起重机变截面复杂梁杆系统稳定性与非线性大位移研究

发布时间：2018-01-02 00:14

本文关键词：起重机变截面复杂梁杆系统稳定性与非线性大位移研究　出处：《哈尔滨工业大学》2013年博士论文　论文类型：学位论文

【摘要】：具有复杂梁杆系统的起重机械在重载吊装机械中极为典型，其结构高耸细长，承载形式复杂，对其进行准确的稳定性与几何非线性分析是保证其安全工作的重要基础。同时，为合理利用材料、减轻结构自重，起重机金属结构通常会存在变截面格构式构件及其组合结构，其特殊的边界条件和结构形式为起重机金属结构的理论分析和设计计算带来了很大困难，这一直是行业中众多技术人员关注的焦点。为此，本文在国家十二五科技支撑计划项目(2011BAJ02B01-02)资助下，以具有变截面格构式构件的起重机复杂梁杆系统为研究背景和应用对象，对起重机复杂梁杆系统的稳定性、几何非线性大位移与变截面结构的抗扭性能进行深入的研究和探讨。基于纵横弯曲理论，对惯性矩沿轴向二次变化的变截面悬臂梁柱的侧向位移和稳定性进行了分析。运用微分方程法建立了考虑轴力影响的变截面Bernoulli-Euler梁的挠曲微分方程，推导了变截面悬臂梁柱在复合载荷作用下的挠度精确表达式和失稳特征方程，并在Timoshenko放大系数与精确理论放大系数基础上，给出了形式简单的变截面悬臂构件轴力影响系数的近似表达式。分析结果表明，在工程中常用锥度范围内，当轴力与欧拉临界力的比值小于0.6时，该近似表达式所引起的误差均小于2%，因此，惯性矩二次变化的变截面悬臂梁顶端挠度可以使用统一的近似放大系数公式乘以相应仅有横向载荷作用所产生的最大挠度表出。同时在上述研究的基础之上，讨论了计及二阶效应的情况下，弹性约束对变截面悬臂梁侧向位移与稳定性的影响，分别给出了轴力影响系数、弹性支撑影响系数和屈曲特征方程表达式。在以上变截面梁挠曲微分方程基础上，引入剪切变形的影响，推导出计及二阶效应的惯性矩二次变化变截面Timoshenko梁单元转角位移方程，并列写为有限元格式，给出了计及剪切变形与二阶效应影响的惯性矩二次变化变截面梁单元精确切线刚度矩阵，得到一种新型的变截面梁单元。该精确梁单元能方便的实现变截面梁到等截面梁、计及剪切和不计及剪切变形之间的转化，与传统有限元方法中梁单元自然衔接过渡，便于统一建模求解应用。通过经典的算例分析表明，该精确变截面梁单元在稳定性和二阶效应分析中，只需划分一个单元即可以得到精确的数值解；对于细长梁，可以忽略剪切变形的影响，但当梁较短即杆件高度相对跨度很小，而又须考虑非线性效应时，必须计入剪切变形的影响才能达到满意的计算精度；剪切变形使结构的横向位移增大，使梁杆的屈曲能力减弱。针对空间变截面梁杆结构抗扭刚度问题的研究，本文将空间桁架分解成平面桁架计算，，根据空间桁架扭转时的等效力分配原则，将复杂的空间桁架扭转问题转化为简单变截面单片平面桁架结构的弯曲问题，最终推导出空间变截面结构扭转刚度的表达式。首先以单片变截面桁架结构为研究对象，给出了不同腹杆布置形式的变截面桁架各杆件内力与侧向位移表达式。以单片桁架结构的柔度系数为基础，全面考虑弦杆、腹杆对空间桁架结构的侧向刚度和抗扭刚度的影响，推导出适用于矩形空间桁架结构的侧向位移表达式和扭转刚度计算公式，并给出了扭矩的等效力偶分配系数计算式。最后讨论了腹杆对变截面空间梁杆结构侧向刚度的影响，当构件长细比较大时，可忽略腹杆对结构侧向刚度的影响，可将变截面空间刚架结构等效为惯性矩二次变化的实腹式变截面梁。实际算例表明，应用本文方法计算空间桁架结构的扭转刚度是正确和有效的。基于虚位移原理与更新的拉格朗日(U.L.)格式，提出了一种可用于分析变截面Timoshenko梁单元几何非线性大位移问题的计算方法。采用转角、位移独立插值的方法，给出了考虑剪切变形影响的惯性矩二次变化变截面梁单元插值函数，并建立了同时考虑轴力、剪切、弯曲效应及其耦合项在内的平面惯性矩二次变化变截面梁柱单元几何非线性虚功增量方程，得到了变截面梁单元大位移切线刚度阵。该方法严格计入了剪切变形与变截面因素的影响，当锥度系数 1时，可很好的退化为相应的等截面梁单元，因此，本文分析方法适用于变截面梁、等截面梁以及其组合结构的大位移几何非线性分析。最后，编制了计及剪切变形的变截面梁杆系统大位移几何非线性分析计算程序，通过典型算例分析，验证了本文几何非线性大位移分析建模方法的正确性。
[Abstract]:With the complex beam system of the crane in the heavy hoisting machinery is very typical, the tall slender structure, bearing form complex, stability and geometric nonlinear analysis of the accurate is an important basis to ensure the safety of work. At the same time, for the rational use of materials, reduce the weight of the structure, the metal structure of the crane will usually exist variable cross-section lattice structure and composite structure, difficult boundary conditions and special structure for the theoretical analysis and design calculation of crane metal structure, which has been the focus of many technical personnel in the industry concerned. Therefore, based on the 12th Five-Year National Science and technology support program (2011BAJ02B01-02) funding, with variable cross-section lattice structure of the crane complex beam system as the research background and application object, the stability of the crane complex beam system, geometric nonlinear large The torsion resistance of the shift and variable cross-section structures is studied and discussed in depth.
Based on the theory of longitudinal bending, lateral displacement and stability of moment of inertia along the axial direction two times change of variable cross-section cantilever beam columns is analyzed. A deflection differential equation of variable cross section Bernoulli-Euler beam considering the effect of axial force by using the differential equation method, variable cross-section cantilever Liang Zhu under compound load deflection and the exact expression of instability the characteristic equation is derived, and the Timoshenko amplification coefficient and the amplification coefficient of accurate theoretical basis, the influence of variable cross-section cantilever member axial force form simple approximate expression coefficient is given. The analysis results show that the commonly used in the engineering angle range, the ratio of axial force and Euler critical force is less than 0.6, the error of the approximate expression which were less than 2%, therefore, the moment of inertia two changes of variable section cantilever top deflection can be used to approximate the amplification coefficient multiplied by the corresponding formula only transverse uniform The maximum deflection table generated to load. At the same time on the basis of the above study, discussed and two order effect, the influence of elastic constraints on displacement and stability of variable cross-section cantilever beam lateral, axial force coefficient are given, the elastic support effect coefficient and buckling characteristic equation.
In the above basis of variable section beam deflection differential equation, the effect of shear deformation, and the two order effect of the moment of inertia of the two variable sections of Timoshenko beam element displacement equation is derived for finite element parallel writing format, the moment of inertia two changes are given considering the shear deformation effect and two order effect variable beam element precise tangent stiffness matrix, a new variable cross-section beam element. The exact beam unit can facilitate the realization of variable cross section beam to beam, and conversion between shear and shear deformation and neglected, with the traditional finite element method of beam element natural transition, to facilitate unified modeling and solving the application. Through the example of classical analysis shows that the precision of variable section beam elements in the stability and two order effect analysis, only need to partition a unit that can get the accurate numerical solution; for slender beam, shear can be ignored The influence of shear deformation, but when the beam is short, that is, the relative span length of the bar is very small, and the nonlinear effect must be considered. The influence of shear deformation must be included in order to achieve satisfactory calculation accuracy. Shear deformation will increase the lateral displacement of the structure and weaken the buckling capacity of the beam column.
Study on space variable torsion beam rod structure stiffness, the space truss is divided into plane truss calculation, according to the space truss torsion effect such as the principle of distribution, the space truss complex problem into simple torsion bending problem of variable cross-section plane truss structure, and ultimately derive the space variable cross-section torsion the expression of stiffness. Firstly, with single variable cross-section truss structure as the research object, variable cross-section truss with different arrangement of web members of the bar internal force and lateral displacement are studied. Based on the flexible system monolithic truss structure based on number, comprehensive consideration of the chords, lateral brace of space truss structure and stiffness the torsional stiffness, lateral displacement expressions are derived for rectangular space truss structure and torsion stiffness calculation formula, and calculate the equivalent moment distribution coefficient of torque. Finally, discusses the influence of variable cross-section beam space truss rod structure lateral stiffness, when the slenderness is large, can ignore the impact of brace on lateral stiffness of the structure, the variable cross-section space frame structure is equivalent to a solid two times change of moment of inertia of tapered beam. A practical example show that the space truss structure calculation of the torsional stiffness of application of this method is correct and effective.
Lagrange based on the principle of virtual displacement and update (U.L.) format, can be used to propose a calculation method of variable cross section Timoshenko beam element nonlinear geometric displacement problem. By using the method of displacement angle, independent interpolation, given a moment of inertia two changes the influence of shear deformation of variable section beam interpolating function, and the establishment of considering the axial force, shear, moment of inertia of plane two times change of the bending effect and their coupling, variable cross-section beam column element geometric nonlinear incremental virtual work equation, the large displacement variable cross-section beam element tangent stiffness matrix. The method strictly including the effect of shear deformation and variable cross-section factor, when the taper coefficient
1, can be very good for the degradation of beam unit, therefore, this method is suitable for analysis of variable section beam, analysis of beam and the composite structure of the large displacement nonlinear analysis has been developed. Finally, the linear computation procedure of large displacement non geometric cross-section considering shear deformation of beam system, through the typical the example analysis, to verify the correctness of the modeling method in this paper analysis of geometric nonlinear displacement.

【学位授予单位】：哈尔滨工业大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TH21

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