力加载系数分别为132和128,可知本文基于共旋法得到的ANSYS二次开发用户梁单元提高了非线性计算的效率和能力,可用于平面梁结构的几何非线性分析。  相似文献   

3.
杆系结构的几何非线性分析:Ⅰ.平面问题   总被引:6,自引:0,他引:6  
本文以三维连续体的虚功增量方程为基础,采用平动、转角位移分别插值的方法,导出了梁结构大位移、大转动问题内力分析的UL法。本文考虑了轴向、剪切和弯曲效应,提出了新的几何刚度矩阵。算例表明,依本文方法编制的程序具有分析结果强几何非线性行为的有能力;在满足本文位移假定的条伯下,可以描述任意大角度的刚体转动。  相似文献   

4.
用有限个横向条带法构造了板桁组合结构板段考虑局部屈曲的空间位移模式。基于三维连续体的虚功增量方程,导出了横向条带板段单元的UL列式,并考虑了板段单元位形变化的影响。此计算方法自由度少,计算精度高,能用于大型板桁结构的几何非线性分析。文末计算了广东西江桥板桁组合结构模型梁,计算结果与实测结果吻合较好。  相似文献   

5.
用有限个横条带法构造了板桁组合结构板段考虑局部屈曲的空间位移模式,基于三维连续体的虚功增量方程,导出了横向条带板段单元的UL列式,并考虑了板段单元位形变化的影响,此计算方法自由度少,计算精度高,能用于大型板桁结构的几何非线性分析,文末计算了广东西江桥板桁组合结构模型梁,计算结果与实测结果吻合较好。  相似文献   

6.
以几何精确梁理论为基础,分别采用高阶拉格朗日插值和埃米特插值构造高精度空间梁单元。提出基于单元层次平衡迭代的自由度凝聚方法,以保证单元的通用性。实现了基于载荷控制或柱面弧长控制的结构几何非线性分析算法。算例研究结果表明,提出的改进方法不但提高了计算效率,而且还具有较高的数值稳定性;特别是基于三次埃米特插值构造的单元表现出较好的性态,适用于结构屈曲后分析。  相似文献   

7.
钢管混凝土拱稳定分析的三维退化层合曲梁单元   总被引:3,自引:0,他引:3  
为计算钢管混凝土拱的屈曲荷载,本文在文[1]三维退化梁单元的基础上,采用等效数值积分法,构造,出120-20结点三维退化层合曲梁单元,并考虑几何非线性影响,给出用于层合梁或拱线弹性稳定性分析的有限元列式,最后,以绍兴轻纺大桥为工程背景,计算出轻纺大枯钢管混凝土拱面内及面外屈曲的稳定系数。  相似文献   

8.
本文以三维连续体的虚功增量方程为基础,采用平动、转角位移分别插值的方法,导出了梁结构大位移、大转动问题内力分析的UL法。本文考虑了轴向、剪切和弯曲效应,提出了新的几何刚度矩阵。算例表明,依本文方法编制的程序具有分析结构强几何非线性行为的能力;在满足本文位移假定(即每次加载增量中转角增量是小量)的条件下,可以描述任意大角度的刚体转动。  相似文献   

9.
含铰接杆系结构几何非线性分析子结构方法   总被引:2,自引:0,他引:2  
王刚  齐朝晖  汪菁 《力学学报》2014,46(2):273-283
将细长杆系结构按长度方向划分为多个子结构,由于在子结构坐标系下的节点位移均是小位移,可以将子结构内部自由度凝聚到边界. 考虑到子结构端面在变形过程中保持为刚性截面,将端面节点自由度进一步凝聚到端面形心点,这样每一个子结构就减缩成形式上只有两个节点的广义梁单元,大大减缩了自由度. 大位移大转动是细长杆系结构产生几何非线性效应的一个重要原因,基于共旋坐标法,建立了随单元一起运动的随动坐标系,推导了子结构单元的节点力平衡方程及其切线刚度阵. 同时,考虑到工程机械中细长杆系结构含有相互铰接的刚体加强块,给出了非独立自由度节点力转换到独立参数下的广义节点力及其导数. 最后,通过履带式起重机的副臂工况算例,给出了其在不同载荷下的臂架结构位移,验证了方法的正确性.  相似文献   

10.
应用新近开发的四边形十六自由度离Kirchhoff平板壳单元DKQl6,分析了板壳结构的几何非线性问题,采用Total Lagrange格式,在小应交、中等转动的假定下,建立了该单元几何刚度阵和大位移矩阵.非线性方程采用位移引导或弧长引导的牛顿-拉夫森增量迭代法求解.讨论了网格和加载步效对收敛性的影响,通过对典型算例的计算以及与其它单元的比较,说明了DKQl6单元在板壳结构几何非线性分析中也有良好的精度.  相似文献   

11.
In modeling highly flexible beams undergoing arbitrary rigid–elastic deformations, difficulties exist in describing large rotations using rotational variables, including three Euler angles, two Euler angles, one principal rotation angle plus three direction cosines of the principal rotation axis, four Euler parameters, three Rodrigues parameters, and three modified Rodrigues parameters. The main problem is that such rotational variables are either sequence-dependent and/or spatially discontinuous because they are not mechanics-based variables. Hence, they are not appropriate for use as nodal degrees of freedom in total-Lagrangian finite-element modeling. Moreover, it is difficult to apply boundary conditions on such discontinuous and/or sequence-dependent rotational variables. This paper presents a new geometrically exact beam theory that uses no rotation variables and has no singular points in the spatial domain. The theory fully accounts for geometric nonlinearities and initial curvatures by using Jaumann strains, exact coordinate transformations, and orthogonal virtual rotations. The derivations are presented in detail, fully nonlinear governing equations and boundary conditions are presented, a finite element formulation is included, and the corresponding governing equations for numerically exact analysis using a multiple shooting method is also derived. Numerical examples are used to illustrate the problems of using rotational variables and to demonstrate the accuracy of the proposed geometrically exact displacement-based beam theory.  相似文献   

12.
Presented here are three kinematic representations of large rotations for accurate modeling of highly flexible beam-like structures undergoing arbitrarily large three-dimensional elastic deformation and/or rigid-body motion. Different methods of modeling torsional deformation result in different beam theories with different mathematical characteristics. Each of these three geometrically exact beam theories fully accounts for geometric nonlinearities and initial curvatures by using Jaumann strains, exact coordinate transformations, and orthogonal virtual rotations. The derivations are presented in detail, a finite element formulation is included, fully nonlinear governing equations and boundary conditions are presented, and the corresponding form for numerically exact analysis using multiple shooting methods is also derived. These theories are compared in terms of their appropriate application areas, possible singular problems, and easiness for use in modeling and analysis of multibody systems. Nonlinear finite element analysis of a rotating beam and nonlinear multiple shooting analysis of a torsional bar are performed to demonstrate the capability and accuracy of these beam theories.  相似文献   

13.
The paper presents a formulation of the geometrically exact three-dimensional beam theory where the shape functions of three-dimensional rotations are obtained from strains by the analytical solution of kinematic equations. In general it is very demanding to obtain rotations from known rotational strains. In the paper we limit our studies to the constant strain field along the element. The relation between the total three-dimensional rotations and the rotational strains is complicated even when a constant strain field is assumed. The analytical solution for the rotation matrix is for constant rotational strains expressed by the matrix exponential. Despite the analytical relationship between rotations and rotational strains, the governing equations of the beam are in general too demanding to be solved analytically. A finite-element strain-based formulation is presented in which numerical integration in governing equations and their variations is completely omitted and replaced by analytical integrals. Some interesting connections between quantities and non-linear expressions of the beam are revealed. These relations can also serve as useful guidelines in the development of new finite elements, especially in the choice of suitable shape functions.  相似文献   

14.
A phenomenological definition of classical invariants of strain and stress tensors is considered. Based on this definition, the strain and stress invariants of a shell obeying the assumptions of the Reissner–Mindlin plate theory are determined using only three normal components of the corresponding tensors associated with three independent directions at the shell middle surface. The relations obtained for the invariants are employed to formulate a 15-dof curved triangular finite element for geometrically nonlinear analysis of thin and moderately thick elastic transversely isotropic shells undergoing arbitrarily large displacements and rotations. The question of improving nonlinear capabilities of the finite element without increasing the number of degrees of freedom is solved by assuming that the element sides are extensible planar nearly circular arcs. The shear locking is eliminated by approximating the curvature changes and transverse shear strains based on the solution of the Timoshenko beam equations. The performance of the finite element is studied using geometrically linear and nonlinear benchmark problems of plates and shells.  相似文献   

15.
This paper presents a study on the development of high-performance finite elements for geometrically nonlinear analysis of frame structures with curved members. Based on the geometrically exact beam theory, a highly efficient and accurate mixed finite element is developed. A new approach is proposed for constructing the independent internal force field by including major terms satisfying equilibrium conditions in the deformed configuration. An element-level equilibrium iteration procedure is employed for the condensation of element internal degrees of freedom during the nonlinear solution. Numerical results are presented to demonstrate the excellent performance of the element developed, and it is shown that even when each structural member is modelled with just one element, accurate solutions can still be achieved.  相似文献   

16.
The dynamic stability behavior of thin-walled rotating composite beams is studied by means of the finite element method. The analysis is based on Bolotin’s work on parametric instability for an axial periodic load. The influence of fiber orientation and rotating speeds on the natural frequencies and the unstable regions is studied for symmetrically balanced laminates. The regions of instability are obtained and expressed in non-dimensional terms. The “modal interchange” phenomenon arising in rotating beams is described. The dynamic stability problem is formulated by means of linearizing a geometrically nonlinear total Lagrangian finite element with seven degrees of freedom per node. This finite element formulation is based on a thin-walled beam theory that takes into account several non-classical effects such as anisotropy, shear flexibility and warping inhibition.  相似文献   

17.
This paper is devoted to the modeling of planar slender beams undergoing large displacements and finite rotations. Transverse shear deformation of beams that is trivial for most slender beams is neglected in the present model, though within the framework of the geometrically exact beam theory proposed by Reissner. A weak form quadrature element formulation is proposed which is characterized by highly efficient numerical integration and differentiation, thus minimizing the number of elements as well as the total degrees-of-freedom. Several typical examples are presented to demonstrate the effectiveness of the beam model and the weak form quadrature element formulation.  相似文献   

18.
In this paper, new nonlinear dynamic formulations for belt drives based on the three-dimensional absolute nodal coordinate formulation are developed. Two large deformation three-dimensional finite elements are used to develop two different belt-drive models that have different numbers of degrees of freedom and different modes of deformation. Both three-dimensional finite elements are based on a nonlinear elasticity theory that accounts for geometric nonlinearities due to large deformation and rotations. The first element is a thin-plate element that is based on the Kirchhoff plate assumptions and captures both membrane and bending stiffness effects. The other three-dimensional element used in this investigation is a cable element obtained from a more general three-dimensional beam element by eliminating degrees of freedom which are not significant in some cable and belt applications. Both finite elements used in this investigation allow for systematic inclusion or exclusion of the bending stiffness, thereby enabling systematic examination of the effect of bending on the nonlinear dynamics of belt drives. The finite-element formulations developed in this paper are implemented in a general purpose three-dimensional flexible multibody algorithm that allows for developing more detailed models of mechanical systems that include belt drives subject to general loading conditions, nonlinear algebraic constraints, and arbitrary large displacements. The use of the formulations developed in this investigation is demonstrated using two-roller belt-drive system. The results obtained using the two finite-element formulations are compared and the convergence of the two finite-element solutions is examined.  相似文献   

19.
基于Euler-Bernoulli梁的几何非线性理论,建立了弹性曲梁在任意分布机械载荷和热载荷共同作用下的几何非线性静平衡控制方程。该模型不仅计及了轴线伸长,同时也精确地考虑了梁的初始曲率对变形的影响以及轴向变形与弯曲变形之间的相互耦合效应。应用打靶法数值求解了半圆形曲梁在横向均匀升温作用下的非线性弯曲问题,数值比较了轴向伸长对曲梁变形的影响。  相似文献   

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