THE DYNAMIC STIFFNESS MATRIX OF THE FINITE ANNULAR PLATE ELEMENT

The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then the dynamic stiffness matrix of the finite annular plate element is established in closed form and checked by the direct stiffness method. The paper has given wide convcrage for decomposing the dynamic matrix into the power series of frequency square. By utilizing the axial symmetry of annular elements, the modes with different numbers of nodal diameters at s separately treated. Thus some terse and complete results are obtained as the foundation of structural characteristic analysis and dynamic response compulation.

THE GENERATION OF NON－LINEAR STIFFNESS MATRIX OF TRIANGLE ELEMENT WHENCONSIDERING BOTH THE BENDING AND IN－PLANEME MBRANE FORCES

Using Stricklin Melhod￣[5],we have this paper has derived the formulas for the ge-neration of non-linear element stiffness matrix of a triangle element when considering both the bending and the in-plane membrane forces. A computer programme for the calculation of large deflection and inner forces of shallow shells is designed on theseformulas. The central deflection curve computed by this programme is compared with other pertaining results.

Finite element model for arch bridge vibration dynamics considering effect of suspender length adjustment on geometry stiffness matrix

In this paper, we established a finite element (FEM) model to analyze the dynamic characteristics of arch bridges. In this model, the effects of adjustment to the length of a suspender on its geometry stiffness matrix are stressed. The FEM equations of mechanics characteristics, natural frequency and main mode are set up based on the first order matrix perturbation theory. Applicantion of the proposed model to analyze a real arch bridge proved the improvement in the simulation precision of dynamical characteristics of the arch bridge by considering the effects of suspender length variation.

New Formula for Geometric Stiffness Matrix Calculation

The standard formula for geometric stiffness matrix calculation, which is convenient for most engineering applications, is seen to be unsatisfactory for large strains because of poor accuracy, low convergence rate, and stability. For very large compressions, the tangent stiffness in the direction of the compression can even become negative, which can be regarded as physical nonsense. So in many cases rubber materials exposed to great compression cannot be analyzed, or the analysis could lead to very poor convergence. Problems with the standard geometric stiffness matrix can even occur with a small strain in the case of plastic yielding, which eventuates even greater practical problems. The authors demonstrate that amore precisional approach would not lead to such strange and theoretically unjustified results. An improved formula that would eliminate the disadvantages mentioned above and leads to higher convergence rate and more robust computations is suggested in this paper. The new formula can be derived from the principle of virtual work using a modified Green-Lagrange strain tensor, or from equilibrium conditions where in the choice of a specific strain measure is not needed for the geometric stiffness derivation (which can also be used for derivation of geometric stiffness of a rigid truss member). The new formula has been verified in practice with many calculations and implemented in the RFEM and SCIA Engineer programs. The advantages of the new formula in comparison with the standard formula are shown using several examples.

一种复合驱动并联机构刚度分析

针对直升机旋翼支撑平台,设计了一种复合驱动四自由度并联机构,利用复合驱动分支增大了并联机构工作空间。推导了并联机构中各驱动分支和动平台之间的运动关系式,考虑约束力、驱动力和驱动力矩综合作用下复合驱动分支的横向变形、轴向变形和扭转变形,结合机构的运动学方程推导了复合驱动并联机构的刚度矩阵。利用有限元软件验证了并联机构整体刚度矩阵的正确性。仿真结果表明该并联机构的刚度满足使用需要,为含复合驱动并联机构的应用和推广奠定了理论基础。

GEOMETRICALLY NONLINEAR FINITE ELEMENT MODEL OF SPATIAL THIN-WALLED BEAMS WITH GENERAL OPEN CROSS SECTION

Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such as lateral shear deformation, warp generated by nonuni- form torsion and second-order shear stress, coupling of flexure and torsion, and large displacement with small strain. With an additional internal node in the element, the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian （UL） formulation. Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams.

A Finite Element Method for Cracked Components of Structures

In this paper, a method is developed for determining the effective stiffness of the cracked component. The stiffness matrix of the cracked component is integrated into the global stiffness matrix of the finite element model of the global platform for the FE calculation of the structure in any environmental conditions. The stiffness matrix equation of the cracked component is derived by use of the finite variation principle and fracture mechanics. The equivalent parameters defining the element that simulates the cracked component are mathematically presented, and can be easily used for the FE calculation of large scale cracked structures together with any finite element program. The theories developed are validated by both lab tests and numerical calculations, and applied to the evaluation of crack effect on the strength of a fixed platform and a self-elevating drilling rig.

GEOMETRICALLY NONLINEAR FE FORMULATIONS FOR THE MACRO-ELEMENT UNIPLET OF FOLDABLE STRUCTURES

Geometrically nonlinear stiffness matrix due to large displacement small strain was firstly formulated explicitly for the basic components of pantographic foldable structures,namely, the uniplet, derived from a three node beam element.The formulation of the uniplet stiffness matrix is based on the precise nonlinear finite element theory and the displacement harmonized and internal force constraints are applied directly to the deformation modes of the three node beam element. The formulations were derived in general form, and can be simplified for particular foldable structures, such as flat, cylindrical and spherical structures.Finally, two examples were presented to illustrate the applications of the stiffness matrix evolved.

Stiffness Matrix Derivation of Space Beam Element at Elevated Temperature

<Abstract>Element stiffness equation is very important in structural analysis,and directly influences the accuracy of the results.At present,derivation method of element stiffness equation is relatively mature under ambient temperature,and the elastic phrase of material stress-strain curve is generally adopted as physical equation in derivation.However,the material stress-strain relationship is very complicated at elevated temperature,and its form is not unique,which brings great diffculty to the derivation of element stiffness equation.Referring to the derivation method of element stiffness equation at ambient temperature,by using the continuous function of stress-strain-temperature at elevated temperature,and based on the principle of virtual work,the stiffness equation of space beam element and the formulas of stiffness matrix are derived in this paper,which provide basis for finite element analysis on structures at elevated temperature.

A CATENARY ELEMENT FOR THE ANALYSIS OF CABLE STRUCTURES

Based on analytical equations, a cat ena ry element is presented for the finite element analysis of cable structures. Com pared with usually used element(3_node element, 5_node element), a program with the proposed element is of less computer time and better accuracy.

Gershgorin and Rayleigh Bounds on the Eigenvalues of the Finite-Element Global Matrices via Optimal Similarity Transformations

The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenvalue bounding theorem to this matrix inherently fails to foresee its positive definiteness, predictably, and routinely failing to produce a nontrivial lower bound on the least eigenvalue of this, theoretically assured to be positive definite, matrix. Considered here are practical methods for producing an optimal similarity transformation for the finite-elements global stiffness matrix, following which non trivial, realistic, lower bounds on the least eigenvalue can be located, then further improved. The technique is restricted here to the common case of a global stiffness matrix having only non-positive off-diagonal entries. For such a matrix application of the Gershgorin bounding method may be carried out by a mere matrix vector multiplication.

模件式战术导弹舱内战斗部装配刚度辨识方法研究

为了研究模件式战术导弹舱内战斗部装配刚度的辨识方法,以试验模态参数和有限元模型为基础,提出了一种通过模态特征方程反问题辨识模件式战术导弹舱内战斗部装配刚度参数的新方法。该方法以模态特征方程为基础,利用连接单元刚度矩阵的三对角线特征,推导得到了装配位置连接节点的内力和位移之间的关系方程。随后根据导弹的特点,采用三分段法进行质量和刚度分段,构建导弹动力学模型并进行模态分析。在数值试验中,将模态参数和导弹主体/分支结构的质量与刚度矩阵代入关系方程,最终辨识得到导弹主体结构和分支结构装配位置的刚度矢量值。数值试验结果验证了辨识方法的有效性和可靠性。

主从约束在有限元计算中的实现方式和过程

为明确主从约束这一自由度耦合关系在有限元计算过程中的实现方式和具体过程,从主从约束的基本概念入手,基于直接消除法的思想,采用宏单元的概念,在剔除从节点自由度的同时保留其结构荷载和刚度的贡献,根据有限元分析的基本原理推导得到了宏单元在整体和局部坐标系下的刚度矩阵,从而使其可以与普通单元一起整合到结构整体刚度矩阵中参与计算。另外,对主从约束自身的单元方向、主从约束的组合和联合应用等亦给出了分析和刚度矩阵表达式。最后,采用多个算例根据本文推导方式进行编程计算,并通过midas、ANSYS和ABAQUS进行了对比计算验证,为深入理解主从约束在有限元计算中的实现方式和过程以及实际工程应用提供了参考和帮助。

有限元中弹性连接单元的刚度矩阵

针对常用有限元软件中弹性连接单元的刚度矩阵开展研究。类似普通梁单元刚度矩阵的分析方法,将弹性连接单元的空间受力状态分解为伸缩、弯曲和扭转三种独立的模式进行分析,并提出两种方式推导弯曲受力模式下的刚度矩阵。对于弯曲受力状态下的刚度矩阵,明确了MIDAS中弹性连接单元输入参数包括弯曲和剪切刚度系数、弹性连接长度和剪切距离比R在刚度矩阵中的表现形式,给出了其刚度矩阵的理论表达式;阐明了剪切距离比R的力学意义,即用以考虑弹性支承两端因剪力传递的弯矩,其对结构的影响只体现在杆端位移结果中,杆端力始终满足静力平衡条件而不受R的影响,并且在R取0.5时,MIDAS中弹性连接的单元刚度矩阵与普通欧拉梁单元的刚度矩阵最为接近。同时通过分析对比,明确了ANSYS和ABAQUS中弹性连接单元的弯剪效应是独立的,这与MIDAS中弹性连接单元在不考虑剪切距离比R时的特性一致。研究成果既有助于理解弹性连接单元刚度矩阵,又为其工程应用提供了参考。

基于CR列式的平面体外预应力梁非线性有限元模型

将体外预应力筋视为在锚固位置和转向块位置分别与梁体固结及相连的常应变构件,基于锚固位置和转向块位置处体外预应力筋和梁体的几何关系,采用共旋坐标(co-rotational,CR)法导出体外预应力筋在结构坐标系中的切线刚度矩阵和杆端抗力.结合常规的几何非线性CR平面梁单元,建立体外预应力平面梁的几何非线性有限元模型并编制了程序,对一简支梁算例的两个工况进行了几何非线性分析并与ABAQUS程序进行了比较.结果表明:不管是预应力施加工况还是承受外载工况,对于梁端水平位移、跨中竖向位移和体外筋轴力,两种方法得到的计算结果吻合良好,从体外筋轴力方面而言,本文方法更能体现体外筋为常应变构件的受力性能,因此可用于体外预应力结构的非线性有限元分析.

考虑剪切变形和二阶效应的变截面构件的计算

同时考虑剪切变形和二阶效应来解析计算杆件的临界力,是求解变系数临界微分方程的难题。本研究采用有限元法推导了变截面单元刚度矩阵。采用三次Hermite插值函数和三次拉格朗日插值函数来计算单元内的弯曲变形和惯性矩变化。采用线性插值函数来计算单元内的剪切变形和截面面积变化。利用最小势能原理对总势能进行变分,系统给出了计入弯曲变形、剪切变形以及轴力二阶效应的变截面构件单元刚度矩阵。最后,用自编的有限元程序对算例进行验证。研究结果表明:本算法的计算精度较高,还可分析二阶位移放大系数以及变截面门式刚架立柱之间的支援作用。

二维微动平台柔性机构动力学建模与分析

提出一种基于并联柔性机构的两自由度平动解耦并联微动平台.平台采用复合双平行四杆柔性机构模块,采用结构对称约束消除轴间耦合和寄生位移的产生,实现X,Y方向的平动.采用刚度矩阵法对该并联柔性机构进行理论分析,根据观察法建立微动工作台的整体刚度矩阵,得到系统的运动微分方程,推导出系统各阶固有频率.采用有限元分析法对微动工作台进行模态分析,得到微动工作台的固有频率和振型.经过理论分析、有限元计算和试验测试,并对结果进行对比,结果的一致性说明理论分析的正确性和刚度矩阵分析的有效性.

Numerical Analysis on the Static Performance of Gas Journal Bearing by Using Finite Element Method

In this paper,finite element method is used to calculate the static performance of gas journal bearing,in which rotation speed term is introduced into the stiffness matrix of linear triangular element to realize the performance calculation of the bearing with rotation speed.The results indicate that the average gas film thicknesses corresponding to the maximum load capac-ity and stiffness,and the minimum attitude angle increase with the growth of orifice diameter.Load capacity and stiffness significantly improved with the increase of rotation speed,eccentricity ratio and supply pressure when the bearing has thin average gas film thickness.Attitude angle increases with the growth of rotation speed,while the growth rate slows down or even decreases at high speed.The most effective way of reducing attitude angle is to increase supply pressure.It can be found that rotation speed affects attitude angle through changing gas pressure difference between two orifices,while other parameters have the same effect by changing gas pressure at orifice outlet.

对称几何非线性三角形平面单元研究

为克服现有共旋法的几何非线性平面单元切线刚度矩阵的不对称给非线性方程组求解带来的困难,基于共旋坐标法与几何一致性相结合的原则,对三角形平面单元进行了研究。将单元共旋坐标系的原点坐标分量标始终设为三角形的3个顶点坐标分量的平均值,合理选择共旋坐标系初始时刻及任意计算时刻的坐标轴方向,基于虚功原理,利用微分方程,建立三角形平面单元在大转动、小应变条件下的几何非线性单元切线刚度矩阵和相应的节点抗力算法。研究结果表明:该切线刚度矩阵是对称的;且将该切线刚度矩阵与一种能将位移增量法与荷载增量法形成统一迭代格式的非线性方程组求解方法进行结合,能大幅简化求解过程,依据推导公式与算法开发了相应的计算程序,并利用该计算程序对柔性立柱和大变形悬臂梁的经典算例进行了计算和比较,验证了该研究理论推导结果的正确性与计算程序的可靠性,且算例2显示该算法的计算精度高于ANSYS商业数值软件的。

求解动荷载作用下多层粘弹性半空间轴对称问题的精确刚度矩阵法

利用Laplace-Hankel联合积分变换,推导出了单层粘弹性半空间轴对称问题在动荷载作用下,层间完全接触情况的刚度矩阵,然后按传统的有限元方法组成总体刚度矩阵。通过求解由总体刚度矩阵所构成的代数方程就可解出动荷载作用下多层粘弹性半空间轴对称问题的矩阵。由于刚度矩阵的元素中只含有负指数项,计算时不会出现溢出的现象。本文还成功地应用了Durbin的Laplace逆变换的数值方法,求解出了多层粘弹性体的时域解。最后,文中还给出了路面动弯沉的计算结果与实测结果的对比来证明推导结果的准确性。