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1.
关于结构刚度方程病态问题的疑难分析   总被引:1,自引:0,他引:1  
秦领  刘西拉 《力学季刊》2005,26(3):370-376
本文围绕矩阵位移法求解结构位移的误差,讨论了结构刚度矩阵的病态问题,指出了计算上的病态常常是结构刚度分布和结构拓扑的不合理,而不一定是计算本身的问题。首先,文章依据误差界的概念和范数的性质推导了衡量结构刚度矩阵病态程度的条件数的公式。然后,阐明了基于不同范数的条件数在衡量矩阵病态程度上的等价性。最后,通过两个具有代表性的算例,分别从结构构件的刚度差异和结构几何拓扑两方面,计算和分析了结构刚度矩阵的病态程度随结构本身性质的改变而改变的规律。在特定的算例中,还有使结构刚度矩阵的病态程度降到最低的最佳刚度分布。  相似文献   

2.
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   

3.
含可动机构的杆系结构非线性力法分析   总被引:6,自引:0,他引:6  
推导了基于矩阵奇异值分解的小变形条件下杆系结构的力法分析(LFM)过程,并采用杆件内力修正的方法,提出了考虑大位移的几何非线性力法分析(NFM)方法思想和步骤。该方法有效地解决了结构中同时存在刚体位移、弹性位移的结构分析问题,适合计算机编程,结构的强度计算、机构分析和形态分析,讨论了力法与位移法的优缺点,给出的算例表明所提出的方法是正确的、有效的。  相似文献   

4.
折叠结构几何非线性分析   总被引:1,自引:1,他引:0  
本文提出了一种推导折叠结构宏单元刚度矩阵的新方法,即在所假设普通单元位移模式的基础上直接引入位移约束条件,得到宏单元的形函数矩阵,进而给出宏单元的力与位移间关系。利用该思路,文中简捷地推导出剪式单元三节点梁大位移小变形的几何非线性切线刚度矩阵,并给出了线性刚度矩阵的显式。算例表明,分析折叠结构承载能力和自稳定结构的展开或收纳过程,考虑几何非线性的影响是必要的。  相似文献   

5.
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,导出了空间Timoshenko梁大位移、大转动问题内力分析的UL法(UpdatedLagrangiai1Formulation)。本文考虑了轴向、剪切、弯曲和扭转效应,提出了新的几何刚度矩阵,并建立了描述大转动规律的坐标转换矩阵。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   

6.
伪可变体系几何可变性的研究,对轻型结构的设计分析已变得十分重要。本文先分析能量与平衡之间的普遍关系,进而得出判定体系可变性的能量准则。通过拉格朗日乘子的引入,建立能量泛函,得出判定极值的二次型。然后证明了乘积力法与能量法的一致性,并讨论了宜于计算机分析实现的矩阵表示方法。结果表明,若二次型确定,则体系伪可变;当半确定时,体系部分伪可变部分可变;否则体系含二阶以上的无穷小机构。  相似文献   

7.
刚接与铰接混合连接杆系结构的几何非线性分析   总被引:4,自引:0,他引:4  
本文提出用子结构原理解决具有刚接与铰接混合连接空间杆系结构的几何非线性分析,实现其非线性稳定性分析的载荷-位移全过程跟踪。该法无须单独推导刚接、铰接以及一端刚接一端铰接单元的弹性刚度矩阵和几何刚度矩阵,而可以直接由空间梁单元退化得到,而且可以将平面问题与空间问题、刚接与铰接混合连接体系进行统一处理,算例表明,本文方法对于杆系结构的统一和整体分析是有效的。  相似文献   

8.
针对质量最小化、位移为约束条件的结构材料优化问题,提出了一种变位移约束的结构材料拓扑优化方法。采用分式有理式识别结构材料单元特性参数,以细观单元拓扑变量倒数为设计变量,结合均匀化方法求出宏观结构单元的等效刚度矩阵以及其对细观单元设计变量的导数,进而得到位移的一阶近似展开式。结合变约束限的思想,得到了以结构质量作为目标函数、位移作为约束条件的连续体细观结构拓扑优化近似模型;并采用对偶方法进行求解。对几种典型结构,进行了考虑单个和多个位移约束的结构材料优化设计,所得结果验证了本文方法的有效性和可行性。  相似文献   

9.
针对传统被动隔振器低频隔振性能不足的问题,提出了一种连杆-倾斜弹簧负刚度机构,并将其与线性弹簧并联构成一种新型准零刚度(quasi-zero stiffness, QZS)隔振器。首先,对该隔振器进行静力学分析,建立无量纲力-位移和无量纲刚度-位移关系式,并讨论设计参数对隔振器刚度的影响,进一步得出隔振器在平衡位置处具有零刚度特性的参数条件;其次,通过动力学研究,建立隔振器在位移激励下的非线性动力学方程,并应用谐波平衡法推导出位移传递率;最后,采用四阶龙格库塔法对准零刚度隔振器在不同激励频率下进行数值仿真,并与不含负刚度机构的线性隔振器进行对比分析。结果表明,准零刚度隔振器在低频激励下的隔振效果明显优于线性隔振器,而在高频激励下具备与线性隔振器相当的隔振性能。  相似文献   

10.
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   

11.
Stability conditions for tensegrity structures are derived based on positive definiteness of the tangent stiffness matrix, which is the sum of the linear and geometrical stiffness matrices. A necessary stability condition is presented by considering the affine motions that lie in the null-space of the geometrical stiffness matrix. The condition is demonstrated to be equivalent to that derived from the mathematical rigidity theory so as to resolve the discrepancy between the stability theories in the fields of engineering and mathematics. Furthermore, it is shown that the structure is guaranteed to be stable, if the structure satisfies the necessary stability condition and the geometrical stiffness matrix is positive semidefinite with the minimum rank deficiency for non-degeneracy.  相似文献   

12.
All kinds of numerical methods based on the discretization of first-order velocity-stress hyperbolic system of elastic wave equations are named mixed variable finite-difference method in this paper, and the transmission boundary condition of artificial boundaries is studied here by the mixed variable finite-difference method. The transmission condition of complex geometrical boundaries of a transversely isotropic medium is presented based on the characteristic variables of wavefields propagating in the normal direction of the boundary. The boundary condition proposed in this paper is a local artificial boundary condition, with which the computation cost is very low. Elastic wave propagations in transversely isotropic medium are modelled by the staggered grid finite-difference method incorporated with the boundary condition presented. Numerical results and analysis of reflection coefficients show that the reflections of incoming waves by artificial boundaries are efficiently reduced.Supported by National Natural Science Foundation and Liaoning Province Science Foundation.  相似文献   

13.
Certain classes of slender structures of complex cross-section or fabricated from specialised materials can exhibit a bi-linear bending moment-curvature relationship that has a strong influence on their global structural behaviour. This condition may be encountered, for instance, in (a) non-linear elastic or inelastic post-buckling problems if the cross-section stiffness may be well approximated by a bi-linear model; (b) multi-layered structures such as stranded cables, power transmission lines, umbilical cables and flexible pipes where the drop in the bending stiffness is associated with an internal friction mechanism. This paper presents a mathematical formulation and an analytical solution for such slender structures with a bi-linear bending moment versus curvature constitutive behaviour and subjected to axial terminal forces. A set of five first-order non-linear ordinary differential equations are derived from considering geometrical compatibility, equilibrium of forces and moments and constitutive equations, with hinged boundary conditions prescribed at both ends, resulting a complex two-point boundary value problem. The variables are non-dimensionalised and solutions are developed for monotonic and unloading conditions. The results are presented in non-dimensional graphs for a range of critical curvatures and reductions in bending stiffness, and it is shown how these parameters affect the structure's post-buckling behaviour.  相似文献   

14.
The support structure of a rotor system is subject to vibration excitation,which results in the stiffness of the support structure varying with the excitation frequency(i.e., the dynamic stiffness). However, the dynamic stiffness and its effect mechanism have been rarely incorporated in open studies of the rotor system. Therefore, this study theoretically reveals the effect mechanism of dynamic stiffness on the rotor system. Then,the numerical study and experimental verification are conducted on...  相似文献   

15.
在对含有柔性元件的复杂航天器进行稳定性等动力学行为的分析中, 通常采用的离散化方法, 可能会导致"动力刚化"等现 象.将梁作为带分布参数的子系统(无限自由度)分析, 基于Rumyancev定理, 通过计算系统相对势能泛函的一阶变分得到了系统的定常运动, 把系统定常运动稳定性的分析归结为系统变势能泛函存在孤立极小值的问题.在分析中不需要建立系统的运动微分方程, 简化了建模过程, 由系统相对势能泛函的二阶变分的正定性得到了使系统定常运动稳定的充分条件, 同时这个条件是使用基于李雅普诺夫直接法思想分析运动稳定性问题得到的最为广泛的充分条件.  相似文献   

16.
Pin-jointed structures are first classified to trusses, tensile structures, and tensegrity structures in view of their respective stability properties. A sufficient condition for stability of an equilibrium state is derived for tensegrity structures. The condition is based on the bilinear forms of the linear and geometrical stiffness matrices considering the flexibility of members. The stability is defined by the positive definiteness of the tangent stiffness matrix, whereas the definition of prestress-stability is based on the geometrical stiffness matrix and the infinitesimal mechanisms. Numerical examples verify that the so-called super-stability condition might not be satisfied by a stable tensegrity structure, and that a prestress-stable structure can be unstable if the prestresses are moderately large.  相似文献   

17.
灰色系统模型在结构损伤识别中的应用   总被引:1,自引:0,他引:1  
开发结构健康监测系统是结构损伤识别的一个重要课题。由于建筑结构具有很多不确定因素,通过模态分析识别结构损伤的精度很难保证。本文提出一种灰色系统模型应用于结构损伤识别的方法。建立频率变化率和刚度变化的灰色系统模型,把一阶单变量的灰色模型(M(1,1))作为频率变化率和刚度变化之间的系统,通过一阶单变量的灰色模型(M(1,1))预测来体现结构动力指纹的整体功能,确定频率变化率和刚度变化之间的关系变量。为了验证理论,对多种工况进行了框架结构模型的振动试验并对结果进行了分析。试验结果表明:对于层间剪切结构,通过测量结构频率变化,建立的灰色系统模型可以较准确地确定结构的损伤位置和损伤程度,并使识别精度得到有效提高。  相似文献   

18.
A cracked element is formulated using the two-filed Hellinger–Reissner functional. Due to utilization of the linear elastic fracture mechanics, only geometrical nonlinearities can be considered for the cracked element. A clear step-by-step algorithm for the element state determination is also presented. The element flexibility matrix is derived in a basic coordinate system. Co-rotational approach is used to transform the element stiffness matrix and the resisting force vector from the basic system to the global one. The suggested element is applicable for static and dynamic analysis, as well as, the stress intensity factor calculation, and also inverse crack detection. Various numerical problems verify accuracy of the proposed element for linear and nonlinear structural analysis.  相似文献   

19.
研究了含分数阶微分项的Duffing振子的超谐共振,通过平均法得到了系统的一阶近似解. 提出了超谐共振时等效线性 阻尼和等效线性刚度的概念,分析了分数阶微分项的系数和阶次对等效线性阻尼和等效线性刚度的影响. 建立了超谐共振解的幅频曲线的解析表达式和稳定性判断准则,对分数阶Duffing振子与传统整数阶Duffing振子的超谐共振解进行了比较. 最后通过数值仿真研究了分数阶微分项的参数对超谐共振幅频曲线的影响.  相似文献   

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